Chapter 3 Entering Data into CrimeStat

Chapter 3 Entering Data into CrimeStat

Chapter 3
Entering Data into CrimeStat
Th e gr a ph ic u ser in t er fa ce of Crim eS tat is a t a bbed form (figu r e 3.1). Ther e a r e five
gr ou p s of fu n ct ion s : Da t a s et u p , S pa t ia l d es cr ip t ion , S pa t ia l m od elin g, Cr im e Tr a vel
Dem a n d, an d Opt ion s. Ea ch group, in t u r n is m a de u p of severa l set s of r ou t ines :
D a ta Se t up
P r im a r y file
Secon da r y file
Refer en ce file
Mea su r em en t P a r a met er s
Da t a file of inciden t /poin t loca t ion s (Requ ired )
Secon da r y d a t a file of in cid en t /poin t loca t ion s
F ile for r efer en cin g in t er pola t ion s
Ar ea l a n d lin ea r ch a r a ct er is t ics of s tu dy a r ea
S p a t ia l D e s c r i p ti o n
Spa t ia l Dis t r ibu t ion
Dista nce Ana lysis I
Dista nce Ana lysis II
‘Hot Spot’ Ana lysis I
‘Hot Spot’ Ana lysis II
Ba sic ch a r a ct er is t ics of t h e in cid en t dis t r ibu t ion
Ch a r a cter ist ics of th e dist a n ces bet ween point s
Ma t r ix dist a n ces
Tools for id en t ifyin g ‘H ot Spot s’
More tools for identifying ‘Hot Spots’
S pa ti al Mo de li ng
In t er pola t ion
J our n ey-to-cr im e Ana lysis
Sp a ce-t im e Ana lysis
Th r ee-dim en sion a l den sit y a n a lysis
An a lyzing th e t r a vel beha vior of ser ial offen der s
Th e in t er a ction bet ween sp a ce an d t im e
Cri m e Tra ve l D e m a nd
Tr ip gen er a t ion
Tr ip dis t r ibu t ion
Mode s plit
N et wor k a ss ign m en t
F ile wor ks h eet
Models of cr im e or igin s a n d cr im e dest in a t ion s
Model of t r ip s bet ween or igin s a n d dest in a t ion s
Model of t r a vel m ode u sed for t r ips
Model of r out e t a k en for t r ips
Wor ks h eet of file n a m es
Op ti on s
S ave p ar a m et er s
Loa d p ar a m et er s
Color s
Sim u la t ion
S ave t h e d at a set u p p ar a m et er s
Load a lr ea dy-sa ved p a r a m et er s file
Ch a n ge th e color of t a bs
Ou t pu t sim u la t ion da t a
This section discusses th e Data Setup t abs.
3.1
Figure 3.1:
CrimeStat User Interface
R e q u i r e d D ata
Crim eS tat can input dat a in several form at s - ASCII, dbase III/ IV ‘dbf’, ArcView
‘sh p’, M apIn fo ‘dat ’, an d files tha t su pport th e ODBC sta nda rd, such a s E xcel ® , L otu s 1-23 ® , M icrosoft A ccess ® , a n d Pa ra d ox ® . It is ess en t ial t h a t t h e files ha ve X a n d Y coor din a t es
a s pa r t of t h eir s t r u ct u r e. Th e pr ogra m a ssu m es t h a t t h e a ssign ed X a n d Y coor din a t es
a r e cor r ect . It r ea ds a file - ASCII, ‘dbf’ or ‘sh p’ a n d t a k es t h e given X a n d Y coor din a t es .
If you r ead an ArcView sh a pe file, t h e inciden t ’s X a n d Y coor din a t es a r e
a u t oma t ically a dd ed a s t h e first fields in t h e pr im a r y file by Crim eS tat. If you u se a n y
oth er type of file you m ust add X an d Y coordina tes to the file. To au toma te th is in
ArcView , a dd t h e Aven u e ext en sion Coord in at e Utili ty V1.0 (a va ila ble in Arc Scr ip t s) t o
you r ext en sion list . To do t h is in M apIn fo a dd t h e KG M u t ilit y T a ble Geogra ph y a s a t ool.
Both wor k gr ea t . It is a good id ea t o ad d t h e X an d Y coor din a t es t o an y file. They a r e
u sefu l for a n a lysis in ot h er pr ogr a m s a n d a llow for ea sy r econ st r u ct ion of t h e file if t h e geocodin g is lost .
Co ord in a te s
Crim eS tat a n a lyzes poin t da t a , define d geogra ph ically by X a n d Y coor din a t es .
Th es e X/Y coord in a t es r epr es en t a sin gle loca t ion wh er e eit h er a n in ciden t occur r ed (e.g., a
bu r gla r y) or wh er e a bu ildin g or oth er object can be r epr esen t ed a s a sin gle point . A point
will h a ve X a n d Y coor din a t es in a sp her ica l or Ca r t es ia n sys t em . In a sp her ica l coor din a t e
sys t em , ea ch poin t ca n be defin ed by lon git u de (for X) an d la t it u de (for Y). In a pr oject ed
coor din a t e syst em , such a s St a t e Pla n e or UTM, ea ch X a n d Y is defin ed by feet or m et er s
from a n a r bit r a r y r efer en ce or igin . Crim eS tat ca n h a n dle bot h sph er ica l an d pr oject ed
poin t s. F or s ome u ses, coord in a t es can be pola r , t h a t is d efined a s a n gles fr om a n a r bit r a r y
r efer en ce vect or , u su a lly d ir ect n or t h . 1 One of th e rout ines in t he progra m calculat es the
a n gu la r m ea n a n d va r ia n ce of a collect ion of an gles.
P oint da t a ca n be obt a ined fr om a n u m ber of sour ces. The m ost fr equ en t wou ld be
t h e va r iou s in cid en t da t a ba ses st or ed by a police depa r t m en t , wh ich cou ld in clu de ca lls for
ser vice, crim e r eport s, or closed cas es. Ot h er sou r ces of in ciden t da t a can in clud e
secon da r y d a t a fr om ot h er a gen cies (e.g., h ospit a l r ecor ds, em er gen cy m edica l s er vice
r ecor ds , loca t ions of bu sin es se s) or even sa m ple d d a t a (Levin e a n d Wa chs , 1986a ; 1986b).
Th er e a r e a ls o poin t da t a fr om br oa dca st sou r ces, s u ch a s r a dios , t elevision s, or
microwaves.
To r ea d pr oject ed coor din a t es in t o Crim eS tat, th e u ser doesn’t n eed t o defin e t h e
pa r t icula r pr oject ion (oth er t h a n t o ind icat e t h a t t h e coord in a t es a r e pr oject ed). ArcView
will ou t p u t t he object s in t h e p r oject ed u n it s so t h a t t h ey ca n be r ea d dir ect ly in t o t h a t
p rogr a m or in t o ArcGIS . H owever , t o ou t pu t ca lcu la t ed object s t o M apIn fo r equ ir es t h e
defin ition of t h e specific pr oject ion u sed. 2 See cha pt er 4 for t h e firs t exa m ples of out pu t in g
objects.
3.3
Inten sities and w eig hts
F or some u ses, poin t s can h a ve intensity va lu es or weights. Th ese a r e opt ion a l
in p u t s in Crim eS tat. An intensity is a va lu e a ssign ed t o a poin t loca t ion a sid e fr om t h e
X/Y coordin a t es. It is a n ot h er va r ia ble, t yp ica lly den ot ed a s a Z-va lu e. F or exa m ple, if t h e
poin t loca t ion is t h e loca t ion of a police st a t ion , t h en t h e in t en sit y cou ld be t h e n u m ber of
ca lls for ser vice over a m on t h a t th a t st a t ion . Or , t o u se cen su s geogr a ph y, if t h e p oin t is
t h e cen t r oid of a cen su s t r a ct , th en t h e int en sit y cou ld be th e popula t ion of t h a t cen su s
t r a ct . In ot h er wor ds, a n in t en sit y is a va r ia ble a ssign ed t o a pa r t icu la r loca t ion .
S om e of t h e r ou t in es in Crim eS tat r equ ir e a n in t en sit y valu e (e.g., t h e spa t ia l
a u t ocorr ela t ion in dices) a n d ot h er s ca n u t ilize a point locat ion wit h a n in t en sit y valu e
a ssign ed (e.g., ker n el dens ity int er pola t ion ). If n o int en sit y va lue is a ssign ed, th e r ou t ines
wh ich r equ ire it ca n n ot be ru n wh ile t h e r ou t ines wh ich ca n u t ilize it will a ssu m e t h a t t h e
in t en sit y is 1 (i.e., t h a t a ll poin t s h a ve eq u a l in t en sit y).
A w eigh t occu r s wh en differ en t poin t loca t ion s a r e t o r eceive differ en t ia l s t a t is t ica l
t r ea t m en t . For exam ple, if a police depa r t m en t h a s des ign a t ed differ en t a r ea s for ser vice,
for exa m ple ‘u r ba n ’ a n d ‘r u r a l’, a va lu e ca n be a ssign ed for ea ch of t h ese a r ea s (e.g., ‘1' for
u r ba n a n d ‘2' for r u r a l). Most of t h e r out in es in Crim eS tat will u se t h e weight s in t h e
ca lcu la t ion s. Weigh t s wou ld be u sefu l if differ en t zon es a r e t o be eva lu a t ed on t h e ba sis of
a n ot h er var iable. For exam ple, sup pose a police depa r t m en t h a s divided its ser vice a r ea
in t o u r ba n a n d r u r a l. In t h e r u r a l p a r t , t h er e a r e t wice a s m a n y p a t r ol officer s a ss ign ed
per capita th an in t he ur ban a reas; the higher populat ion densities in t he ur ban a reas a re
assu med to compensa te for t he longer tr avel dista nces in t he ru ra l ar eas. Let’s assu me
t h a t a ll cr imes occu r r ing in t h e r u r a l ar ea s r eceive a weigh t of 2 wh ile t h ose in t h e u r ba n
a r ea r eceive a weigh t of 1. Th e police depa r t m en t t h en wa n t s t o est im a t e t h e den sit y of
h ou seh old bur gla r ies r elat ive t o t h e popula t ion u sin g th e du el ker n el dens ity fu n ct ion (see
Ch a pt er 7). But , t o reflect t h e differ en t ia l a ss ign m en t of police officer s, t h e a n a lyst s u se
t h e ser vice a r ea a s a weigh t . Th e r esu lt would be a per cap it a est im a t e of bu r gla r y den sit y
(i.e., bu r gla r ies per per son ), bu t weigh t ed by t h e ser vice a r ea . It would pr ovide a n est im a t e
of burglar y risk adjusted for different ial service in r ur al an d ur ban a reas. In most cases,
t h er e will n o weigh t s, in wh ich ca se , a ll poin t s a r e a ss u m ed t o ha ve a n equ a l weigh t of ‘1'.
It is possible t o h a ve bot h in t en sit ies a n d weigh t s, a lt h ou gh t h is wou ld be r a r e. F or
exa m p le, if t h e X a n d Y coor d in a t es a r e t h e cen t r oid s of cen s u s t r a ct s , a t h ir d va r ia ble t h e t ot a l popu lat ion of ea ch cen su s t r a ct cou ld be an int en sit y. Ther e cou ld a lso be an
weigh t in g ba se d on ser vice ar ea . In calcu la t in g t h e Mor a n ’s I sp a t ia l a u t ocorr ela t ion in dex,
th e tota l populat ion is used a s an inten sity while th e service ar ea is used as a weight. In
t h is ca se , Crim eS tat ca lcu la t es a weigh t ed Mor a n ’s I spa t ia l a u t ocor r ela t ion .
Bu t t h e u se of bot h a n in t en sit y a n d a weigh t wou ld be less com m on . F or m ost of
th e stat istics, a variable could be used as eit her a weigh t or a n in t en sit y, an d t h e r esu lt s
will be t h e sa m e. H owever , be car eful in a ss ignin g t h e sa m e va r ia ble a s both a n in t en sit y
a n d a weigh t . In su ch in st a n ces, cas es m a y en d u p be in g weigh t ed t wice, wh ich will
produce distort ed results. 3
3.4
Ti m e Me a su re s
Crim eS tat n ow in clu des r ou t in es for a n a lyzin g s pa t ia l ch a r a ct er is t ics in r ela t ion t o
t im e. Ma n y s er ia l cr im e in cid en t s occu r in a sh or t per iod of t im e. F or exa m ple, a gr ou p of
ca r t h ieves m a y s t ea l ca r s fr om a n eigh bor h ood over a ver y s h or t per iod of t im e, for
exa m ple a few da ys. Th u s, t h er e is often a n in t er a ction bet ween a con cent r a t ed sp a t ia l
pa t t er n of event s occu r r ing in a sh or t t ime p er iod. Beca u se of t h is, police depa r t m en t s
r ou t ine collect infor m a t ion on t h e t ime of t h e event , th e da y an d t ime.
Th er e a r e t h r ee r ou t in es wh ich a n a lyze spa t ia l con cen t r a t ion in r ela t ion t o t im e: t h e
Kn ox in dex, th e Ma n t el in dex, an d a cor r elat ed wa lk m odel. But for u sin g an y of t h ese
r out in es , t h e u se r h a s t o defin e t im e in a con sis t en t m a n n er . Both t h e pr im a r y a n d
secon da r y files ca n a llow a t im e va r ia ble. H owever , t h ese h a ve t o be defined in a con sisten t
ma nn er for a ll records in a file. There are five time periods th at ar e allowed:
H ou r
Da y (defau lt )
Week
Mon t h
Yea r
Th e defau lt is ‘da y’. Th a t is, t h e pr ogr a m will a ss u m e t h a t a n y t im e va r ia ble is in
da ys, eit h er a n a r bit r a r y n u m ber of da ys (e.g., da ys fr om J a n u a r y 1 s t ) or t h e n u m ber of
da ys fr om J a n u a r y 1, 1900, wh ich is t h e defa u lt t im e r efer en ce for m ost com pu t er sys t em s.
If t h e t im e u n it is n ot in da ys, t h e u ser n eed s t o in dica t e t h e a pp r opr ia t e u n it .
Mi s s i n g Va lu e C o d e s
Un for t u n a t ely, da t a is fr equ en t ly m essy. In m ost police depa r t m en t s, t h e crim e
in cid en t da t a ba se is bein g con t in u a lly u pda t ed, d a ily a n d, p er h a ps, h ou r ly. At a n y on e
t im e, m a n y of th e r ecor ds will n ot h a ve been geocoded or will h a ve been in com plet ely
geocoded .
B la n k r e cor d s
Crim eS tat a llows t h e in clus ion of codes for m iss in g valu es, t h a t is va lu es of eligible
fields t h a t a r e n ot com plet e or a r e n ot cor r ect . These codes a r e a pplied t o t h e fields defin ed
on t h e pr im a r y or s econ da r y da t a set s (X, Y, weigh t , in t en sit y). Aut oma t ically, Crim eS tat
will exclu de r ecor ds wit h bla n k fields or wit h fields h a vin g a n y n on-n u m er ic valu e (e.g.,
a lph a n u m er ic cha r a cter s, #, *) for t h e eligible fields . Th e st a t ist ics will be calcula t ed only
on t h ose r ecor ds wh ich h a ve eligible n u m er ical va lu es. Fields for oth er va r ia bles in t h e
dat a base th at ar e not defined in t he prima ry and seconda ry data sets will be ignored.
3.5
Ot h er m iss in g v a lu e cod es
In a dd it ion t o blan k a n d n on-n u m er ic valu es , Crim eS tat ca n exclud e a n y ot h er
va lu e t h a t h a s been u se d for a m iss in g va lu es code (e.g., 0, -1, 99). Tha t is, if t h e pr ogra m
en cou n t er s a field wit h a m is sin g va lu e code, it will exclu de t h a t r ecor d fr om t h e
ca lcu la t ion s . N ext t o t h e X, Y, weigh t a n d in t en s it y field s on bot h t h e p r im a r y a n d
secon da r y files is a m iss in g valu es code box. Th e defau lt h a s been set t o blan k . Th a t is, if
Crim eS tat find s n o infor m a t ion in a field, it will ignore t h a t r ecor d. However, th er e a r e
eight options t ha t can be selected:
1.
2.
3.
4.
5.
6.
7.
8.
<b l a nk > fields a r e a u t oma t ically exclud ed. Th is is t h e defau lt ;
<non e> in dica t es t h a t n o record s will be exclud ed. If th er e is a bla n k field,
Crim eS tat will t r ea t it a s a 0;
0 is excluded;
-1 is excluded;
0 a n d -1 indicat es tha t both 0 and -1 will be excluded;
0, -1 a n d 9999 ind ica t es t h a t a ll t h r ee valu es (0, -1, 9999) will be exclud ed;
An y ot h er n u m er ica l va lu e ca n be t r ea t ed a s a m is sin g va lu e by t yp in g it
(e.g., 99); an d
Mu l t i p l e n u m er ica l va lues ca n be tr ea t ed a s m issin g va lues by typing t h em ,
sepa r a t in g ea ch by comm a s (e.g., 0, -1, 99, 9999, -99).
It is im por t a n t for u se r s t o un der st a n d t h eir da t a set s p r ior t o us in g Crim eS tat. If
t h e da t a a r e ‘clean ’, t h a t is a ll X/Y fields a r e popu la t ed wit h cor r ect va lu es a s a r e a ll
weigh t /int en sit y fields (if u se d), t h en t h e pr ogra m will h a ve n o pr oblem s r u n n in g r out in es .
On t h e ot h er h a n d, in la r ge adm inist r a t ive da t a ba ses, su ch a s in m ost police depa r t m en t s,
t h er e will be m a n y r ecor ds t h a t a r e in com ple t e or h a ve m iss in g va lu es codes (e.g., 0).
Un less Crim eS tat is t old wh a t a r e t h e m is sin g va lu e codes, wit h t h e except ion of bla n k or
n on -n u m er ic valu es, it will in clud e t h em in t h e ca lcu lat ion s. For exa m ple, som e da t a ba se
pr ogra m s p u t a 0 for a n X or Y field wh ich h a s n ot been geocoded . Crim eS tat d oes n ’t k n ow
t h a t t h e 0 is a m is sin g va lu e a n d will u se it in ca lcu la t ion s sin ce 0 is a per fect ly good
n u m ber . It is im por t a n t t h a t u ser s eit h er clea n t h eir da t a t h orou gh ly or define t h e m iss in g
valu e codes com plet ely for t h e pr ima r y an d secon da r y files.
P rim ary Fi le
Th e Prim ary File is r equ ir ed a n d p r ovides t h e coord in a t es of poin t s of inciden t s. On
t h e pr im a r y file t a b, t h e u ser m u st fir st click on S elect Files. A d ia log box a p pea r s t h a t
a llows t h e u se r t o select wh ich of six file form a t s a pp lies t o th e pr im a r y file (F igu r e 3.2).
F or ea ch of t h e file form a t s, t h e u ser m u st define t wo ch a r a cter ist ics - t h e t ype of file
(ASCII, ‘.d bf’, ‘da t ’, ‘.s h p’, ‘m db’, or ODBC) a n d t h e n a m e of t h e file. Th er e is a br owse
win dow wh ich a llows t h e u se r t o fin d t h e file.
In developin g t h is pr ogr a m , we h a ve t a r get ed it t owa r ds u ser s of ArcView , M apIn fo
an d Atlas*GIS . Th ese GI S p r ogr a m s eit h er st ore t h eir a t t r ibu t e da t a in dB ase III/ IV
for m a t in a file wit h a ‘dbf’ ext en sion (e.g., pr ecin ct 1.d bf) or ca n r ea d a n d wr it e dir ect ly ‘dbf’
3.6
Figure 3.2:
File Format Selection
Linking CrimeStat III to MapInfo
Richard Block
Professor of Sociology and Criminal Justice
Loyola University of Chicago
MapInfo point ‘dat’ files can be inputted to CrimeStat as primary or secondary files.
However, x and y coordinates need to be added to the file. If the point data are in
latitude/longitude, this is easily done with a free extension, Table Geography, available through
the Directions Magazine website as part of the KGM utilities at:
http://www.directionsmag.com/tools/Default.asp?a=file&ID=11 . Add this extension to your
MapInfo toolbox. Click on the tool. You will first be asked for a table to add coordinates. The
program automatically adds columns for longitude and latitude.
If you are using another projection, you will need to add and update columns to your file.
To do this, add columns for x and y coordinates to your table (Table–>Maintenance–>Table
Structure–>Add Field) in an appropriate numeric format for your projection. As shown in left
figure, update these new columns with the coordinates (Table–>update column). Choose the data
file and column that you want to update. Next, click assist and then functions. Choose centroidx
to update the horizontal field and centroidy to update the vertical field. Within CrimeStat,
identify the file type as MapInfo ‘dat’.
For some CrimeStat require a reference file. These are identified by the lower-left and
upper-right coordinates of a rectangle. To derive these coordinates, make the top map (cosmetic)
layer editable. Draw a rectangle identifying the study area. Select the rectangle. Convert it to a
region (objects-Æ convert to region). Double click on the rectangle, and the appropriate
coordinates and area of the rectangle will appear.
Several CrimeStat routines output geographic features that can be added as a layer in
MapInfo. To output these graphics, first designate an output file. If you are working in
longitude/latitude, choose a MapInfo ‘mif ‘file as output. In MapInfo, import the mif file (Table–
>Import), and open the file as a layer in your map. For any other projection, output to an ESRI
shape file and use the Universal Translator tool (right figure) to import your file (Tools-->Universal Translator). Choose ESRI shape and the file that you designated in CrimeStat.
Next, choose the appropriate projection. Identify the destination format–chose MapInfo tab
and, finally, identify the directory for storage of the file. The table can then be opened as a layer
on your map. CrimeStat graphic output is brought into MapInfo as regions and has all the
functionality of a regions layer. Figure 7.6 includes STAC and single kernel density output.
files. Ma n y ot h er GIS pr ogr a m s, h owever , a ls o ca n r ea d ‘dbf’ files. F or ArcView a n d
M apIn fo, t h e X an d Y coor din a t es wh ich d efin e crim e in ciden t poin t s a r e n ot d ir ect ly pa r t
of t h e ‘dbf’ file, but ins t ea d exist on t h e geogra ph ic file.
Input File Forma ts
ArcView
I n ArcView t h e coord in a t es a r e st ore d on t h e ‘sh p’ file, not t h e ‘dbf’ file. Crim eS tat
can r ea d d ir ect ly a ‘sh p’ file so th e ‘dbf’ file is n ot r equ ir ed t o ha ve t h e X an d Y coor din a t es .
Ma pIn fo
H owever , in M apIn fo, th e coordina tes ar e stored in ‘ta b’ files. To use Crim eS tat
wit h M apIn fo, t h er efor e, r equ ir es t h a t t h e X a n d Y coor din a t es be a ss igned t o two fields in
t h e ‘t a b’ file a n d t h en sa ved a s a ‘dbf’ file. See t h e en dn otes for dir ection s on doing t h is. 4
E ven in ArcView , som e u ser s m a y wish t o expor t t h e poin t s a s a ‘dbf’ file beca u se of ot h er
inform at ion t ha t a re on t he records. The endnotes also list th ese directions. 5 M apIn fo also
u se s a ‘da t ’ for m a t , wh ich is sim ila r t o ‘dbf’. Th is ca n be r ea dy by Crim eS tat.
Atla s *GIS
I n Atlas*GIS , on t h e oth er h a n d, a poin t file is a lr ea dy a ‘dbf’ file an d w ill h a ve
fields for t h e X a n d Y coor din a t es.
Mi c ro s o ft Ac c e s s
‘Mdb’ F iles fr om M icrosoft A ccess ® 97 (or ea r lier ) ca n a lso be r ea d by Crim eS tat.
Th e u ser will h a ve to ensu r e t h a t t h e file h a s a n X a n d Y coor din a t e.
OD B C
Sim ila r ly, Crim eS tat can r ea d a n y file t h a t u ses Open Da t a ba se Conn ectivity
(ODBC). ODBC is a pr ogr a m m in g int er face t h a t en a bles pr ogr a m s t o access d a t a in
dat abase m an agement systems t ha t u se Stru ctu red Query Lan gua ge (SQL) as a dat a
a ccess s t a n da r d, su ch a s E xcel ® , P a r a dox ® , Micr osoft Access, Lot u s 1-2-3 ® , a n d F oxP r o® .
ASCII
F or a n ASCI I file, however , t h r ee a dd it ion a l a t t r ibu t es m u st be defined. Th e firs t is
t h e t yp e of ch a r a ct er t h a t is u sed t o sepa r a t e t h e va r ia bles in t h e file. Th er e a r e fou r
possibilities:6
Sp a ce (one or m ore, t h e defau lt )
Com m a
Sem icolon
3.9
Ta b
Th e secon d cha r a ct er ist ic is t h e n u m ber of r ows wh ich h a ve la bels on t h em (H ea d er
R ow s). Som e ASCII files will h a ve rows wh ich label t h e n a m es of t h e var iables. The u ser
sh ou ld indicat e t h e n u m ber if t h is is t h e ca se oth er wise Crim eS tat will p r odu ce a n er r or
code. The defau lt is 0, th at is th e progra m a ssum es tha t t here ar e no headers u nless
in st r u cted ot h er wise. To ch a n ge t h is, t h e u ser sh ould in ser t t h e cur sor in t h e a pp r opr ia t e
cell, ba cks pa ce to era se t h e defa u lt n u m ber a n d t ype in t h e cor r ect n u m ber .
Th e t h ir d ch a r a ct er is t ic of a n ASCII file t h a t m u st be defin ed is t h e n u m ber of
va r ia bles (colu m n s or fields) in t h e file. Wit h sp h er ical or pr ojected coord in a t es, t h er e will
be at leas t t wo var iables (th e X a n d Y coor din a t e) a n d t h er e m a y be more if ot h er var iables
a r e inclu ded in t h e file. H owever, with dir ect ion a l coor din a t es (see below), th er e m a y be
only on e. Crim eS tat assu mes th at th e num ber of column s in t he ASCII file is two un less
in st r u cted ot h er wise. Aga in , t h e u ser sh ould inser t t h e cur sor in t h e a pp r opr ia t e cell,
ba cks pa ce to era se t h e defa u lt n u m ber a n d t ype in t h e cor r ect n u m ber . Afte r definin g t h e
file t yp e a n d n a m e, t h e u ser sh ou ld click on OK.
Ide n tify in g Vari ab le s
Aft er definin g a file, eit h er ‘.dbf’, ASCII , ‘da t ’, or ‘.sh p’, it is n ecessa r y t o iden t ify th e
var iables. Two var iables a r e r equ ired a n d t wo a r e opt ion a l. The r equ ired var iables a r e t h e
X a n d Y coor din a t es . Th e u ser sh ou ld in dica t e t h e file n a m e t h a t con t a in s t h e coor din a t es
by click in g on t h e d r op down m en u a n d h igh ligh t in g t h e cor r ect n a m e. Aft er h a vin g
ide n t ified wh ich file con t a in s t h e X an d Y coor din a t es , it is n ecessa r y t o iden t ify th e
va r ia ble n a m e. Click on t h e d rop down m en u u n der Colum n a n d h igh ligh t t h e n a m e of t h e
va r ia ble for t h e X an d Y coor din a t es r es pectively. 7 F igu r e 3.3 sh ows a cor r ect defin in g of
file a n d var iable n a m es for t h e pr ima r y file.
Mu ltiple files ca n be ent er ed on t h e pr ima r y file t a b. However , on ly on e ca n be
u t ilized a t a t im e. I n t h eor y, on e ca n h a ve sepa r a t e files con t a in in g t h e X a n d Y
coor din a t es , t h ou gh in pr a ct ice t h is will r a r ely occu r .
We ig h t Varia ble
Somet imes , a point loca t ion is weigh t ed. As m en t ion ed a bove, weigh t s a r e u sed
wh en poin t s r epr esen t s a r ea s a n d t h e a r ea s a r e st a t is t ica lly t r ea t ed differ en t ly. F or m ost
of t h e st a t ist ics, Crim eS tat can weigh t t h e st a t ist ics du r in g t h e calcula t ion (e.g., t h e
weigh t ed m ea n cen t er , t h e weigh t ed n ea r est n eigh bor in dex).
By defa u lt , Crim eS tat a ssign s a weigh t of 1 t o ea ch poin t . If t h e u ser does n ot
define a weigh t va r ia ble, t h en t h e pr ogra m a ss u m es t h a t ea ch p oint h a s equ a l weigh t (i.e.,
1). On t h e ot h er h a n d, if t h er e a r e weigh t s, t h en t h e weigh t va r ia ble sh ou ld be defin ed on
th e primar y file screen an d its n am e listed.
3.10
Figure 3.3:
Primary File Definition
Int e n si ty Varia ble
Sim ila r ly, a poin t loca t ion ca n h a ve a n in t en sit y a ssign ed t o it . Most of th e
st a t ist ics in Crim eS tat ca n u se a n in t en sit y va r ia ble a n d som e st a t is t ics r equ ir e it (Mor a n ’s
I, Gea r y’s C a n d Loca l Mora n ). If n o int en sit y is d efin ed, Crim eS tat will n ot ca lcula t e
st a t is t ics r equ ir in g a n in t en sit y va r ia ble a n d, in st a t is t ics wh er e a n in t en sit y is opt ion a l
(e.g., int er pola t ion ), will a ss u m e a defau lt in t en sit y of 1. On t h e oth er h a n d, if th er e is a n
in t en sit y var ia ble, t h en t h is s h ould be defined on t h e pr im a r y file scr een a n d it s va r ia ble
na me ident ified.
In gen er a l, be ver y car efu l a bout u sin g both a n int en sit y va r iable a n d a weigh t in g
va r ia ble. U se bot h only wh en t h er e a r e sepa r a t e weigh t s a n d in t en sit ies. Most of th e
r out in es can u se both in t en sit ies a n d w eigh t in g a n d m a y, con se qu en t ly, dou ble-weigh t
ca ses. F igu r e 3.4 shows a pr ima r y file screen with a n int en sit y va r iable defin ed.
Tim e Varia ble
F in a lly, a t im e va r ia ble can be defined for u se in t h e special Spa ce-t im e a n a lysis
t ools u n der Sp a t ia l m odelin g. Crim eS tat allows five different time references:
H ou r s
Da ys
We ek s
Mon t h s
Yea r s
Th e defa u lt is ‘da ys’ bu t t h e u se r can choose on e of t h e oth er fou r cat egories .
H owever , t h e pr ogr a m a ss u m es t h a t a ll r ecor ds a r e con sis t en t defined . For exa m ple, all
r ecor ds m u st be in da ys or in h ou r s. If some r ecor ds a r e in da ys, for exam ple, an d oth er
r ecor ds a r e in h our s, t h e pr ogr a m will n ot k n ow th a t t h er e is a n in con sis t en cy a n d will
t r ea t ea ch of th e r ecor ds in t h e wa y t h ey h a ve been define d. I t ’s im por t a n t , t h er efor e, t h a t
a u se r en su r e t h a t a ll r ecor ds a r e con sis t en t in t h e wa y t h a t t im e is define d. F igu r e 3.5
illu st r a t es t h e defin ing of a t ime va r iable on t h e pr ima r y file pa ge.
Co ord in a te S ys te m
In a dd it ion t o th e pr im a r y file na m e a n d va r ia ble a ss ign m en t , it is n ecessa r y t o
ide n t ify th e t ype of coord in a t e syst em u se d a n d t h e u n it s of mea su r em en t . Crim eS tat
recognizes thr ee coordina te systems:
S ph e ri ca l c oo rd in a te s (lon git u de a n d la t itu de)
Th is is a u n iver sa l coor din a t e sys t em t h a t m ea su r es loca t ion by a n gles fr om
r efer en ce p oin t s on E a r t h .8
3.12
Figure 3.4:
Primary File With Intensity Variable Defined
Figure 3.5:
Time Variable Definition
P r oje c te d co ord in a te s
P r oject ed coor din a t es a r e a r bit r a r y coor din a t es ba sed on a pa r t icu la r pr oject ion of
t h e ea r t h t o a fla t pla n e. Th ey h a ve a n a r bit r a r y or igin (t h e pla ce w h er e X=0 a n d Y=0) a n d
a r e a lmost a lways d efined in u n its of feet or m et er s. 9
Crim eS tat ca n wor k wit h eit h er sp her ica l or pr oject ed coor din a t es . On t h e p rim a r y
file t a b, th e u ser ind ica t es wh ich coor din a t e syst em is being us ed. If t h e coor din a t e syst em
is s ph er ical, t h en u n it s a r e a u t oma t ically a ss u m ed t o be lat it u de a n d longit u de in decima l
degr ees. If t h e coor din a t e syst em is pr oject ed, th en it is n ecessa r y to specify whet h er t h e
measu rem ent u nits a re feet or m eters.
D ire c ti on a l c oo rd in a te s
F or some u ses, a pola r coor din a t e syst em ca n be us ed. Point loca t ion s a r e defin ed
by an gles from a n a r bitr a r y referen ce lin e, usu a lly t r u e n or t h a n d var y between 0 0 a n d 360 0
in a clock wis e r ot a t ion . All loca t ion s a r e m ea s u r ed a s a n a n gu la r d evia t ion fr om t h e
r efer en ce poin t a n d w it h dis t a n ce bein g m ea su r ed from a cent r a l loca t ion. Crim eS tat h a s
t h e a bilit y t o rea d in a n gles for u se in calcu la t in g t h e a n gu la r m ea n a n d va r ia n ce. In
a ddit ion , if dir ect ion a l coor din a t es a r e u sed, a n opt ion a l d is t a n ce va r ia ble for ea ch
m ea su r em en t can be u se d.
If t h e file cont a in s d ir ection a l coor din a t es (an gles), defin e t h e file na m e a n d va r ia ble
n a m e (colum n ) t h a t con t a ins t h e dir ect ion a l mea su r em en t s. If u sed, defin e t h e file n a m e
an d var iable nam e (column ) th at cont ains t he distan ce var iable. Figur e 3.6 shows the
pr im a r y file defin it ion u sin g dir ect ions .
Se co n da ry F ile
Crim eS tat a lso a llows for t h e in pu t t in g of a secon da r y file. For exa m ple , t h e
pr im a r y file cou ld be locat ion s wh er e m otor veh icles wer e st olen wh ile t h e secon da r y file
cou ld be t h e loca t ion wh er e st olen veh icles wer e r ecover ed. Alt er n a t ively, th e pr im a r y file
cou ld be bu r gla r y loca t ions wh ile t h e secon da r y file could be p olice st a t ions . Crim eS tat ca n
con s t r u ct t wo d iffer en t t yp es of in d ices wit h a s econ d a r y file. F ir s t , it ca n ca lcu la t e t h e
dis t a n ce fr om ever y pr im a r y file poin t t o every second a r y file poin t . For exa m ple, t h is
m igh t be u sefu l in a ssessin g wh er e t o pla ce police ca r s in or der t o m in im ize t r a vel d is t a n ce
in r es pon se t o ca lls for ser vice. Second , Crim eS tat ca n u t ilize bot h pr im a r y a n d secon da r y
files in es t im a t in g a t h r ee-dim en sion a l d en sit y s u r fa ce (s ee Ch a pt er 7). F or exa m ple, if t h e
pr im a r y file a r e r esid en t ia l bu r gla r ies a n d t h e secon da r y file con t a in s t h e cen t r oid s of
cens u s block gr oup s wit h t h e popu la t ion wit h in ea ch block gr oup a ss igned a s a n in t en sit y
var iable, th en Crim eS tat ca n est im a t e t h e den sit y of bu r gla r ies r ela t ive t o t h e den sit y of
popu la t ion (i.e ., bu r gla r y r is k ).
Th e secon da r y file ca n a lso be eith er a ‘.dbf’, ‘.sh p’ or ASCII. As wit h a pr ima r y file,
t h er e m u st be an X a n d Y var iable defin ed, but it m u st be in t h e sa m e coor din a t e syst em
a n d da t a u n its a s t h e pr ima r y file. The s econ da r y file ca n a lso h a ve weight s a n d in t en sit ies
3.15
Figure 3.6:
File Definition With Angles (Directions)
a ssign ed, bu t n ot a t im e va r ia ble.. F igu r e 3.7 sh ows t h e in pu t t in g of a n ASCII file for t h e
secon da r y dat a set wh ile figu r e 3.8 shows a cor r ect defin ition of t h e secon da r y file.
Re fere n ce Fi le
Sever a l of th e r out in es in Crim eS tat gen er a lize t h e poin t da t a t o all loca t ion s in t h e
st u dy ar ea , in pa r t icu lar t h e on e-var iable a n d t wo-var iable den sit y in t er pola t ion r ou t ines
(ch a pt er 8), a n d t h e r is k-a dju st ed nea r es t n eigh bor h ier a r ch ica l clu st er in g r ou t in e (ch a pt er
6). Th e gen er a liza t ion u se s a r efer en ce file pla ced over t h e st u dy a r ea . Th e STAC pr ogra m
a lso uses a r efer en ce file for sea r chin g (cha pt er 7). Typica lly, th e r efer en ce file is a
r ect a n gu la r gr id file (t r u e gr id), t h a t is a r ect a n gle wit h cells d efin ed by colu m n s a n d r ows.;
ea ch grid cell is a r ect a n gle a n d colum n -r ow com bina t ion s a r e u sed. It is possible t o u se a
n on -r ect a n gu la r gr id file u n der specia l cir cu m st a n ces (e.g., a gr id wit h wa t er , m ou n t a in s or
ot h er ju r isdict ion s r em oved), but a r ect a n gula r grid would be u sed in m ost ca ses.
Crim eS tat can crea t e a gr id file d ir ect ly or ca n r ea d in a n ext er n a l gr id file. F igu r e 3.9
sh ows a grid pla ced over bot h t h e Cou n t y of Balt imore a n d t h e City of Balt imore.
Crea ting a Refere nc e Grid
Crim eS tat can also creat e a tr ue grid. There are t wo steps:
1.
The user selects Create Grid fr om t h e Refer en ce F ile t a b a n d in p u t s t h e X
a n d Y coor din a t es of t h e lower -left a n d u pp er -righ t coord in a t es of t h e gr id.
Th es e coord in a t es m u st be t h e sa m e a s for t h e pr im a r y file.
Th u s, if th e pr im a r y file is u sin g sp h er ical (lat /lon ) coor din a t es, t h en t h e gr id file
coor din a t es m u st a lso be lat /lon . Con vers ely, if t h e pr ima r y file coor din a t es a r e pr oject ed,
t h en t h e gr id file coor din a t es m u st a lso be pr ojected, usin g t h e sa m e m ea su r em en t u n it s
(feet or m et er s). Th e lower -left a n d u pper -r igh t coor din a t es a r e t h ose fr om a gr id wh ich
cover s t h e geogr a ph ica l a r ea . A u ser sh ou ld id en t ify t h es e wit h a GIS p rogr a m or fr om a
properly indexed map. In M apIn fo, t h is is ea sily d on e by eit h er dr a win g a r ect a n gle a r ou n d
t h e st u dy a r ea a n d d ouble click in g t o get in for m a t ion a bout t h e a r ea or by checkin g t h e
cu r s or p os it ion . In ArcView , you ca n dr a w a sh a pe file of t h e a ppr opr ia t e r efer en ce
r ect a n gle a n d t h en u se t h e Coor din a t e Ut ilit y scr ipt t o get t h e X a n d Y coor din a t es.
2.
Th e u se r selects w h et h er t h e gr id is t o be crea t ed by cell sp a cing or by t h e
n u m ber of colu m n s.
Wit h B y cell sp acin g, t h e size of t h e cell is defined by it s h orizont a l widt h , in t h e
sa m e u n it s a s t h e m ea su r em en t u n it s of t h e pr im a r y file. Th is would be u sed t o ma in t a in
a cert a in size of sp a cing for a cell. F or exa m ple, if t h e coord in a t e syst em is s ph er ical a n d
t h e lower -left coor din a t es a r e -76.90 an d 39.20 degrees a n d t h e u pper -r igh t coor din a t es a r e
-76.32 a n d 39.73 degr ees (a gr id wh ich over la ps Ba lt im or e Cit y a n d Ba lt im or e Cou n t y),
t h en t h e h or izon t a l dist a n ce - t h e differ en ce in t h e t wo lon git u des (0.58 degrees ) m u st be
divided in t o ap pr opr ia t e sized in t er va ls. At t h is la t it u de, t h e differ en ce in longit u des is
34.02 miles. If a u ser wa n t ed cell spa cing of 0.01 degr ees, th en t h is wou ld be ent er ed a n d
3.17
Figure 3.7:
Ascii File Selection of Secondary File
Figure 3.8:
Secondary File Definition
Figure 3.9: Grid Cell Structure for Baltimore Region
108 Width x 100 Height Grid Cells
!Upper-right
Coordinate
Baltimore County
City of Baltimore
Miles
0
2
D
4
Lower-left Coordinate
!
Crim eS tat wou ld ca lcu la t e 59 colu m n s (cells) in t h e h or izon t a l d ir ect ion , on e for ea ch
int er val of 0.01 an d one for t h e fr a ct ion a l rem a ind er . If t h e coor din a t e syst em is pr oject ed,
t h en sim ila r calcu la t ions would be m a de u sin g t h e pr oject ed u n it s (feet or m et er s).
P r oba bly an ea sier wa y to specify th e grid is t o ind ica t e t h e n u m ber of colum n s. By
checkin g B y n u m ber of colu m n s, t h e u se r define s t h e n u m ber of colu m n s t o be calcu la t ed.
Crim eS tat will a u t om a t ica lly ca lcu lat e t h e cell spa cing n eeded a n d will ca lcu lat e t h e
r equ ired n u m ber of r ows. For exa m ple, usin g th e sa m e coor din a t es a s a bove, if a u ser
wa n t ed h a lf m ile squ a r es for t h e cells, t h en t h ey would n eed a pp r oxim a t ely 68 cells in t h e
h orizon t a l dir ect ion s in ce 34.02 m iles divid ed by 0.5 m ile squ a r es equ a ls a bout 68 cells.
F igu r e 3.10 shows a cor r ect ly defin ed r efer en ce file wh er e Crim eS tat cr ea t es t h e r efer en ce
grid wit h t h e n u m ber of colum n s being defined; in t h e exam ple, 100 colum n s a r e r equ est ed.
Sa vi n g a Re fer e n ce Fi le
Th e u ser ca n sa ve t h e lower -left a n d u pper -r igh t coor din a t es of a defin ed r efer en ce
grid a n d t h e n u m ber of colum n s. Type S a ve <filena m e>. Th e coor din a t es a n d colum n sizes
will be sa ved in t h e syst em r egist r y. To loa d a n a lrea dy defined r efer en ce file, t ype Loa d
a n d t h en ch eck t h e a ppr opr ia t e filen a m e, followed by click in g on ‘Loa d’.
In a ddit ion , t h e u ser ca n sa ve t h e r efer en ce pa r a m et er s t o a n ext er n a l file. To do
t h is, it h a s t o be alr ea dy sa ved in t h e syst em r egist r y. Type Loa d a n d t h en ch eck t h e
a pp r opr ia t e filena m e, followed by clickin g on ‘Sa ve t o File”. Define t h e dir ectory a n d file
n a m e a n d click ‘Sa ve’. Th e file will be sa ved wit h a n ‘r ef’ ext en sion (e.g.,
Ba lt im or eCou n t y.r ef).
Us e an Ex te rn al Grid Fi le
Ma n y GIS pr ogr a m s ca n cr ea t e u n ifor m gr id s wh ich cover a geogr a ph ica l a r ea . As
wit h t h e pr im a r y a n d secon da r y files, t h ese n eed t o be con ver t ed t o eit h er ‘.d bf’, ASCII or
‘.s h p’ files. To u se a n exist in g gr id file cr ea t ed in a GIS or a n ot h er pr ogr a m , t h e u ser clicks
on From File on t h e Refer en ce File t a b a n d s elect s t h e file.
Th er e a r e t h r ee ch a r a ct er ist ics wh ich sh ou ld be ident ified for a n exist ing grid file:
1.
Th e n a m e of t h e file. Th e u ser select s t h e file fr om a dia log box s im ila r t o t h e
pr ima r y file.
2.
If t h e exist ing r efer en ce file is a t r u e grid, t h e T rue Grid box should be
checked.
3.
If it is a t r u e gr id, t h e n u m ber of colu m n s s h ould be en t er ed. Crim eS tat will
a u t om a t ica lly cou n t t h e n u m ber of r ecor ds in t h e file a n d pla ce it in t h e Cells
box. Whe n t h e n u m ber of colu m n s is en t er ed, Crim eS tat will a u t oma t ically
calcu la t e t h e n u m ber of r ows.
3.21
Figure 3.10:
Create Reference Grid Setup
Figur e 3.11 shows a cor r ect ly defined r eferen ce file us ing an exist ing grid file. On e
m u st be ca r efu l in u sin g a file wh ich is n ot a gr id. Crim eS tat ca n ou t p u t t he r es u lt s of t h e
in t er pola t ion r ou t in es in sever a l GIS form a t s - S u rfer for Win d ow s, ArcView S patial
An alyst, ArcView , M apIn fo an d Atlas*GIS . Of t h ese, on ly t h e ou t pu t t o S u rfer for Win d ow s
will a llow t h e r efer en ce t o be a sh a pe ot h er t h a n a t r u e gr id . F or t h e in t er pola t ion ou t pu t s
of ArcView S pat ial A n alyst, ArcView , M apIn fo an d Atlas*GIS , it is es sen t ia l t h a t t h e
r efer en ce file be a t r u e gr id.
Us e of Re fer e n ce Fi le
A r efer en ce grid can be very us efu l. Fir st , a n u m ber of t h e r ou t ines u se it for eith er
in t er pola t ion (sin gle a n d d u el k er n el r out in es; nea r est n eigh bor h ier a r chical clu st er in g
r out in e) or keyin g a sea r ch r a diu s (STAC). Secon d, a gr id p r odu ced by Crim eS tat ca n be
u sed a s a sepa r a t e la yer in a GIS pr ogr a m in ord er t o refer en ce ot h er da t a t h a t is
displa yed, aside from s t a t ist ica l ca lcu lat ion s. H ist or ica lly, ma n y ma p u ses a r e r efer en ced
t o a gr id in or der t o pr odu ce a sys t em a t ic in ven t or y (e.g., pa r cel m a ps; t a x a ssessor m a ps;
U.S. Geologica l Sur vey 7.5" ‘qu a d’ m a ps). In sh or t , it is a r ou t ine wit h m u ltiple pu r poses.
Me as u re m e n t P ara m e te rs
Th e fina l pr oper t ies t h a t com ple t e da t a definit ion a r e t h e m ea su r em en t pa r a m et er s.
On th e Measur ement Pa ra met ers ta b, th e user defines the geogra phical ar ea an d th e
len gt h of s tr eet n et wor k for t h e s tu dy a r ea , a n d in dica t es wh et h er dir ect or in dir ect
dist a n ces a r e t o be us ed. Figur e 3.12 shows t h e m ea su r em en t pa r a m et er s t a b pa ge.
Area a n d Le n gth of Stre e t Ne tw ork
In ca lcu lat ing dist a n ces bet ween poin t s for t wo of t h e st a t ist ics - th e n ea r est
n eigh bor ind ex an d t h e Ripley ‘K’ ind ex, t h e a r ea for wh ich t h e poin t s fall wit h in n eeds t o
be defin ed (th e st u dy ar ea ). The u ser ind ica t es t h e a r ea of t h e geogra ph ica l covera ge an d
t h e m ea su r em en t u n its t h a t dist a n ces a r e ca lcu lat ed (feet , met er s, m iles, n a u t ica l miles,
kilom et er s). Un like t h e da t a u n its for t h e coor din a t e syst em , which m u st be con sist en t ,
Crim eSt a t ca n ca lcu lat e dista n ces in a n y of t h ese un its. In som e ca ses, an a lysis will be
con d u ct ed on a su bs et of t h e s t u dy a r ea , r a t h er t h a n t h e en t ir e a r ea . F or ea ch a n a lys is , t h e
u ser sh ou ld ident ify th e a r ea of t h e su bset for wh ich dist a n ce st a t ist ics a r e t o be ca lcu lat ed.
In a ddit ion , th e lin ea r n ea r est n eigh bor st a t ist ic u ses t h e t ot a l len gth of t h e st r eet
n et wor k a s a ba se lin e for com pa r ison (see cha pt er 5). If th is s t a t ist ic is t o be u se d, t h e
t ot a l len gt h of t h e st r eet n et wor k sh ou ld be defin ed. Most GIS pr ogr a m s ca n su m t h e t ot a l
len gt h of t h e s t r eet n et wor k . Aga in , if s u bs et s of t h e s t u dy a r e u s ed , t h e u s er s h ou ld
in d ica t e t h e a p pr op r ia t e len gt h of s t r eet n et wor k for t h e s u bs et s o t h a t t h e com p a r is on is
a ppr opr iat e.
3.23
Figure 3.11:
Reference File Definition With An External File
Figure 3.12:
Measurement Parameters Page
Ty pe o f D is ta n ce Me a su re m e n t
Di rect d ist a nce
Cr im eSt a t can calcu la t e dist a n ce in t h r ee d iffer en t wa ys: dir ect , in dir ect , a n d
n etwork dist a n ces. Dir ect dist a n ces a r e th e sh or t est dist a n ce between t wo point s. On a
flat plan e, th a t is wit h a p r oject ed coor dina t e system , th e sh or t est dist a n ce between t wo
poin t s is a st r a igh t lin e. H owever , on a sph er ica l coor din a t e sys t em , t h e sh or t est dis t a n ce
bet ween t wo poin t s is a Gr ea t Circle lin e. Depend ing on t h e coor din a t e syst em , Crim eSt a t
will ca lcu lat e Gr ea t Circle dist a n ces u sin g sph er ica l geom et r y for sph er ica l coor din a t es a n d
E u clidea n dis t a n ces for pr oject ed coor din a t es. Th e dr a win gs in figu r e 3.13 illu st r a t e dir ect
dist a n ces wit h a pr oject ed a n d sp h er ica l coor din a t e syst em . The sh or t est dist a n ce bet ween
poin t A an d poin t B is eit h er a st r a igh t lin e (pr oject ed) or a Gr ea t Cir cle (sph er ica l). F or
det a ils see McDon n ell, 1979 (cha pt er 1) or Sn yd er , 1987 (pp. 29-33).
Ind ir ect d ist a nce
In dir ect dis t a n ces a r e a n a ppr oxim a t ion of t r a vel on a r ect a n gu la r r oa d n et wor k .
Th is is fr equ en t ly ca lled Ma n h a t t a n dis t a n ce, r efer r in g t o t h e gr id -lik e st r u ct u r e of
Ma n h a t t a n . Ma n y cit ies, bu t cert a in ly not a ll, lay ou t t h eir st r eet s in grids . Th e degr ee in
wh ich t h is is t r u e var ies. Older cities will not u su a lly h a ve gr id st r u ct u r es wh er ea s n ewer
cit ies t en d t o u se gr id la you t s m or e. Of cou r se, n o r ea l cit y is a per fect gr id , t h ou gh som e
com e close (e.g., Sa lt La k e Cit y). Dis t a n ces m ea su r ed over a st r eet n et wor k a r e a lwa ys
lon ger t h a n a dir ect lin e or a r c. In a per fect gr id , t r a vel ca n on ly occu r in h or izon t a l or
ver t ica l d ir ect ion s s o t h a t dis t an ces ar e t h e s um of t h e h or izon t a l a n d ver t ica l s tr eet
lengt h s t h a t h a ve been t r a veled (i.e., on e ca n n ot cu t dia gon a lly a cr oss a block). Dist a n ces
a r e m ea su r ed a s t h e su m of h orizont a l a n d ver t ical dist a n ces t r a veled bet ween t wo point s.
Indirect dista nce approximat e actu al tr avel pat tern for a city where str eets a re
a r r a n ged in gr id pa t t er n . This is wh y th is t ype of dist a n ce is fr equ en t ly ca lled Man hattan
Dist an ce. In t h is ca se, in dir ect dis t a n ces wou ld be a m or e a ppr opr ia t e dis t a n ce
m ea su r em en t t h a n dir ect dis t a n ces. Also, t h er e is a lin ea r n ea r est n eigh bor in dex wh ich
m ea su r es t h e dist r ibut ion of poin t loca t ion s in r elat ion t o t h e st r eet n et wor k r a t h er t h a n
th e geograph ical ar ea a nd u ses indirect dista nces. This will be discussed in Cha pter 5. In
t h is ca se, th e u se of ind irect d ist a n ces would be pr efer a ble th a n dir ect dist a n ces. 1 0
Net w ork d ist a nce
Net wor k dis t a n ces a r e t r a vel on a n a ct u a l n et wor k . Th e n et wor k ca n be a r oa d
n et wor k , a t r a n sit n et wor k , or a r a il n et wor k . Tr a vel is con st r a in ed t o t h e n et wor k wh ich
u su a lly will ma k e it lon ger t h a n dir ect dis t a n ce mea su r em en t . H owever , t h e a dva n t a ge is
t h a t t r a vel is m ea su r ed a lon g th e a vailable r ou t es, ra t h er t h a n a s a n a bst r a ct ‘st r a igh t lin e’
or even a bs t r a ct ‘gr id ’. An ot h er a d va n t a ge of n et wor k dis t a n ce is t h a t t he n et wor k ca n be
weight ed by tr a vel t ime, t r a vel speed or t r a vel cost . Thu s, it’s possible to mea su r e
a pp r oxim a t e t r a vel t im e or t r a vel cost t h r ough t h e n et work , an d n ot ju st dis t a n ce. It is
gen er a lly recogn ized t h a t t r a vel t im e is a m ore r ea list ic dim en sion t h a n dis t a n ce sin ce it
3.26
Figure 3.13:
Direct and Indirect Distances
B
Indirect
Two-dimensional
Projected
Geometry:
Euclidean distance
A-B distance ('dotted route') =
A-B distance('dashed route')
Direct
A
Indirect
B
Indirect
A-B distance ('dotted route') <
A-B distance ('dashed route')
Three-dimensional
Spherical
Geometry:
Great Circle distance
Direct
A
Indirect
will va r y by t im e of da y. F or exa m ple, it gen er a lly t a k es a lot lon ger t o t r a vel a n y d is t a n ce
in a n u r ba n a r ea d u r in g t h e p ea k even in g ‘r u s h hou r s ’ (4-7 P M) t h a n a t , s a y, 3 AM in t h e
m orn in g. Dist a n ce is a lwa ys in va r ia n t wh er ea s t r a vel t im e va r ies. An even m ore r ea list ic
dim en sion t r a vel is cost . Tr ip s over a m et r opolit a n a r ea a r e gover n ed by a n u m ber of
va r ia bles a sid e from t r a vel t im e - vehicle oper a t in g cost s, p a r k in g cost s a n d, even , likely
r isk cost s (e.g., likelihood of being ca u ght ). For a n offen der wh o is t r a veling, th ose oth er
cos t fa ct or s m a y be a s im p or t a n t a s t h e a ct u a l t im e it t a k es in det er m in in g wh et h er t o
m a k e a cr im e t r ip . In ch a pt er 15, t h er e is a dis cu ssion of t r a vel cos t s in t h e con t ext of
tr avel decisions.
Th er e a r e t wo ma jor dis a dva n t a ges in u sin g net work dis t a n ce, however . Fir st ,
t h er e a r e er r or s in n et wor ks . For exam ple, a n et wor k m a y not h a ve in cor pora t ed a ll n ew
r oa ds or con ver t ed r oa ds. Th u s, t h e n et wor k a lgor it h m will n ot ch oose a pa r t icu la r r ou t e
wh en , in fa ct , it a ct u a lly exist s a n d people use it . It’s crit ica l th a t n et wor ks be up da t ed t o
en su r e a ccu r a cy. See ch a pt er 12 for a discuss ion of n et wor k er r or s a n d t h e n eed t o
t h or ou gh ly clea n t h em .
Secon d, it can t a ke a lon g tim e t o ca lcu lat e dist a n ce a lon g a n et wor k. Th e sh or t est
pa t h a lgor it h m t h a t is u sed m u st explor e m a n y a lt er n a t ive r out in es, a t im e con su m in g
pr ocess. F or sim ple st a t is t ics , t h is is n ot lia ble t o be a pr oblem . Bu t , for som e of t h e m or e
com plica t ed m a t r ix oper a t ion s (e.g., t h e dis t a n ce fr om ever y poin t t o ever y ot h er poin t ),
ca lcu la t ion t im e in cr ea ses exp on en t ia lly wit h t h e n u m ber of ca ses . I’ve h a d r u n s t h a t t ook
five da ys on a fas t com pu t er . For a n y com ple x calcu la t ion, it becomes im pr a ctica l t o ha ve
t o wa it a long t im e ju st for a lit t le ext r a pr ecision . In sh ort , it m a y n ot be wor t h t h e t r ouble.
At some point in th e near futu re, we will ha ve 64 bit operat ing systems a nd su per-fast
com p ut er s . At t h a t poin t , r u n n in g a ll ca lcu la t ion s on a n et wor k m a y be a m u ch m or e
pr a ct ica l pr oposition . For n ow, I highly recom m en d t h a t n et wor k d ist a n ce be us ed
spar ingly for calculat ions.
D is ta n ce Ca lc u la tio n s
Dist a n ces in Cr im eSt a t a r e calcu la t ed wit h t h e followin g form u la s:
D ire c t, P r oje c te d Co ord in a te S ys te m
Dis t a n ce is m ea su r ed a s t h e h ypot en u se of a r igh t t r ia n gle in E u clidea n geomet r y.
______________________
d AB = % (XA + XB )2 + (YA + YB )2
(3.1)
wh er e d AB is t h e dist a n ce bet ween t wo poin t s, A a n d B, XA an d XB ar e the X-coordina tes for
poin t s A a n d B in a pr oject ed coord in a t e syst em , YA an d YB a r e t h e Y-coor din a t es for poin t s
A a n d B in a pr oject ed coor din a t e s ys t em .
3.28
D ire c t, S ph e ri ca l Co ord in a te S ys te m
Dist a n ce is m ea su r ed a s t h e Gr ea t Circle dist a n ce bet ween t wo poin t s. All lat itu des
(N) an d longitu des (8) a r e fir s t con ver t ed in t o r a d ia n s u sin g:
2B
Radians (N) = ----------360
(3.2)
2B
Radians (8) = ----------360
(3.3)
Th en , t h e dis t a n ce bet ween t h e t wo poin t s is det er m in ed fr om
d AB = 2* Ar csin { Sin 2 [(NB - NA )/2] + Cos NA *Cos NB *Sin 2 [(8B - 8A )/2]1 /2 }
(3.4)
with a ll a n gles being defined in r a dia n s wh er e d AB is t h e dist a n ce bet ween t wo poin t s, A
a n d B, NA an d NB ar e the latitu des of points A an d B, an d 8A an d 8B a r e t h e lon git u des of
poin t s A an d B (S n yd er , 1987, p. 30, 5-3a ).
Indirect, Projec ted Coordin ate S yste m
Dis t a n ce is m ea su r ed a s t h e side s of a r igh t t r ia n gle u sin g E u clidea n geomet r y.
d AB = (XA - XB ) + (YA - YB )
(3.5)
wh er e d AB is t h e dist a n ce bet ween t wo poin t s, A a n d B, XA an d XB ar e the X-coordina tes for
poin t s A a n d B in a pr oject ed coord in a t e syst em , YA an d YB a r e t h e Y-coor din a t es for poin t s
A a n d B in a pr oject ed coor din a t e s ys t em .
Indirect, Sphe rical Coordin ate S yste m
Dista n ce is mea su r ed by th e aver a ge of su m m ed Gr eat Circle dist a n ces of t wo
r out es, on e in t h e ea st -west dir ection followed by a n ort h -sout h dir ection a n d t h e oth er in
t h e n or t h -sou t h dir ect ion followed by a n ea st -west dir ect ion .
d AB =
[d AB (1) + d AB (2)]
---------------------2
(3.6)
wh er e d AB is t h e dist a n ce bet ween t wo poin t s, A a n d B, d AB (1) is t h e su m of dist a n ces
bet ween poin t s A a n d B by mea su r ing t h e Gr ea t Circle dist a n ce of t h e ea st or west
d ir ect ion fr om a p a r t icu la r la t it u d e fir s t , a n d a d din g t h is t o t h e Gr ea t Cir cle d is t a n ce of t h e
nort h or sout h direction from t ha t sa me latitu de, an d d AB (2) is t h e su m of dist a n ces
bet ween poin t s A an d B by m ea su r in g t h e Gr ea t Cir cle dis t a n ce of t h e n or t h or sou t h
d ir ect ion fr om a p a r t icu la r lon git u d e fir s t , a n d a d din g t h is t o t h e Gr ea t Cir cle d is t a n ce of
t h e ea st or west dir ect ion fr om t h a t sa m e lon git u de.
3.29
N e t w o r k D is t a n c e
Net wor k d ist a n ce is ca lcu lat ed wit h a sh or t est pa t h a lgor ith m . Cha pt er s 12 a n d 16
pr ovide m or e in for m a t ion on n et wor k s a n d h ow dis t a n ce is ca lcu la t ed on t h em . A sh or t
su m m a r y will be given h er e. In gen er a l, dist a n ce is ca lcu lat ed by a s h or t est pa t h
a lgor it h m . In a shortest path for a sin gle t r ip (fr om a sin gle or igin t o a sin gle dest in a t ion ),
t h e r out e wit h t h e lowest over a ll im p ed a n ce is select ed. Im peda n ce ca n be defined in t er m s
of dis t a n ce, t r a vel t im e, s peed, or gen er a lized cost .
Th er e a r e a n u m ber of sh or t est pa t h a lgor ith m s t h a t h a ve been developed
(Sedgewick, 2002). They differ in t er m s of wh et h er t h ey a r e br ea dt h -fir st (i.e., sea r ch a ll
possibilities) or dept h -firs t (i.e., go st r a igh t t o t h e t a r get) algor ith m s a n d wh et h er t h ey
exa m in e a on e-t o-m a n y r ela t ion sh ip (i.e., fr om a sin gle or igin n ode t o m a n y n odes) or a
m a n y-t o-m a n y r ela t ion sh ip (All p a ir s; fr om ea ch n ode t o ever y ot h er n ode).
Th e a lgor ith m t h a t is m ost com m on ly u sed for sh or t est pa t h a n a lysis of m oder a t esized da t a set s (up t o a m illion ca ses) is ca lled A *, wh ich is pr on ou n ced “A-st a r ” (Nilsson ,
1980; St out , 2000; Ra bin 2000a , 2000b; Sedgewick, 2002). It is a one-t o-m a n y a lgor it h m
bu t is an imp r ovemen t over a n ot h er com m on ly-u sed a lgor ith m ca lled Dijkst ra (Dijkst ra ,
1959). Th er efor e, I’ll st a r t firs t by des crib in g t h e Dijk st r a a lgorit h m before expla in in g t h e
A* a lgor it h m .
D i jk s t r a a l g or i t h m
Th e Dijk st r a a lgor it h m is a on e-t o-m a n y s ea r ch st r a t egy in wh ich a sh or t es t p at h
fr om a s in gle n od e t o a ll ot h er n od es is ca lcu la t ed . Th e r ou t in e is a br ea d t h -fir s t a lgor it h m
in t h a t it sea r ches a ll possible pa t h s, bu t it bu ilds t h e pa t h one s egm en t a t a t im e. St a r t in g
fr om a n or igin loca t ion (n od e), it id en t ifies th e n od e t h a t is nea r es t t o it a n d wh ich h a s n ot
a lr ea dy been id en t ified on t h e sh or t est pa t h . Aft er ea ch n ode h a s been id en t ified t o be on
t h e sh ort est pa t h , it is r em oved from t h e sea r ch p ossibilit ies. Th e a lgor it h m pr oceed s u n t il
t h e sh ort es t pa t h t o all n odes h a s been det er m in ed.
Th e a lgor it h m can a lso be st r u ctu r ed t o fin d t h e sh ort est pa t h bet ween a pa r t icula r
or igin n ode a n d a pa r t icu la r dest in a t ion n ode. In t h is ca se, it will qu it on ce t h e dest in a t ion
n ode h a s been ident ified on t h e sh or t est pa t h . The a lgor ith m ca n a lso be st r u ct u r ed t o
fin d t h e s hor t es t p at h fr om ea ch or igin n od e t o ea ch des t in a t ion n od e. It does th is on e p at h
a t a t im e (e.g., it fin ds t h e sh ort est pa t h from n ode A to all ot h er n odes; th en it fin ds t h e
sh or t est pa t h fr om n ode B t o a ll ot h er n odes; a n d so fort h ).
A* Al gor i t h m
The biggest problem with t he Dijkst ra algorith m is th at it sear ches th e path to
ever y sin gle n ode. If th e pu r pose wer e t o fin d t h e sh ort est pa t h from a sin gle n ode t o all
ot h er n odes, t h en t h is wou ld pr odu ce t h e best solu t ion . H owever , wit h a m a t r ix of dis t a n ce
fr om on e s et of p oin t s t o a n ot h er s et of p oin t s (a n or igin -d es t in a t ion m a t r ix), we r ea lly
wa n t t o kn ow t h e dist a n ce bet ween a pa ir of n odes (on e origin a n d on e des t in a t ion).
Conse qu en t ly, t h e Dik jst r a a lgorit h m is ver y, ver y slow com pa r ed t o wha t we n eed . It
wou ld be a lot qu icker if we cou ld find t h e dist a n ce fr om ea ch or igin-dest ina t ion pa ir one a t
a t ime, but quit t he algorith m a s soon a s th at dista nce has been determined.
3.30
Th is is wh er e t h e A* a lgor it h m com es in . A* was d eveloped wit h in t h e a r t ificial
in t elligen ce res ea r ch a r ea a s a m ea n s for developin g a h eu ristic r u le for solvin g a pr oblem
(Nilsson, 1980). In t h is ca se, th e h eu r ist ic r u le is t h e r em a inin g dista n ce fr om a solved
n ode t o th e fina l des t in a t ion . Th a t is, a t ever y st ep in t h e Dijk st r a r out in e, a n est im a t e is
m a de of t h e r em a inin g dista n ce fr om ea ch possible ch oice t o t h e fina l dest ina t ion . The
n ode t h a t is chosen for t h e sh ort est pa t h is t h a t wh ich h a s t h e lea st t ota l com bin ed
dis t a n ce fr om t h e pr eviou sly det er m in ed n ode t o t h e fin a l goa l. Th u s, for a n y s t ep, if D i1 is
th e dista nce to a n ode, i, which h as n ot a lready been put on t he short est pat h a nd D i2 is a n
est im a t e of t h e dis t a n ce fr om t h a t n ode t o t h e fin a l d est in a t ion , t h e est im a t ed t ot a l
dista nce for t ha t n ode is:
D i = D i1 + D i2
(3.7)
Of a ll t h e n odes t h a t cou ld be ch osen , t h e n ode, i, wh ich h a s t h e sh or t est t ot a l
dis t a n ce is s elect ed n ext for t h e sh ort es t pa t h . Th er e a r e t wo ca vea t s t o th is s t a t em en t .
F irs t , th e n ode, i, ca n n ot h a ve alr ea dy been s elect ed for t h e sh or t est pa t h ; t h is is ju st r est a t ing t h e r u les by which we sea r ch for n odes wh ich h a ve not yet been pu t on t h e sh or t est
pa t h list . Secon d, th e est ima t e of t h e r em a inin g dista n ce t o t h e fina l dest ina t ion m u st be
les s t h a n or equ a l t o th e a ctu a l dis t a n ce to th e fina l dest in a t ion. In oth er wor ds , t h e
es t im a t ed dis t a n ce, D i2 , ca n n ot be an overes t ima t e (Nilsson, 1980). However , th e closer t h e
es t im a t ed dis t a n ce is t o th e r ea l dis t a n ce, th e m ore efficient will be t h e sea r ch.
H ow t h en do we det er m in e a r ea son a ble est im a t e for D i2 ? The a n sw er is a st r a igh t
line fr om t h e possible n ode t o t h e fina l dest ina t ion sin ce t h e sh or t est dist a n ce bet ween t wo
poin t s is a st r a igh t lin e (or , on a sph er e, a Gr ea t Cir cle dis t a n ce sin ce t h e sh or t est dis t a n ce
bet ween t wo poin t s is a n a r c). If we sim ply ca lcu lat e t h e st r a igh t -line fr om t h e n ode t h a t
we a r e explor in g t o th e fina l n ode, t h en t h e h eu r ist ic will work . Th e effect of t h is
sim plifyin g heu r ist ic is t o cu t down su bst a n t ially on t h e n u m ber of n odes t h a t h a ve to be
sea r ched . As wit h t h e Dijk st r a a lgor it h m , A* ca n be a pp lied t o mu lt iple or igins. It does it
on e or igin -d es t in a t ion com bin a t ion a t a t im e.
In gen er a l, if V is t h e n u m ber of n odes in t h e n et work , t h e Dijk st r a a lgor it h m
requires V2 sea r ch es wh er ea s t h e A* algor it h m r equ ir es only V sea r ch es (Sedgewick , 2002).
As can be seen, this is mu ch m ore efficient th an ha ving to search every single possible
node, which is what Dijkst ra requires.
As m en t ion ed, ch a pt er s 12 a n d 16 discuss in m or e det a il n et wor ks a n d h ow sh or t est
p at h is ca lcu la t ed in t h em .
Sa vi n g P ara m e te rs
All da t a set u p p a r a m et er s ca n be s a ved. In t h e Op t ions section , t h er e is a ‘Sa ve
pa r a m et er s’ but t on . The pa r a m et er file m u st be sa ved with a ‘pa r a m ’ exten sion . To r eloa d a sa ved pa r a m et er s file, u se t h e ‘Loa d pa r a m et er s’ bu t t on .
Au t om a ti n g P a ra m e te r S e tu p
Cr im eSt a t h a s t h e a bilit y t o be a u t om a t ica lly con figu r ed t h r ou gh Micr osoft ’s
Dyn a m ic Da t a E xch a n ge (DDE ) cod e. DDE is a n op er a t in g s ys t em la n gu a ge t h a t a llow on e
3.31
a pplica t ion t o call u p a n ot h er . Th e DDE code in Cr im eSt a t a llows t h e defin in g of t h e
pr ima r y va r iable, th e secon da r y va r iable, th e r efer en ce file, a n d t h e m ea su r em en t
pa r a m et er s. Appen dix A gives t h e specific code in st r u ct ion s. Ron Wils on ’s exa m ple below
illu st r a t es h ow Cr im eSt a t ca n be lin k ed t o a n ot h er a pplica t ion .
S ta tis tic al R ou t in e s an d Ou t pu t
St a t ist ical r out in es a r e select ed from t h e t wo grou pin gs of st a t ist ics - Sp a t ia l
Description a nd Spa tial Modeling. The user selects t he routines and inpu ts a ny
pa r a m et er s, if r equ ired . Clickin g on t h e Com pu t e but t on a ll t h e r ou t ines t h a t h a ve been
select ed. Since Crim eSt a t is m u lti-th r ea ded, differ en t r ou t ines r u n in sep a r a t e t h r ea ds
a n d m a y finish a t differ en t t imes . Wh en a r ou t ine is fin ish ed, a F inish ed m essa ge will be
dis pla yed a t t h e bot t om of th e scre en .
Virtu ally all th e rout ines out put to eith er GIS packa ges or t o sta nda rd ‘dbf’ files
wh ich ca n be r ea d by s pr ea dsh eet , d a t a ba se, a n d gr a ph ics pr ogr a m s. Wh ile ea ch ou t pu t
t a ble ca n be pr in t ed a s a n Ascii file t o a pr in t er , it is r ecom m en ded t h a t t h e u ser ou t pu t t h e
r esu lts in ‘dbf’ a n d r ea d it int o a pr ogra m t h a t h a s bet t er ou t pu t ca pa bilit ies. For exam ple,
t h e n ea r est n eigh bor a n d Ripley’s K r ou t in es out pu t colu m n s ca n be sa ved a s st a n da r d ‘dbf’
files which ca n be rea d by spr ea dsh eet pr ogra m s, su ch a s E xcel or Lot u s 1-2-3. The
spr ea dsh eet da t a , in t u r n , ca n be im por t ed in t o m ost gr a ph ics pr ogr a m s, s u ch a s
P ower P oint or F r eelan ce, for cr ea t ing bet t er qua lity gra ph ics. For ‘cu t -a n d-pas t e’
op er a t ion s , u s er ca n cop y p or t ion s of t h e ou t p u t t a bles a n d p a st e t h em in t o wor d pr oces sin g
pr ogra m s. One s h ou ld see Cr imeS t a t a s a collect ion of specialized st a t ist ica l rout ines t h a t
ca n p r od u ce ou t p u t for ot h er p r ogr a m s , r a t h er t h a n a s a fu ll-blown p a ck a ge.
A Tu t o ri a l w i t h t h e S a m p le D a t a S e t
Le t ’s r u n t h r ou gh t h e da t a set u p a n d r u n n in g of sever a l r ou t in es wit h one of th e
sa m ple dat a set s t h a t were pr ovided (Sam pleDat a .zip). Unzipping t h is file reveals t wo
files called In cid en t.dbf an d B altPop.dbf. The incident file is a collect ion of inciden t
loca t ion s t h a t h a ve been r a n dom ly s im u la t ed wit h t h e ot h er file in clu d es t h e 1990
popu la t ion of cen su s block gr oup s in t h e Ba lt im ore r egion.
1.
St a r t t h e Crim eS tat pr ogra m by eit h er double-clickin g on t h e Crim eS tat icon
on t h e desk t op (if in st a lled) or els e open in g Windows E xplorer a n d loca t in g
t h e dir ect or y wher e Crim eS tat is st or ed a n d double-clickin g on t h e file ca lled
crim estat.exe.
2.
On ce t h e pr ogra m spla sh pa ge closes, t h e u ser will be lookin g at t h e Data
S e tu p pa ge wit h t h e Pr ima r y File pa ge open .
3.
Click on ‘Select F iles’ followed by ‘Br owse’. Loca t e t h e file ca lled Incident .dbf
a n d click on ‘Open ’ followed by ‘OK’.
4.
Th e file na m e will n ow be list ed for t h e X, Y, Z(int en sit y), Weight , an d Tim e
fields. Th is va r ia ble, h owever , on ly ha s t h r ee fields - ID, Lon, La t , indica t in g
a n r ecor d n u m ber , t h e lon git u de a n d la t it u de of t h e in cid en t loca t ion .
3.32
Using Dynamic Data Exchange (DDE) to Develop Software for
Interfacing with CrimeStat
Ronald E. Wilson
Mapping and Analysis for Public Safety Program
National Institute of Justice
Washington, DC
CrimeStat has the capability to allow software developers to write programs that
interface directly with it via Dynamic Data Exchange (DDE). The purpose is to allow for the
population of CrimeStat’s input parameters directly from a separate software application,
such as a GIS. Parameters can be specified for automatic population such as the primary and
secondary files along with key field variables or reference file coordinates for the area under
which CrimeStat’s algorithms will run an analysis. In addition, measurement parameters
can be calculated to provide CrimeStat with coverage area or length of street network of an
entire region or subset.
Coordinates are often difficult to work with, especially when trying to capture them
for measurement or analysis. The Regional Crime Analysis GIS (RCAGIS) program,
developed by the U.S. Department of Justice, was designed to interface with CrimeStat to
provide the coordinates of the bounding rectangle of the area under analysis in order to
populate the grid area input boxes of the Reference File with precise coordinates. Instead of
writing them down by hand and typing them in manually, the interface between the two
applications automates this process easily and more accurately.
X: 986767.3528
Y: 672150.6849
The lower left and upper right
coordinates of the bounding rectangle
are captured in RCAGIS and sent
directly to CrimeStat via Dynamic
Data Exchange (DDE) for area surface
analysis.
X: 852007.9538
Y: 544890.1373
List of General DDE Parameters
Primary File
Secondary File
Reference Files
Measurement Parameters
5.
Iden t ify t h e a ppr opr ia t e field s u n der t h e Colu m n h ea din g by click in g on t h e
cell an d s crollin g down t o th e a pp r opr ia t e n a m e. F or t h e X var ia ble, t h e
r eleva n t n a m e is Lon. For t h e Y var ia ble, t h e r eleva n t n a m e is La t (i.e.,
t h a t ’s t h e n a m es u sed in t h is file. H owever, t h e var iables will not a lways be
sim ply n a m ed). F or t h is exa m ple, t h er e a r e n o in t en sit y, weigh t or t im e
var iables.
6.
Un der Type of Coordina te System, be sur e tha t ‘Longitu de/latitude
(spherical)’ is checked since this dat a set u se spherical coordina tes.
7.
Becau se the coordina te system ar e spherical, th e data un its ar e
a u t om a t ica lly decim a l degrees. If th ey were pr oject ed, on e wou ld h a ve to
ch oos e t h e p a r t icu la r u n it s - feet , m et er s , m iles , k ilom et er s , or n a u t ica l
m iles .
8.
Th is fin ish es t h e set u p for t h e pr im a r y file. Click on t h e Secon da r y F ile t a b.
9.
Again , click on s elect files, loca t e a n d ope n t h e Ba lt P op.dbf file.
10.
On ce loa ded, t h is file h a s s ix va r ia bles : Blockgr oup , lon, la t , a r ea , a n d
den sit y.
11.
Define t h e pa r t icu lar var iables. For t h is file, t h e X var iable is Lon a n d t h e Y
va r ia ble is La t . Also, define a Z (in t en sit y) var ia ble w it h Totpop. Note , t h a t
you cou ld a ls o a s sign t h is n a m e t o t h e Weigh t va r ia ble. Wh et h er t h e
popu la t ion va r ia ble is a ssign ed t o t h e In t en sit y or Weigh t va r ia ble does n ot
m a t t er t o t h e ca lcu la t ion . H owever , d o n ot a ss ign t h is na m e t o bot h t h e
in t en sit y a n d t h e weigh t (i.e., on ly u se on e). Th is fin is h es t h e set u p for t h e
secon da r y va r iable.
12.
Click on t h e Refer en ce File t a b. F or t h ese da t a , you will define a r ecta n gle
t h a t cover s t h e st u dy a r ea by iden t ifyin g t h e X an d Y coordin a t es for t h e
lower -left corn er of th e r ect a n gle a n d t h e u pper -r igh t corn er of th e
r ect a n gles. Th e followin g coor din a t es will wor k :
Lower -left cor n er
X
-76.91
Y
39.19
Up per -r igh t cor n er
-76.32
39.72
13.
You will a ls o n eed to t ell t h e p rogr a m h ow m a n y colu m n s you wa n t it t o
calcula t e. Th e defau lt va lu e of 100 is fin e. If you wa n t it fin er , t ype in a
la r ger n u m ber . If you wa n t it cru der , t ype in a sm a ller n u m ber . Th is
finishes th e Reference File setu p.
14.
Clock on t h e Mea s u r em en t P a r a m et er s t a b. Th er e a r e t h r ee p a r a m et er s t h a t
h a ve t o be define d.
3.34
A.
F or m a n y rout ines , an a r ea est ima t e is need ed. For t h is sa m ple set ,
684 squ a r e m iles wor k s.
B.
For t he linear near est neighbor st at istic only, th e progra m n eeds th e
t ota l len gt h of t h e st r eet n et wor k . In t h is d a t a , t h e t ota l st r eet len gt h
of t h e Tiger F iles for Ba lt im ore Cit y a n d Ba lt im ore cou n t y a r e 4868.9
m iles .
C.
F in a lly, t h e t yp e of dis t a n ce m ea su r em en t h a s t o be defin ed, d ir ect or
ind irect. F or t h is exam ple, use d irect m ea su r em en t .
15.
Th e da t a set u p is n ow fin is h ed. If you wa n t t o r e-u se t h is da t a set u p, click on
t h e Opt ion s pa ge an d ‘Sa ve par a m et er s’. Define a file n a m e a n d be su r e t o
give it a ‘pa r a m ’ ext en sion (e.g., Sa m pleDa t a .p a r a m ). Th e n ext t im e you
wa n t t o r u n t h is da t a set , all you ’ll n eed t o do is click on t h e Op ti on s pa ge,
click on ‘Loa d pa r a m et er s ’, a n d click on t h e n a m e of t h e p a r a m et er s file t h a t
you sa ved.
16.
You a r e n ow r ea d y t o r u n som e s t a t is t ics . F or t h is exa m p le, we’ll r u n on ly
four sta tistics.
17.
F irs t , click on t h e S p a t ia l D e s c r i p ti o n p a ge a n d t h en click on t h e S pa t ia l
Dis t r ibu t ion t a b.
1.
Ch eck t h e Mea n cen t er a n d st a n da r d dis t a n ce (Mcsd) box. Th en , click
on t h e ‘Sa ve r esu lt t o’ bu t t on a n d id en t ify wh ich GIS pr ogr a m you a r e
wr it in g t o (Ar cView/Ar cGis ‘sh p’; At la s*GIS ‘BNA’; or Ma pIn fo ‘MIF )
a n d give it a n a m e (e.g., Sa m pleDa t a ).
2.
Also, ch eck t h e St a n da r d d evia t iona l ellipse (Sde ) box a n d, s im ila r ly,
ch oos e a file ou t pu t wit h a n a m e. You ca n u se t h e s am e n a m e (e.g.,
Sa m ple Da t a ). Crim eS tat will a ssign a u n iqu e pr efix t o ea ch gr a ph ica l
object .
18.
Secon d, click on t h e ‘H ot Spot’ An a lysis I t a b. Then , ch eck t h e Nea r est
Neighbor H iera r ch ica l Clu st er ing (Nn h ) box. For t h is exam ple, keep t h e
defau lt search r adius, minimu m points per cluster, and n um ber of sta nda rd
devia t ion s for t h e ellipses. Also, click on ‘Sa ve ellips es t o’, select a GIS file
ou t p u t , a n d give it a n a m e. Aga in , you ca n u s e t h e s a m e n a m e a s wit h t h e
oth er sta tistics.
19.
Th ird , click on t h e S pa ti al Mo de li ng pa ge a n d t h en t h e In t er pola t ion t a b.
Ch eck t h e du el k er n el de n sit y int er pola t ion box. Th is r out in e will in t er pola t e
t h e in cid en t dis t r ibu t ion (pr im a r y file) r ela t ive t o t h e popu la t ion dis t r ibu t ion
(seconda ry file). For t his exam ple, keep the defau lt kernel para met ers (th ese
a r e exp la in ed in m or e det a il in ch a pt er 8). H owever , be su r e t o ch eck t h e
Us e int en sit y va r iable box towar ds t h e bot t om . This en su r es t h a t t h e du el
k er n el r ou t in e will u se t h e popu la t ion va r ia ble t h a t you a ssign ed wh en you
set u p t h e secon da r y file.
3.35
20.
You a r e n ow r ea d y t o r u n t h e s t a t is t ics . Click on t h e ‘Com p u t e’ bu t t on . Th e
r ou t in e will r u n u n t il a ll four r ou t in es t h a t you select ed a r e fin is h ed; t h e
t im e will d epen d on t h e speed of your com pu t er .
21.
E a ch of t h e out pu t s a r e disp la yed on a sepa r a t e r esu lt s t a b. You can pr in t
a n y of t h ese r esu lt s by click in g on ‘Sa ve t o t ext file’ (one a t a t im e).
22.
You can also display the graph ical objects creat ed by th e rout ine in your GIS.
Click on ‘Clos e’ t o clos e t h e r es u lt s win d ow. Th en , br in g u p you r GI S a n d
fin d t h e object s cr ea t ed by t h is r u n . Th er e will be a n u m ber of gr a ph ica l
object s a ss ocia t ed wit h t h e m ea n cent er r out in e (ha vin g pr efixes of Mc, Xyd,
Sdd, Gm , a n d H m ; see ch a pt er 4 for det a ils). Th er e will be t wo gr a ph ica l
object s a ssociat ed wit h t h e n ea r est n eigh bor clus t er ing r ou t ine (with pr efixes
of Nn h 1 a n d N n h 2). Fin a lly, th er e will be a gr id object cr ea t ed by th e du el
k er n el r out in e wit h a Dk pr efix. You can loa d t h ese object s in a n d d isp la y
th em along with th e data file. For t he duel kernel grid, you will need to
gr a ph t h e va r ia ble ca lled “Z” t o see t h e pa t t er n .
23.
For example, figur e 3.14 shows an ArcView ® m a p of 1996 veh icle t h efts in
Ba lt im or e Cit y a n d Ba lt im or e Cou n t y a lon g wit h t h e s t a n da r d devia t ion a l
ellips e of t h e veh icle t h efts, calcula t ed wit h Crim eS tat. Crim eS tat ou t pu t s
t h e ellip se a s a sh a pe file, wh ich is t h en br ou gh t dir ect ly in t o ArcView . A
sim ila r ou t pu t cou ld h a ve been don e for M apIn fo® . Most of t h e st a t ist ics in
Crim eS tat ha ve similar visua l represent at ions t ha t can be displayed in a GIS
p rogr a m .
24.
Wh en you a r e finis h ed wit h Crim eS tat, click on ‘Qu it ’ t o exit t h e pr ogra m .
Th is fin ish es t h e qu ick t u t oria l. Crim eS tat is very easy to set u p an d to run . In t he
n ext cha pt er , t h e focus will be on t h e st a t ist ics in t h e pr ogr a m , st a r t in g wit h t h e a n a lysis
of spat ial distr ibut ions.
3.36
Figure 3.14:
Baltimore Vehicle Thefts: 1996
Location of Incidents and Standard Deviational Ellipse
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Vehicle thefts
Standard deviational ellipse
Beltway
Arterials
County of Baltimore
City of Baltimore
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E n d n ot es for Ch a p t er 3
1.
Th e sp h er ica l ‘lat /lon ’ syst em is, of cou r se, on e t ype of pola r coor din a t e syst em . But ,
it is a pola r coor din a t e syst em with pa r t icu lar r est r ict ion s. Lat itu des a r e a n gles u p
t o 90 0 , n or t h or sou t h of t h e E qu a t or . Lon git u des ar e a n gles fr om 0 0 t o 180 0 , east
a n d west of t h e Gr een wich Mer idian . In t h e u su a l polar coor din a t e syst em , an gles
ca n va r y fr om 0 0 t o 360 0 .
2.
Some M apIn fo us ers in E u r ope h a ve fou n d difficu lty in directly rea ding MIF /MID
files fr om Crim eS tat a n d con ver t in g t h em t o th e pa r t icula r n a t ion a l coor din a t e
sys t em (e.g., Br it is h Na t ion a l Gr id , F r en ch Na t ion a l Geogr a ph ic In st it u t e). F or
exam ple, in t h e Un ited Kingdom, P et e J on es of t h e Nort h Wales P olice Depa r t m en t
h a s developed a wa y ar ou n d t h is pr oblem. H e wr ites
“To s a ve t h e r es u lt a s a M apIn fo (.mif) for m a t t h e following is r equ ired :
MIF Options
N a m e of P r oject ion : E a r t h P r oject ion
P r oject ion Nu m ber : 8
Da t u m Nu m ber 79
Befor e im por t in g t h e .m if t a ble in t o M apIn fo you n eed t o edit it . Ope n t h e .m if file
wit h a t ext ed it or . You kn ow n eed t o cha n ge t h e followin g lin e:
Coor dSys E a r t h P r oject ion 8, 79
Ch a n ge it t o
Coor dSys E a r t h P r oject ion 8, 79, 7, -2, 49, 0.9996012717, 400000, -100000
Now sa ve t h e .m if file. You ca n n ow im por t t h e file in t o M apIn fo.”
In F r a n ce, J . Ma r c Za n in et t i of t h e Un iver sit y of Or léa n s figu r ed ou t h ow t o im por t
gr a ph ica l object s in t o M apIn fo u sin g th e Fr en ch coor din a t e syst em . He wr ites
“F ir s t con ver t wit h M apIn fo you r m a p t o t h e in t er n a t ion a l E u r op ea n
La t itu de/Lon git u de E D87 pr oject ion syst em .
Secon d, pr odu ce t h e X a n d Y coor din a t es a n d expor t t h e da t a t a ble in Dba se.
Th ir d , wit h Crim eS tat II, m od ify t h e S a ve Ou t p u t pa r a m et er in or d er t o ch a n ge t h e
origin of t h e pr oject ion. By d efa u lt , t h e MI F Op t ions a r e t h e followin g:
N a m e of p r oject ion : E a r t h pr oject ion
P r oject ion n u m ber : 1 (La t it u de lon git u de)
Da t u m n u m ber :
33 (in t er n a t ion a l GRS 80 or igin 0°E , 0°N)
3.38
Th e E u r opea n n orm E D87 h a s t h e Da t u m n u m ber 108, s o you h a ve t o ch a n ge only
t h is pa r a m et er . Th e n ew opt ion s a r e t h e followin g :
N a m e of p r oject ion : E a r t h pr oject ion
P r oject ion n u m ber : 1 (La t it u de lon git u de)
Da t u m n u m ber :
108 (E u r opea n da t a E D87).
F in a lly, you ca n n ow im por t t h e MIF ou t pu t t a bles dir ect ly in t o you r M apIn fo
ma ps.”
3.
An a lt er n a t ive wa y t o t h in k in g a bou t in t en sit ies an d weigh t s is to t r ea t bot h a s t wo
differ en t weigh t s - weight #1 an d weight #2. For exam ple, weight #1 cou ld be th e
popu la t ion in a su r r oun din g zon e wh ile weigh t #2 cou ld be t h e em ploymen t in t h a t
sa m e zone. Th u s, in ciden t s (e.g., bu r gla r ies ) could be weigh t ed both by t h e
su r r oun din g popu la t ion a n d t h e su r r oun din g em ploymen t . Th e a n a logy wit h dou ble
weight s is n ot qu ite cor r ect sin ce sever a l of t h e st a t ist ics (Mor a n ’s I, Gea r y’s C a n d
Loca l Mor a n ) u se only an int en sit y, but n ot a weigh t . Th e dist inction bet ween
in t en sit ies a n d weigh t s is h is t or ica l, r ela t in g t o t h e m a n n er in wh ich t h e st a t is t ics
ha ve been derived.
4.
I n M apIn fo, p oin t da t a a r e st or ed in a t a ble. If t h e X an d Y coordin a t es a r e n ot
already part of th e table, it will be necessary to add t hese fields.
A.
Click on T able Main tenan ce T ableS tru ctu re <t a blen a m e>
B.
Click on Ad d Field
C.
Defin e t h e X field . If t h e coor din a t es ar e s ph er ica l, t h en a n a pp rop ria t e
n a m e m igh t be Lon git u de or Lon . If t h e coor din a t es a r e pr oject ed, t h en X or
XCoord m ight be appr opriat e nam es.
D.
F ill in t h e pa r a m et er s of t h e n ew n a m e.
E.
i.
Th e t ype sh ould be d ecim a l.
ii.
Th e wid t h sh ould be s u fficien t t o ha n dle t h e longes t st r in g. With
sp h er ical coor din a t es , 12 would be s u fficient .
iii.
Be s u r e t o define a n a pp r opr ia t e n u m ber of decima ls p la ces. Wit h
lon git u de, t h er e sh ould be a t lea st 4 decima ls p la ces wit h 6 pr ovidin g
m or e a ccu r a cy. In a pr oject ed coor din a t e sys t em , t h e n u m ber of
decim a l places wou ld be us u a lly 0 or 1.
Click OK when finished.
3.39
F.
If a Ma p Ba sic Win dow is n ot a lr ea dy op en , click on Op tion s
S h ow M a pB a sicW in d ow .
G.
Ma ke t h e Ma p Ba sic Win dow active by clickin g on its t op border .
H.
Inside th e window, type
u pda t e <t a blen a m e> set <Xva r ia blen a m e> = cen t r oidX(obj)
u pda t e <t a blen a m e> set <Ya r ia blen a m e> = cen t r oidY(obj)
Aft er ea ch lin e, h it <E n t er >. Th e a p pr op r ia t e n a m es wou ld be ch os en . F or
exam ple, if t h e poin t t a ble was n a m ed r obber ies a n d t h e coor din a t es wer e
sph er ica l, t h en t h e st a t em en t s would be
u pda t e r obber ies set lon =cen t r oidX(obj)
<E n t er >
u pda t e r obber ies set la t =cen t r oidY(obj)
<E n t er >
5.
I.
Th e X an d Y field n a m es sh ou ld be popu la t ed wit h t h e cor r ect va lu es for ea ch
poin t . To view t h e t a ble, click on W in d ow N ew B row serW in d ow <filen a m e>.
J.
Sa ve t h e t a ble a s a ‘dbf’ wit h ‘Sa ve Copy As <n a m e>’. Be s u r e t o spe cify t h a t
t h e file is t o be sa ved in ‘dbf’ for m a t .
Th e followin g s t eps wou ld be followed t o a dd X an d Y coordin a t es t o a ‘dbf’ file of
p oin t loca t ion s in ArcView .
A.
Ma k e t h e poin t t a ble a ctive by click in g on it .
B.
Open t h e t h em e t a ble by clickin g on t h e Open T h em e T able bu t t on .
C.
Click on T a ble S t art Ed it in g.
D.
Click on E d it A d d Field .
E.
In t h e F ield Defin it ion win dow, d efin e a n a m e for t h e X field (e.g., X,
Lon git u de, Lon ).
F.
Define the par am eters for t he X field.
a.
Make sur e tha t t he type is N um ber
b.
Be s u r e t h a t t h e wid t h is la r ge en ough t o ha n dle t h e la r gest va lu e.
F or s ph er ical coord in a t es (i.e., lon git u de, lat it u de), 12 colu m n s s h ould
be su fficien t . F or a pr oject ed coor din a t e sys t em , t h e n u m ber of
3.40
colu m n s sh ou ld be t wo la r ger t h a n t h e la r ges t va lu e.
c.
Be su r e t h a t t h er e a r e su fficien t decim a l p la ces. Wit h a sph er ica l
coor d in a t e s ys t em , t h e m in im u m s h ou ld be 4 d ecim a l p la ces wit h 6
bein g m or e a ccu r a t e. Wit h a pr oject ed coor din a t e sys t em , 0 or 1
decim a l places wou ld be su fficient .
G.
Click OK when finished.
H.
Repeat st eps E t h r ou gh G for t h e Y field.
I.
F or t h e X a n d Y var ia ble in t u r n , click on t h e field n a m e t o high light it .
J.
Click on t h e Calculate bu t t on .
K.
Dou ble-click on t h e [S h a pe] field n a m e.
L.
In t h e dia log box, t ype .GetX for t h e X field a n d .GetY for t h e Y field after
[S h a pe], t h a t is
[Sh a pe].Get X
[Sh a pe].Get Y
M.
Click OK wh en finish ed. The field will be popu lat ed wit h t h e X a n d Y valu es
for t h e poin t s in t h e sa m e u n it s a s t h e da t a (e.g., la t /lon , feet or m et er s for
UTM or St a t e P la n e Coor din a t es).
6.
Note t h a t in a n ASCII file, a t a b look s lik e it is s epa r a t ed by spa ces. H owever , t h e
un derlying ASCII code is different an d Crim eS tat will t r ea t t h ese ch a r a ct er is t ics
d iffer en t ly. Th a t is , if t h e s ep a r a t or is a t a b bu t t h e u s er in d ica t es t h a t it is a sp a ce,
Crim eS tat will not pr operly read t he dat a.
7.
H int : If you t ype th e firs t lett er of t h e n a m e (e.g., ‘L’ for lon git u de), t h en t h e
pr ogra m will find t h e firs t n a m e t h a t begin s wit h t h a t lett er ). Typin g th e lett er
a ga in will fin d t h e secon d n a m e, a n d so for t h .
8.
Sin ce th e wor ld is a pp r oxim a t ely r oun d, a ll line s a r e a ctu a lly cir cles t h a t even t u a lly
com e back on t o t h em selves. These a r e ca lled Great Ci rcles beca u se t h ey divide t h e
E a r t h in t o tw o equ a l h a lves (Gr een h ood, 1964). On a sp h er e, su ch a s t h e E a r t h , t h e
sh ort est dis t a n ce bet ween a n y t wo point s is a Gr ea t Cir cle. Th er e a r e a n in finit e
n u m ber of Gr ea t Cir cles, bu t coord in a t es a r e only r efer en ced t o tw o Gr ea t Cir cles.
Nort h-sout h lines ar e called M erid ia n s (an d ar e half Great Circles) an d east-west
lines ar e called Parallels. Th e ba sic r efer en ce pa r a llel is t h e E qu a t or, wh ich is a
Great Circle, an d th e two reference meridian s ar e the Greenwich Meridian an d th e
In t er n a t ion a l Da t e Lin e (wh ich is a ct u a lly t h e sa m e Gr ea t Cir cle on t wo sid es of th e
ea r t h ).
3.41
Th er e a r e t wo coordin a t es - L on git ud e an d L a tit ud e. For lon git u de, all ea st -west
dir ect ion s a r e defin ed a s a n a n gle fr om 0 0 t o 180 0 wit h 0 0 bein g a t t h e Gr een wich
Mer idian a n d 180 0 be in g t h e In t er n a t ion a l Da t e Lin e. All dir ect ion s ea st of th e
Gr een wich M er idia n h a ve a posit ive lon git u de wh er ea s a ll dir ection s west of t h is
mer idian ha ve a negative longitu de. For example, in t he Un ited Stat es,
Was h ingt on , DC, h a s a lon git u de of a ppr oxim a t ely -77.03 degr ees beca u se it is west
of t h e Gr een wich Mer id ia n wh er ea s New Delh i, In dia h a s a lon git u de of
appr oximat ely +77.20 degrees becau se it is east of th e Greenwich Meridian . These
loca t ion s a r e a p pr oxim a t e beca u s e cit ies cover a r ea s a n d on ly a s in gle p oin t wit h in
t h e cit y h a s been cla ssified (t h e cen t er or cen troid of th e cit y).
F or la t it u de, a ll n or t h -sou t h dir ect ion s a r e defin ed in t er m s of a n a n gle fr om t h e
equ a t or , wh ich h a s a la t it u de of 0 0 . Th e m a xim u m is t h e N or t h or S ou t h P oles
wh ich h a ve la t itu des of +90 0 a n d -900 r espect ively. Locat ion s t h a t a r e n or t h of th e
E qu a t or h a ve a posit ive la t it u de wh ile loca t ions t h a t a r e sout h h a ve a n ega t ive
la t it u de. Th u s, in t h e U n it ed St a t es, Los An geles h a s a la t it u de of a pp r oxim a t ely
+34.06 degr ees wh er ea s Bu en os Air es in Argen t in a h a s a n a ppr oxim a t e la t it u de of 34.60 degrees.
To mea su r e va r ia t ions bet ween degr ees , su bdivision of t h e a n gles a r e n ecessa r y.
Th e t r a dit ion a l us e of sph er ica l coor din a t es divides a n gles in t o m u ltiples of 60 an d
defines a n gles in r ela t ion t o th e r efer en ce Gr ea t Cir cles. Th u s, ea ch d egr ee is
su bdivided in t o 60 min u t es a n d ea ch m inu t e, in t u r n , ca n be divided in t o 60
secon ds. F or exam ple, New Yor k Cit y ha s a n a ppr oxim a t e lon git u de of 73 degrees
58 m inu t e 22 secon ds West a n d a n a ppr oxim a t e lat itu de of 40 degrees 52 min u t es
46 secon ds N or t h . However , wit h t h e a dvent of com pu t er s, m ost coor din a t es a r e
n ow conver t ed in t o decima l degr ees . Th u s, N ew Yor k Cit y ha s a n a pp r oxim a t e
lon git u de of -77.973 degr ees a n d a n a ppr oxim a t e lat itu de of +40.880 degrees . The
con ver sion is s im ply
Decima l degrees = Degr ees + Minu t es/60 + Secon ds/3600
9.
Beca u se t h e Ea r t h is cu r ved, an y two dimen sion a l rep r esen t a t ion pr odu ces
dis t ort ion . Th e sph er ical la t it u de/lon git u de sys t em (ca lled ‘la t /lon ’ for sh ort ) is a
u n iver sa l coor din a t e syst em . It is u n iver sa l becau se it u t ilizes t h e sph er ical n a t u r e
of t h e E a r t h a n d ea ch loca t ion h a s a u n iqu e s et of coor d in a t es . Mos t ot h er
coor d in a t e s ys t em s a r e p r oject ed beca u s e t h ey a r e p or t r a yed on a t wo-d im en s ion a l
flat pla n e. St r ictly s pea k in g, sp h er ical coor din a t es - lon git u des a n d la t it u des, a r e
n ot X an d Y coor din a t es sin ce th e wor ld is r oun d. H owever , by con ven t ion, t h ey a r e
oft en r efer r ed t o a s X a n d Y coor din a t es, pa r t icu lar ly if a sm a ll section of t h e Ea r t h
is projected on a flat plane (a compu ter screen or a print ed map).
P r oject ion s differ in h ow t h ey ‘fla t t en ’ or project a s ph er e on t o a t wo d im en s ion a l
pla n e. Typica lly, th er e a r e fou r pr oper t ies of m a ps wh ich ca n n ot a ll be m a int a ined
in a n y t wo dim en sion a l r epr esen t a t ion :
3.42
Sha pe - ma inta ining corr ect sh ape of a land body
Ar ea - if t h e spa ce r epr esen t ed on a m a p cover s t h e sa m e a r ea t h r ou gh ou t
th e map, it is called an equal-ar ea ma p. The proport iona lity is ma inta ined.
Dis t a n ce - t h e dist a n ce bet ween t wo point s is in con st a n t sca le (i.e., t h e scale
does not cha n ge)
Dir ect ion - t h e d ir ect ion fr om a p oin t t owa r d s a n ot h er p oin t is t r u e.
An y p roject ion cr ea t es on e or m or e t yp es of d is t or t ion a n d p ar t icu la r pr oject ion s a r e
ch osen in order t o h a ve accu r a cy in on e or t wo of t h ese pr oper t ies. Differ en t
pr oject ion s port r a y differ en t t ypes of infor m a t ion . Most pr oject ion s a ssu m e t h a t t h e
E a r t h is a s ph er e, a sit u a t ion t h a t is not com plet ely t r u e. The E a r t h 's diam et er a t
t h e equ a t or is sligh t ly gr ea t er t h a n t h e dist a n ce bet ween t h e poles (Sn yder , 1987).
Th e cir cu m fer en ce of t h e E a r t h bet ween t h e P oles is a bou t 24,860 m iles on a
m er idian ; t h e circum fer en ce a t t h e Equ a t or is about 75 miles m or e.
Th er e is an infin ite n u m ber of pr oject ion s. H owever, on ly a cou ple dozen h a ve been
u sed in pr a ct ice (Gr een h ood, 1964; Sn yder , 1987; Sn yder a n d Voxla n d, 1989). They
a r e ba se d on pr oject ions of t h e sph er e ont o a cylin der , con e or flat pla n e. In t h e
Un it ed St a t es , sever a l com m on coor din a t e syst em s a r e u se d. Th eor et ically, t h e
pr ojection a n d t h e coord in a t e syst em can be dist in gu ish ed (i.e., a pa r t icula r
pr oject ion could u se one of sever a l coord in a t e syst em s, e.g. m et er s or feet ).
H owever , in pr a ctice, p a r t icula r pr oject ions u se com m on coor din a t es . Am ong t h e
m ost com m on in u se in t h e Un ited St a t es a r e:
A.
Mer ca t or - The M ercator is a n ea r ly pr oject ion , a n d on e of t h e m ost fa m ou s,
wh ich is u sed for world m a ps . Th e pr ojection is d one on a cylin der , wh ich is
ver t ically cent er ed on a m er idia n , bu t t ouchin g a pa r a llel. Th e globe is
pr oject ed on t h e cylind er a s if light is em a n a t ing fr om t h e cen t er of t h e globe
wh ile t h e E a r t h t u r n s. Th e m er idia n s cu t t h e equ a t or a t equ a l in t er va ls.
H owever , t h ey m a in t a in pa r a llel lin es , u n lik e t h e globe wh er e t h ey con ver ge
a t t h e poles. Th e lon git u des a r e st r et ch ed wit h in cr ea sin g la t it u de (in bot h
n or t h a n d sout h dir ect ion s) up u n t il t h e 80 t h par allel. The effect is tha t sh ape
is a pp r oxim a t ely cor r ect a n d d ir ection is t r u e. Dist a n ce, however , is
distort ed. For example, on a Mercator m ap, Greenlan d appear s as big as t he
Un it ed St a t es, wh ich it is n ot . Dis t a n ces ca n be m ea su r ed in a n y u n it s for a
Mercat or t hough usu ally th ey ar e measu red in miles or k ilomet ers.
B.
Tr a n sver se Mer ca t or - If t h e Mer ca t or is r ot a t ed 90 0 so t h a t t h e cylin der is
center ed on a par allel, ra th er th an a m eridian , it is called a T ran sverse
M ercator. Th e cylinder is p r oject ed a s bein g h orizon t a l bu t is t ouch in g a
m er idian . The Tr a n sver se Mer ca t or is divided in t o n a r r ow n or t h -sout h zon es
in ord er t o red u ce dist ort ion . Th e m er idia n t h a t t h e cylin der is t ouchin g is
ca lled th e Central Meridian of t h e zone. Dist a n ces a r e a ccu r a t e wit h in a
3.43
limit ed dist a n ce fr om t h e cen t r a l mer idian . Thu s, t h e bou n da r ies of zon es
a r e select ed in ord er t o ma in t a in r ea son a ble d ist a n ce accu r a cy. In t h e U .S.,
m a n y st a t es u se t h e Tr a n sver se Mer cat or a s t h e ba sis for t h eir st a t e pla n e
coor d in a t e s ys t em in clu d in g Ar izon a , H a w a ii, I llin ois , a n d N ew Yor k .
C.
Un iver sa l Tr a n sver se Mer ca t or (UTM) - In 1936, t h e In t er n a t ion a l U n ion of
Geodesy a n d Geophysics est a blished a st a n da r d u se of t h e Tra n sver se
Mer ca t or , ca lled th e Un iversal T ran sverse M ercator (or UTM). In or der t o
r edu ce dist ort ion , t h e globe is divid ed in t o 60 zon es, 6 degr ees of lon git u de
wide. For lat itu de, each zon e is divided fur t h er int o st r ips of 8 degrees
lat itu de, fr om 84 o N t o 80 o S. Wit h in ea ch ba n d, t h er e is a cent r a l m er idia n
wh ich , in t h eor y, wou ld be geodet ica lly t r u e. Bu t , t o r edu ce dis t or t ion a cr oss
t h e a r ea covered by each zon e, sca le alon g th e cen t r a l mer idian is r edu ced t o
0.9996. This p r odu ces t wo pa r a llel lin es of zero distort ion a ppr oxim a t ely 180
k m a wa y fr om t h e cent r a l m er idia n . Scale a t t h e boun da r y of th e zone is
a pp r oxim a t ely 1.0003 a t U.S. la t it u des. Coor din a t es a r e expr essed in
m et er s. By con ven t ion , t h e or igin is t h e lower left cor n er of t h e zon e. F r om
t h e origin , E as tin gs a r e disp la cemen t s ea st wa r d a n d fr om t h e origin ,
N orth in gs a r e displa cem en t s n or t h wa r d. The cent r a l mer idian is given a n
E a st in g of 500,000 m et er s. Th e Nor t h in g for t h e equ a t or va r ies depen ds on
t h e h em is ph er e. F or t h e n or t h er n h em is ph er e, t h e equ a t or h a s a Nor t h in g of
0 m et er s. F or t h e sou t h er n h em is ph er e, t h e E qu a t or h a s a Nor t h in g of
10,000,000 m et er s. The U TM syst em wa s a dopted by th e U.S. Ar m y in 1947
a n d h a s been a dopt ed by m a n y n a t iona l a n d in t er n a t iona l m a pp in g a gen cies.
Dista n ces a r e alwa ys mea su r ed in m eter s in U TM.
D.
Obliqu e Mer ca t or - Th er e a r e a n u m ber of cylin dr ica l p r oject ion s wh ich a r e
n eit h er cent er ed on a m er idia n (as in t h e Mer cat or) or on a pa r a llel (as in t h e
Tran sverse Mercator). These ar e called Oblique Mercator p r oject ion s
beca u se t h e cylin der is cen t er ed on a lin e wh ich is obliqu e t o pa r a llels or
m er idian s. In t h e U.S., th e H otin e Obliqu e M ercator is u sed for Ala s ka .
E.
La m ber t Conform a l Conic - The L am bert Con form al Con ic is a pr ojection
m a de on a con e, r a t h er t h a n a cylin der . La m ber t 's con for m a l p r oject ion
cen t er s t h e con e over a cen t r a l loca t ion (u su a lly t h e Nor t h P ole) a n d t h e con e
'cut s' th rough th e globe at par allels chosen to be sta nda rds. Within th ose
sta nda rds, shapes ar e tru e and m eridian s ar e stra ight . Outside those
st a n da r ds, p a r a llels a r e spa ced a t in cr ea sin g in t er va ls t h e fu r t h er n or t h or
sou t h t h ey go t o r edu ce dis t a n ce dis t or t ion . Th e pr oject ion is t h e ba sis of
m a n y s t a t e pla n e coor din a t e sys t em s, in clu din g Ca lifor n ia , Con n ect icu t ,
Ma r yla n d, Michiga n , a n d Vir gin ia .
F.
Alber’s E qu a l-Ar ea - An ot h er pr oject ion on a con e is th e Albers E qu al-Area
except t h a t pa r a llels a r e spa ced a t decr ea sin g in t er va ls t h e fu r t h er n or t h or
sout h t h ey ar e pla ced from t h e st a n da r d pa r a llels. The m a p is a n equa l-a r ea
pr oject ion a n d sca le is t r u e in t h e ea st -west dir ect ion .
3.44
G.
St a t e Pla n e Coor din a t es - E ver y st a t e in t h e U n it ed St a t es h a s a n officia l
coor d in a t e s ys t em , ca lled t h e S tate Pl an e Coord in ate S ystem . E a ch st a t e is
divid ed in t o on e or m or e zon es a n d a pa r t icu la r pr oject ion is u sed for ea ch
zon e. Wit h t h e except ion of Ala sk a , wh ich u ses t h e H ot in e Obliqu e Mer ca t or
for on e of it s eigh t zon es , a ll s t a t e p la n e coor d in a t e s ys t em s u se eit h er t h e
Tr a n sver se Mer cat or or t h e La m ber t Confor m a l Con ic. Ea ch st a t e's sh a pe
det er m in es wh ich p r oject ion is chose n t o repr es en t t h a t st a t e. Typ ically,
st a t es ext en din g in a n or t h -sou t h dir ect ion u se Tr a n sver se Mer ca t or
pr oject ion s wh ile st a t es exten din g in a n ea st -west dir ect ion u se La m ber t
Conform a l Conic pr ojection s. Bu t , t h er e a r e except ion s, s u ch a s Ca liforn ia
wh ich u ses t h e Lam ber t . Pr oject ion s a r e ch osen t o m inim ize dist or t ion over
t h e st a t e. Sever a l s t a t es u se bot h pr oject ion s (F lor id a , N ew York ) a n d
Alas ka u ses a ll t h r ee. Dist a n ces a r e m ea su r ed in feet.
See Sn yder (1987) a n d Sn yder a n d Voxla n d (1989) for m or e det a ils on t h ese a n d
ot h er p r oject ion s in clu d in g t h e m a t h em a t ica l t r a n s for m a t ion s u sed in t h e va r iou s
pr oject ion s. Ot h er good r efer en ces a r e Ma lin g (1973), Robin son , S a le, Mor r is on a n d
Mu eh r cke (1984), a n d t h e Com m it t ee on Ma p P r oject ion s (1986).
10.
With a pr ojected coordina te system, indirect dista nces can be measu red by
per pen dicu la r h or izon t a l or ver t ica l lin es on a fla t pla n e beca u se a ll dir ect pa t h s
bet ween t wo poin t s h a ve equa l dist a n ces. For exa m ple in figur e 3.13, wh et h er t h e
dist a n ce is m ea su r ed from poin t A n or t h t o t h e Y-coor din a t e of poin t B an d t h en
ea st wa r d u n t il poin t B is r ea ch ed or , a lt er n a t ively, fr om poin t A ea st wa r d t o t h e Xcoor dina t e of point B, t h en n or t h wa r d u n t il point B is r eached, t h e dista n ces will be
t h e sa m e. One of t h e a dva n t a ges of a Ma n h a t t a n geom et r y is t h a t t r a vel dist a n ces
t h a t a r e dir ect (i.e., th a t a r e poin t ed t owar ds t h e fina l dir ection ) ar e equ a l.
With a sph er ica l coor din a t e syst em , however , Man h a t t a n dist a n ces a r e n ot equa l
wit h differ en t r out es. Becau se t h e dist a n ce bet ween t wo point s a t t h e sa m e la t it u de
decrea ses wit h increa sin g la t itu de (nor t h or sout h ) fr om t h e equa t or , th e pa t h
bet ween t wo poin t s will d iffer on t h e r ou t e wit h Ma n h a t t a n r u les. In figu r e 3.13, for
exa m ple, it is a lon ger dis t a n ce t o t r a vel fr om poin t A ea st wa r d t o t h e lon git u de of
poin t B, befor e t r a velin g n or t h t o poin t B t h a n t o t r a vel n or t h wa r d fr om poin t A t o
t h e sa m e la t it u de a s p oint B befor e t r a velin g ea st wa r d t o point B. Conse qu en t ly,
Crim eS tat m odifies t h e Ma n h a t t a n r u les for a sph er ica l coor din a t e syst em by
ca lcu lat ing bot h r ou t es bet ween t wo poin t s a n d a vera gin g th em . This is ca lled a
M od ified S ph erical M an h attan Distan ce.
3.45