Chapter 15
Mode Split
In t h is ch a pt er , t h e t h ir d m odelin g st ep in t h e crim e t r a vel dem a n d m odel is
dis cus se d, m ode s plit . M od e split in volves sepa r a t in g (s plit t in g) t h e pr edict ed t r ip s fr om
ea ch or igin zon e t o ea ch dest ina t ion zon e int o dist inct t r a vel m odes (e.g., walk ing, bicycle,
dr ivin g, t r a in , bu s).
Th is m odel h a s bot h a dva n t a ges a n d dis a dva n t a ges for cr im e a n a lysis . At a
t h eor et ical level, it is t h e m ost developed of t h e fou r st a ges sin ce th er e h a s been ext en sive
resear ch on t ra vel mode choice. For crime an alysis, on t he oth er ha nd, it r epresents t he
‘wea k est lin k ’ in t h e a n a lysis sin ce t h er e is ver y lit t le a va ila ble in for m a t ion on t r a vel m ode
by offen der s. Since res ea r ch er s can n ot int er view t h e gener a l pu blic in order t o docu m en t
cr imes com m itt ed by res ponden t s n or , in m ost ca ses, even in t er view offen der s a ft er t h ey
h a ve been cau ght , th er e is very lit t le in for m a t ion on t r a vel m ode by offen der s t h a t h a s been
collected. 1 Con sequ en t ly, we h a ve t o depen d on t h e exist in g t h eor y of t r a vel m ode ch oice
a n d a da pt it in t u it ively t o cr im e da t a . Th e a ppr oa ch is solely t h eor et ica l a n d depen ds on
t h e va lidit y of th e exist in g t h eory a n d on t h e in t u it iven ess of guesses. H opefully, in t h e
fu t u r e, th er e will be m or e infor m a t ion collect ed t h a t wou ld a llow t h e m odel t o be ca libra t ed
a gain st some r ea l da t a . But , for t h e t ime bein g, we a r e lim ited in wh a t ca n be don e.
Th e o r e t i c a l B a c k g ro u n d
Th e t h eor et ical ba ckgr oun d beh in d t h e m ode s plit m odu le is pr es en t ed firs t . Next ,
t h e specific pr ocedu r es a r e dis cu ssed wit h t h e m odel bein g illu st r a t ed wit h da t a fr om
Ba lt im ore Coun t y.
Utility of Trave l and Mode Choice
Th e key a im of m ode choice a n a lysis is t o dist ingu ish t h e t r a vel m ode t h a t t r a veler s
(or , in t h e ca se of cr im e, offen der s) u se in t r a velin g bet ween a n or igin loca t ion a n d a
dest ina t ion loca t ion . In t h e t r a vel dem a n d m odel, th e ch oice is for t r a vel bet ween a
par ticular origin zone an d a pa rt icular destinat ion zone. Thus, the t rips th at ar e
dis t r ibu t ed from ea ch origin zon e t o each dest in a t ion zon e in t h e t r ip d ist r ibu t ion m odu le
ar e fur th er split int o distinct t ra vel modes.
Wit h few excep t ion s, t h e a ssu m pt ion be h in d t h e m ode split decis ion is for a t wo-wa y
t r ip. Th a t is, if an offend er decides on dr iving t o a pa r t icula r crim e loca t ion , we n orm a lly
a ssu m e t h a t t h is per son will a ls o dr ive ba ck t o t h e or igin loca t ion . Sim ila r ly, if t h e
offen d er t a k es a bu s t o a cr im e loca t ion , t h en t h a t per s on will a ls o t a k e t h e bu s ba ck t o t h e
origin locat ion . Th er e a r e, of cou r se, except ion s. A ca r t h ief ma y t a k e a bu s t o a crim e
loca t ion , t h en s t ea l a ca r a n d d r ive ba ck . Bu t , in gen er a l, wit h ou t in for m a t ion t o t h e
con t r a r y, it is a ss u m ed t h a t t h e t r a vel m od e is for a r ou n d t r ip jou r n ey.
15.1
Un der lying t h e ch oice of a t r a vel m ode is a ssu m ed t o be a u tility fun ction . This is a
fu n ct ion t h a t des cr ibes t h e ben efit s a n d cos t s of t r a vel by t h a t m od e (Or t u za r a n d
Willu m sen , 2001). Th is ca n be wr it t en wit h a con cept u a l equ a t ion :
Ut ility = F(benefits, costs)
(15.1)
wh er e ‘f’ is s ome fun ction of t h e ben efits a n d t h e cost s. Th e ben efits h a ve t o do wit h t h e
a dva n t a ges in t r a velin g t o a pa r t icu la r dest in a t ion fr om a pa r t icu la r or igin wh ile t h e cost s
h a ve t o do wit h t h e r ea l a n d p er ceived cost s of u sin g a pa r t icula r m ode. Sin ce th e ben efits
of t r a velin g a p ar t icu la r d es t in a t ion fr om a p a r t icu la r or igin a r e p r oba bly equ a l, t h e
differ en ces in u t ilit y between t r a vel m odes es sen t ially repr esen t differ en ces in cost s. Thu s,
equ a t ion 15.1 br ea k s down t o:
Ut ility cost = F(costs)
(15.2)
If differ en t t r a vel m odes (e.g., dr ivin g, bik in g, wa lk in g) ar e ea ch r epr es en t ed by a
sepa r a t e u t ilit y cost fu n ct ion , th en t h ey ca n be com pa r ed:
Ut ilit y cos t 1 = F 1 (cost 1 + cos t 2 + cos t 3 + .....+cost k )
(15.3a
Ut ilit y cos t 2 = F 2 (cost 1 + cos t 2 + cos t 3 + .....+cost k )
(15.3b)
Ut ilit y cos t 3 = F 3 (cost 1 + cos t 2 + cos t 3 + .....+cost k )
(15.3c)
.
.
.
Ut ilit y cos t L = F L (cost 1 + cos t 2 + cos t 3 + .....+cost k )
(15.3d)
where Utility cost 1 th rough Ut ility cost L represent s L distinct t ra vel modes, cost 1 t h r ou gh
cost k r ep res en t k cost component s an d ar e var iables, an d F 1 t h r ou gh F L r ep res en t L
differ en t u t ilit y fu n ct ion s (one for ea ch m ode).
Th er e a r e sever a l obser va t ion s t h a t can be m a de a bout t h is r epr esen t a t ion . Fir st ,
ea ch of t h e cost com ponen t s can be ap plied t o a ll m odes. H owever, t h e cost com ponen t s a r e
va r ia bles in t h a t t h e va lu es m a y or m a y n ot be t h e sa m e. F or exa m ple, if cost 1 is t h e
oper a t ing cost of t r a veling fr om a n or igin t o a dest ina t ion , th e cost for a dr iver is, of cou r se,
a lot h igh er t h a n for a bus pa ssen ger s ince th e lat t er per son sh a r es t h a t cost with ot h er
pa ssen ger s. Sim ila r ly, if cost 2 is t h e t r a vel t im e fr om a pa r t icu la r or igin zon e t o a
pa r t icu lar dest ina t ion zon e, th en t r a vel by priva t e a u t om obile m a y be a lot quicker t h a n by
pu blic bu s. As m en t ion ed in t h e la st ch a pt er , t im e differ en ces ca n be con ver t ed in t o cost s
by a pplyin g s om e t yp e of h ou r ly wa ge/pr ice t o t h e t im e. To t a k e on e m or e exa m ple, for
dr ivin g m ode, t h er e cou ld be a cost in pa r k in g (e.g., in a cen t r a l bu sin ess dis t r ict ); for
t r a n sit u se, on t h e ot h er h a n d, t h is cost compon en t is zer o. In ot h er wor ds, ea ch of th e
t r a vel m odes h a s a differ en t cost st r u ct u r e. Th e sa m e cost s ca n be en u m er a t ed, bu t som e
of t h em will n ot a pp ly (i.e., th ey h a ve a va lu e of 0).
15.2
Secon d, t h e cost s ca n be p er ceived cost s a s w ell a s r ea l cost s. F or exa m ple , a
n u m ber of st u dies h a ve dem on st r a t ed t h a t pr iva t e a u t om obile is seen a s fa r m or e
con ven ien t t o m os t peop le t h a n a bu s or t r a in (e.g., s ee S ch n ell, S m it h , Dim s da le, a n d
Th r a sh er , 1973; Roem er a n d S in h a , 1974; WASH COG , 1974; Ca r n egie-Mellon U n iver sit y,
1975; J oh n son, 1978; Levin e a n d Wa ch s, 1986b). ‘Con venien ce’ is defin ed in t er m s of ea se
of a ccess a n d effor t in volved in t r a vel (e.g., h ow lon g it t a k es t o wa lk t o a bu s st op fr om a n
or igin loca t ion , t h e n u m ber of t r a n s fer s t h a t ha ve t o m a d e t o r ea ch a fin a l d es t in a t ion , a n d
t h e t im e it t a k es t o walk from t h e la st bu s s t op t o th e fina l des t in a t ion ). While it is
somet imes difficu lt t o sepa r a t e t h e effect s of con venien ce fr om t r a vel its elf, it is clear t h a t
m ost people per ceive t h is a s dim en sion in t r a vel ch oice. In t u r n , con venien ce ca n be
con ver t ed in t o a m on et a r y va lu e in or der t o a llow it t o be ca lcu la t ed in a cost equ a t ion , for
exa m ple h ow m u ch people a r e willin g t o pa y in t im e sa vin gs t o yield a n equ iva len t a m ou n t
of con ven ien ce (e.g., as k in g how ma n y m ore m in u t es in t r a vel t im e by bu s a n in dividu a l
wou ld be willin g t o absor b in ord er t o give up h a vin g t o dr ive).
Th ir d, t h ese cost s ca n be con sid er ed a t a n a ggr ega t e a s well a s in divid u a l level. At
a n a ggr egat e level, t h ey repr esen t a vera ge or m edia n cost s (e.g., th e a vera ge tim e it t a kes
t o t r a vel bet ween zon e A an d zon e B by pr iva t e a u t om obile, bu s, t r a in , wa lk in g, or bik in g;
t h e a ver a ge dolla r va lu e a ssign ed by a sa m ple of su r vey r espon den t s t o t h e con ven ien ce
t h ey a ss ocia t e in t r a velin g by car a s opp osed t o bus).
On t h e oth er h a n d, a t a n in divid u a l level, t h e cost s a r e specific to t h e in divid u a l.
F or exa m ple, t r a vel t im e differ en ces bet ween car a n d bu s ca n be con ver t ed in t o an h our ly
wa ge usin g th e individu a l’s in com e; someone m a kin g $100,000 a yea r is going t o pr ice t h a t
t im e sa vin gs d iffer en t ly t h a n som eone m a k in g only $2 5,000 a yea r .
F ou r t h , a m or e con t r overs ial poin t , th e specific m a t h em a t ica l fu n ct ion t h a t t ies t h e
cos t s t oget h er in t o a p ar t icu la r u t ilit y fu n ct ion m a y a ls o d iffer . Typ ica lly, m os t t r a vel
dem a n d m odels h a ve ass u m ed t h a t a sim ilar m a t h em a t ica l fu n ct ion is us ed for a ll t r a vel
m odes; t h is is t h e n ega t ive exp on en t ia l fu n ct ion descr ibed below (Dom en cich a n d
McFa dden , 1975; Ort u zar an d Willum sen , 2001). However, th ere is n o rea son why
differ en t fu n ct ion s ca n n ot be u sed. Th u s, t h e equ a t ion s a bove id en t ify differ en t fu n ct ion s
for t he modes, F 1 t h r ou gh F L . On e ca n t h in k of th is in t er m s of weights. E a ch of t h e
differ en t m a t h em a t ical fu n ction weigh t t h e cost com pon en t s d iffer en t ly.
It is a n em pir ica l qu est ion wh et h er in divid u a ls a pply differ en t fu n ct ion s t o
evalu a t ing t h e differ en t m odes. F or exam ple, most p eople wou ld n ot dr ive ju st t o t r a vel
on e block (un less it wa s pour ing r a in or u n less a h ea vy object h a d t o be deliver ed or picked
u p). Even t h ough it is con ven ien t t o get in t o a veh icle a n d d r ive t h e one block , m ost people
se e t h e effor t in volved (an d, m ost likely, t h e fuel a n d oil cost s) a s n ot bein g wort h it .
In ot h er wor ds, it a ppea r s t h a t a differ en t u t ilit y fu n ct ion is being ap plied t o
wa lk in g a s opp osed t o dr ivin g (i.e., wa lk for dis t a n ces u p t o a cer t a in dis t a n ce; dr ive
t h er ea fte r ). A st r ict u t ilit y t h eor ist m igh t dis a gr ee w it h t h is in t er pr et a t ion s a yin g t h a t t h e
per m in u t e cost of wa lkin g t h e one block a n d ba ck wa s les s t h a n m onet a r ized p er m in u t e
cost of oper a t in g t h e veh icle (wh ich m a y in clu de open in g a ga r a ge door , get t in g in t o t h e
15.3
veh icle, st a r t in g t h e veh icle, dr ivin g out of t h e pa r k in g sp ot, closin g t h e ga r a ge door , a n d
t h en dr iving t h e one block ). In oth er words , it cou ld be a r gu ed t h a t t h e differ en ce in
beh a vior s h a s t o do with t h e valu es of t h e differ en t cost com ponen t s, r a t h er t h a n t h e wa y
t h ey ar e weighted t oget h er (th e m a t h em a t ical fun ction). In r et r ospect, one can expla in
a n y d iffer en ce. We a r gu e in t h is ch a pt er , h owever , t h a t cr im e t r ip s a ppea r t o sh ow
d iffer en t lik elih ood s by t r a vel m od e a n d t h a t t r ea t in g ea ch of t h es e fu n ct ion s a s d is t in ct
a llows m ore flexibilit y in t h e fra m ework .
Disc rete Choice Ana lysis
No m a t t er h ow t h e u t ilit y fu n ct ion s a r e defin ed, t h ey h a ve t o be com bin ed in su ch a
wa y a s t o a llow a dis cr et e ch oice. Th a t is , a n offen der in t r a velin g fr om zon e A t o zon e B
m a k es a dis cr et e ch oice on t r a vel m ode. Th er e m a y be a pr oba bilit y for t r a vel by ea ch
m ode, for exa m ple 60% by ca r a n d 40% by bu s. Bu t , for a n in divid u a l, t h e ch oice is ca r or
bu s, n ot a pr oba bilit y. Th e pr oba bilit ies a r e obt a in ed by a sa m ple of in divid u a ls , for
exam ple of 10 individua ls 6 went by car an d 4 went by bus. But , still, at th e individua l
level, t h er e is a d ist inct choice t h a t wa s m a de.
Mu l ti n o m i a l Lo g i t F u n c t i o n
A com m on m a t h em a t ica l fr a m ewor k t h a t u sed is for m od e ch oice m od elin g a t a n
a ggr egat e level is t h e m u ltin om ial logit fu n ction (Dom incich a n d McFa dden , 1975; St oph er
a n d Meybu r g, 1975; Op pen h eim , 1980; Or t u za r a n d Willu m sen , 2001):
e (-$C ijL )
P ijL = --------------
(15.4)
P
E[ e (-$C ijL ]
L=1
wh er e P ijL is t h e pr obabilit y of us in g a m ode for a n y pa r t icula r t r ip p a ir (pa r t icula r origin
a n d p a r t icula r dest in a t ion) L is t h e t r a vel m ode, C ij is t h e cost of t r a velin g fr om or igin zon e
i t o des t in a t ion zon e j, e is th e base of th e nat ur al logar ithm , an d $ is a coefficien t .
Severa l obser vat ion s can be m a de a bou t t h is fu n ct ion . Fir st , each t r a vel m ode, L,
h a s it s own cost s a n d ben efit s, a n d ca n be eva lu a t ed by it self. Th a t is , t h er e is a dis t in ct
$C
)
u t ilit y fun ction for ea ch m ode. Th is is t h e n u m er a t or of th e equ a t ion, e (- ijL . However ,
t h e ch oice of an y on e m ode is depen den t on it s u t ilit y va lu e r ela t ive t o oth er m odes (t h e
den om ina t or of t h e equa t ion ). The m or e ch oices t h a t a r e a vailable, obviou sly, t h e less
lik ely a n in divid u a l will u se t h a t m ode. Bu t t h e va lu e a ssocia t ed wit h t h e m ode (t h e
u t ilit y) d oes n ot ch a n ge. As m en t ion ed a bove, we gen er a lly a ssu m e t h a t t h e ben efit of
t r a veling bet ween a n y two zon es is iden t ica l for a ll m odes a n d, hen ce, an y differ en ces a r e
du e t o cost s.
15.4
Secon d, t h e m a t h em a t ical for m is t h e n ega t ive expon en t ia l. Th e exponen t ia l
fu n ct ion is a gr owt h fu n ct ion in wh ich gr owt h occu r s a t a con st a n t rate (eit h er posit ive gr owt h , or n ega t ive - declin e). Th e u se of t h e n ega t ive exp on en t ia l a ssu m es t h a t t h e cost s
a r e r ela t ed t o th e lik elih ood a s a fun ction t h a t declines a t a con st a n t r a t e. It is a ctu a lly a
‘dis in cent ive’ or ‘dis cou n t ’ fun ction r a t h er t h a n a u t ilit y fun ction , per se. That is, as t he
cost s in crea se , t h e pr obabilit y of u sin g t h a t m ode d ecr ea se s, a ll oth er t h in gs bein g equ a l.
St ill, for h is t or ica l r ea son s, it is st ill ca lled a u t ilit y fu n ct ion .
Th ir d, for a n y on e m ode, t h e t ot a l cos t is a loga r it h m ic fu n ct ion of in divid u a l cos t s:
Ut ilit y cos t i = e (-$C ijL )
(15.5)
Ln(Ut ility cost L ) = C ijL = " + $1 X1 + $2 X2 + ......+ $k Xk
(15.6)
wh er e C ijL is a cum u lat ive cost m a de u p of com ponen t s X1 , X2 t h r ou gh Xk , " is a con st a n t ,
an d $1 t h r ou gh $k a r e coefficient s for t h e individu a l cost com ponen t s. Thu s, we see t h a t t h e
u t ilit y fu n ction is a loglinea r m odel, a s wa s s een in cha pt er 12. Th u s, t h e u t ilit y fu n ction is
Poisson distr ibut ed, declining at a const an t rate wit h in cre a sin g cum u la t ive cost s.
Dom incich a n d McFa dden (1975) su ggest t h a t t h e er r or t er m s a r e n ot P oisson dist r ibut ed,
bu t sk ewed in a Weibu l fu n ct ion . As dis cu ssed in ch a pt er 12, t h er e a r e a va r iet y of
differ en t m odels t h a t incor pora t e sk ewed er r or t er m s (negat ive binomia l, a sim ple lin ea r
cor r ect ion of disper sion ) so th a t t h e Weibu l is bu t one of a n u m ber of poss ible d es crip t ors .
Never t h eless, t h e m ea n u t ilit y is a P ois son -t yp e fu n ct ion .
Ge n e r a li z e d Re l a ti v e U t i li t y F u n c t i o n
On e can gen er a lize t h is fu r t h er t o allow a n y t ype of ma t h em a t ical fun ction. While
t h e P ois son h a s a lon g h is t or y a n d is wid ely u sed, a llowin g ot h er n on -lin ea r fu n ct ion s
a llows gr ea t er flexibility. It is p ossible t h a t ind ividu a ls a pply differ en t w eigh tin g s ys t em s
in eva lu a t in g d iffer en t m odes (e.g., a n ega t ive exp on en t ia l for wa lk in g, bu t a logn or m a l
fu n ct ion for d r ivin g). We cer t a in ly s ee wh a t a p pea r t o be d iffer en t fu n ct ion s wh en t h e
a ctu a l t r a vel beh a vior of in dividu a ls a r e exa m in ed (e.g., homeless in dividu a ls d on’t wa lk
everywh er e even t h ou gh t h e cost of wa lkin g lon g dista n ces is chea per in t r a vel t ime t h a n
t a k in g a bu s 2 ; people don ’t dr ive or t a k e a bu s for ver y sh ort dis t a n ces, s a y a block or t wo).
Th er efor e, if we a llow t h a t t h er e a r e differ en t t r a vel fu n ct ion s for differ en t m odes, t h en
m ore flexibilit y is p ossible t h a n by a ss u m in g a sin gle m a t h em a t ical fu n ction .
We ca n , th er efor e, writ e a gen eralized relative u tility fu n ction as:
F L (-$C )
P ijL = ------------------ =
I ijL
-----------------
ijL
P
E[F
P
L
E[I
(-$C ijL )]
L=1
L=1
15.5
ijL
]
(15.7)
wh er e t h e t er m s a r e t h e sa m e a s in 15.4 except t h e fun ction , F L , is some fun ction t h a t is
sp ecific t o th e t r a vel m ode, L. Th e n u m er a t or is defined a s t h e im peda n ce of mode L in
t r a veling bet ween t wo zon es i an d j, wh ile t h e den om ina t or is t h e su m of a ll imp eda n ces.
Notice t h a t t h e r a t io of t h e cost fun ction for one m ode r ela t ive t o th e t ota l cost s is
a ls o t h e r a t io of t h e im peda n ce for m ode L r ela t ive t h e t ot a l im peda n ce. Th e t ot a l
im peda n ce wa s defin ed in ch a pt er 14 a s t h e dis in cen t ive t o t r a vel a s a fu n ct ion of
sepa r a t ion (dist a n ce, tr a vel t ime, cost ). We see t h a t t h e sh a r e of a pa r t icu lar m ode,
t h er efor e, is t h e pr opor t ion of t h e t ot a l im peda n ce of t h a t m ode. Th is sh a r e will va r y, of
cou r se, with t h e degree of sepa r a t ion . For a n y given sepa r a t ion , th er e will u su a lly be a
differ en t sh a r e for ea ch m ode. For exa m ple, at low sepa r a t ion bet ween zon es (e.g., zon es
t h a t a r e n ext t o each ot h er ), walk in g a n d bik in g a r e m u ch m ore a t t r a ctive t h a n t a k in g a
bu s or a t r a in a n d, per h a ps even dr iving. At grea t er sepa r a t ion (e.g., zon es t h a t a r e 5
m iles a pa r t ), wa lkin g a n d bik in g a r e a lm ost ir r eleva n t choices a n d t h e lik elih ood of dr iving
or u sing public tr an sit is mu ch great er. In oth er words, the sha re th at an y one mode
occu p ies is n ot con s t a n t , bu t va r ies wit h t h e im p ed a n ce fu n ct ion .
Why th en can ’t we estima te t he m ode split directly at t he t rip distr ibut ion st age? If
t h e t r ip d ist r ibu t ion fun ction is
T ij =
" P i 8 $ AjJ I ij
(14.12 repea t )
a n d if t h ese t r ips, in t u r n , ar e split int o dist inct m odes u sin g equa t ion 15.7, cou ldn ’t 14.12
be r e-wr itt en a s
T ijL = " P i 8 $ AjJ I ijl
(15.8)
wh er e T ijL is t h e n u m ber of t r ips bet ween t wo zon es , i a n d j, by m ode L, P i is t h e pr odu ction
cap a city of zon e i, Aj is t h e a t t r a ction of zone j, " an d $ a r e con s t a n t s t h a t a r e a p plied t o t h e
pr odu ction s a n d a t t r a ction s r es pectively, 8 an d J a r e ‘fin e t u n in g’ expon en t s of th e
productions a nd a tt ra ctions r espectively, an d I ijL , is t h e imp eda n ce of u sin g mode L to
t r a vel bet ween t h e t wo zon es? Th e a n swer is , ye s, it could be ca lcu la t ed dir ect ly. If I ijL
wa s a per fect ly defin ed m ode im peda n ce fu n ct ion (with n o er r or ), th en t h e m ode sh a r e
cou ld be ca lcu la t ed dir ect ly a t t h e d is t r ibu t ion s t a ge in s t ea d of s ep a r a t in g t h e ca lcu la t ion s
in t o t wo d is t in ct s t a ges . Th e p r oblem , h owever , is t h a t t he im p ed a n ce fu n ct ion s a r e n ever
per fect (fa r from it , in fact ) an d t h a t r e-scalin g is r equ ir ed both t o get t h e origin s a n d
dest in a t ion s ba la n ced in t h e t r ip d ist r ibu t ion st a ge a n d t o ens u r e t h a t t h e pr obabilit ies in
equ a t ion 15.7 a dd t o 1.0. Th e effect of t h ese a dju st m en t s gen er a lly t h r ows off a m odel s u ch
a s 15.8.3 Con sequ en t ly, th e t r ip dist r ibut ion a n d m ode sp lit st a ges ar e u su a lly ca lcu lat ed
as separ at e operat ions.
Mea su ring Travel Costs
Th e n ext qu est ion is wh a t t yp es of t r a vel cos t s a r e t h er e t h a t defin e im peda n ce? As
m en t ion ed a bove, t h er e a r e r ea l a s well a s per ceived cost s t h a t a ffect a t r a vel m ode
15.6
decision . Some of t h ese can be m ea su r ed ea sily, wh ile oth er s a r e ver y difficult r equ ir in g
det a iled sur veys of ind ividu a ls. Am on g th ese cost s a r e:
1.
Dis t a n ce or t r a vel t im e. As m en t ion ed t h r ou gh ou t t h is dis cu ssion , d is t a n ce
is on ly a r ough in dica t or of cost sin ce it is in va r ia n t wit h r es pect t o tim e.
Act u a l t r a vel t im e is a m u ch bet t er in d ica t or beca u s e it va r ies t h r ou gh ou t
t h e da y a n d ca n be ea sily con ver t ed in t o a t ra vel tim e v alu e, for exam ple by
m u ltiplying by a u n it wa ge.
2.
Ot h er r ea l cost s, s u ch a s t h e oper a t in g cost s of a pr iva t e veh icle (fu el, oil,
m a int en a n ce), par kin g, a n d in su r a n ce. Som e of t h ese can be su bsu m ed
u n der t r a vel t im e va lu e by wor k in g ou t a n h our ly pr ice for t r a vel.
3.
P er ceived cost s, su ch a s con venien ce, fea r of being ca u ght by an offen der ,
ea se of escap e from a crim e scene, difficult ies in m oving s t olen goods , a n d
fea r of ret a lia t ion by ot h er offen der s or ga n gs ).
Som e of t h ese cost s ca n be m ea su r ed a n d som e ca n n ot . F or exa m ple, t h e va lu e of
t r a vel t im e can be in fer r ed from t h e m edia n h ous eh old in com e of a zone for a ggr ega t e
a n a lysis or from t h e a ct u a l househ old incom e for ind ividu a l-level an a lysis. Pa r kin g ca n be
a vera ged by zon e. Ins u r a n ce cost s can be est ima t ed from zon e a vera ges if t h e da t a ca n be
obtained.
Ma n y perceived cost s a lso ca n be m ea su r ed. Con venien ce, for exam ple, cou ld be
m ea su r ed fr om a gen er a l s u r vey. Th e fea r of be in g ca u gh t ca n be in fer r ed fr om t h e a m ou n t
of su r veilla n ce in a zon e (e.g., t h e n u m ber of police per son n el, secur it y gua r ds , secu r it y
ca m er a s). Even t h ou gh it m a y be a difficu lt en u m er a t ion pr ocess, it is s t ill possible t o
m ea su r e t h ese cost s a n d com e u p wit h some a vera ge estim a t e.
Ot h er per ceived cost s, on t h e ot h er h a n d, m a y not be ea sily m ea su r ed. For exa m ple,
t h e fea r a n offen der belon gin g t o on e ga n g h a s a bou t r et a lia t ion fr om a n ot h er ga n g is n ot
ea sily m ea su r ed. Sim ila r ly, th e cost s in m ovin g st olen goods by a t h ief is n ot ea sily
m ea su r ed; on e wou ld n eed t o kn ow t h e loca t ion of th e dist r ibu t ors of t h es e goods .
In pr a ct ice, t r a vel m odeler s m a k e sim ple a ssu m pt ion s a bou t cost s be ca u se of th e
difficult y in m ea su r in g m a n y of th em . For exa m ple, t r a vel t im e is t a k en a s a pr oxy for a ll
t h e oper a t in g cos t s. P a r k in g cos t s ca n be in cor por a t ed t h r ou gh sim ple a ssu m pt ion s a bou t
t h e dist r ibu t ion a cross zon es (e.g., zon es wit h in t h e cen t r a l bu sin es s d ist r a ct - CBD, a r e
given a n a ver a ge h igh pa r k in g cos t s; zon es th a t a r e cen t r a l, bu t n ot in t h e CBD, a r e
a ss ign ed m oder a t e pa r k in g cost s; zone s t h a t a r e su bu r ba n a r e a ss ign ed low pa r k in g cost s).
It wou ld be ju st t oo t ime con su m ing t o docu m en t ea ch a n d every cost a ffect ing t r a vel
beh a vior , pa r t icula r ly if we a r e developin g a m odel of offend er t r a vel.
Never t h eles s, t h eor et ically, t h es e a r e a ll pot en t ia lly m ea su r a ble cost s. Th ey a r e
r ea l a n d pr oba bly h a ve a n im pa ct in t h e t r a vel d ecis ion s t h a t offen der s m a k e. As
15.7
r esea r cher s, we h a ve t o wor k t owar ds a r t icula t in g a s m a n y of th ese cost s a s p ossible in
or d er t o p r od u ce a r ea lis t ic r ep r es en t a t ion of offen d er t r a vel.
Ag g r e g a te a n d I n d i v id u a l U ti li t y F u n c t i o n s
One of th e big debat es in t ra vel modeling is wheth er to use aggregate or individua l
u t ilit y fu n ct ion s t o ca lcu la t e m ode sh a r e. Th e a ggr ega t e a ppr oa ch m ea su r es com m on cost s
for ea ch zon e, ass u m ing a n a vera ge va lue. The d isa ggr egat e a ppr oa ch (somet imes ca lled
‘secon d gener a t ion ’ m odels) m eas u r es u n ique cost s for individu a ls, t h en s u m s u pwa r d t o
yield va lu es for ea ch zon e pa ir . E ven t h ou gh t h e en d r esu lt is a n a lloca t ion of cost s t o ea ch
zon e pa ir , t h e a r t icu la t ion of u n iqu e cost s a t t h e in divid u a l level ca n , in t h eor y, a llow a
m or e r ea list ic a ssessm en t of t h e u t ilit y fu n ct ion t h a t is a pplied t o a r egion .
Th e a ggr ega t e a ppr oa ch will m ea su r e cost s by a ver a ges. Th u s, a t yp ica l equ a t ion
for dr iving m ode m igh t be:
Tot a l cos t ij = " + $1 T ij + $2 P j
(15.9)
wh er e T ij is th e avera ge tra vel time between two zones, i an d j, an d P ij is t h e a ver a ge
pa r k in g cost for pa r k in g in zon e j. Notice th a t t h er e a r e a lim it ed n u m ber of va r ia bles in
a n a ggrega t e m odel (in t h is ca se, on ly two) a n d t h a t t h e a ss igned a ver a ge is for a n en t ir e
zon e. N ot ice a ls o t h a t t he p ar k in g cos t is ap plied on ly t o t h e d es t in a t ion zon e. It is
a ssu m ed t h a t a n y t r a veler will p a y t h a t fee in t h a t zon e ir r espect ive of wh ich or igin zon e
h e/sh e cam e from.
A disaggregate appr oach can allow more cost component s, if th ey ar e measu red.
Th u s, a t ypica l equa t ion for dr iving m ode m igh t be:
Tot a l cos t ijk = " + $1 T ijk + $2 P j + $3 C ijk + $4 CM ijk + $5 S ijk
(15.10)
wh er e T ijk is t h e t r a vel t im e for in dividu a l k bet ween t wo zon es , i a n d j, P ij is t h e a ver a ge
pa r k in g cost for pa r k in g in zone j, Cijk is t h e con venien ce of t r a veling t o zon e j fr om zon e i
for in dividu a l k , CM ijk is t h e com for t a n d p r ivacy exper ien ced by in dividu a l k in t r a velin g
from zone i t o zon e j, a n d S ijk is t h e per ceived sa fety exper ien ced by in dividu a l k in
t r a velin g fr om zon e i t o zon e j. N ot ice t h a t t h er e a r e m or e cost va r ia bles in t h e equ a t ion
a n d t h a t t h e m odel is t a r get ed sp ecifica lly t o th e in divid u a l, k . Two in divid u a ls w h o live
next door t o each oth er an d who tr avel to th e same destinat ion m ay evalua te th ese
com p on en t s differ en t ly. If t h es e in d ivid u a ls h a ve s u bs t a n t ia lly d iffer en t in com es , t h en t h e
valu e of t h e t r a vel t ime will differ . If on e valu es pr iva cy enorm ou sly while th e ot h er
does n ’t , t h en t h e cost of dr ivin g for t h e first is less t h a n for t h e secon d. S im ila r ly,
con ven ien ce is a ffect ed by bot h t r a vel t im e a n d t h e ea se of get t in g in a n d ou t of veh icle.
F ina lly, th e per cept ion of sa fet y ma y differ for t h ese t wo h ypot h et ica l in dividu a ls. Ther e
a r e m a n y st u die s t h a t h a ve docu m en t ed t h e sign ifica n t r ole pla yed by sa fet y in a ffect in g,
pa r t icu la r ly, t r a n sit t r ip s (Levin e a n d Wa ch s, 1986b).
15.8
In oth er words , t h e a ggrega t e a pp r oach a pp lies a ver y elem en t a r y t ype of ut ilit y
fun ction wh er ea s t h e disa ggrega t e a pp r oach a llows m u ch m ore comp lexit y a n d in dividu a l
va r ia bilit y. Of cour se , one h a s t o be a ble t o mea su r e t h e in divid u a l cost com pon en t s, a
difficult t ask un der most circum sta nces.
Th er e is a lso a qu est ion a bout wh ich a pp r oach is m ore a ccu r a t e for cor r ectly
for eca s t in g a ct u a l m od e s plit s . H is t or ica lly, m os t Met r op olit a n P la n n in g Or ga n iza t ion s
h a ve u sed t h e a ggr ega t e m et h od beca u se it ’s ea sier . H owever , m or e r ecen t r esea r ch
(Dom in cich a n d McF a dden , 1975; Ben -Akiva a n d Ler m a n , 1985; McF a dden , 2002) h a s
su ggest ed t h a t t h e disa ggrega t e m odelin g m a y be m ore a ccu r a t e. At t h e ver y m in im u m ,
t h e disa ggr ega t e is m ore a m en a ble t o policy in t er pr et a t ions beca u se it is m ore beh a viora l.
If on e cou ld in t er view t r a veler s wit h a su r vey, t h en it is possible t o exp lor e t h e va r iet y of
cos t fa ct or s t h a t a ffect a decis ion on bot h des t in a t ion a n d m od e s plit , a n d a m or e r ea lis t ic
(if n ot u n iqu e) ut ilit y fun ction der ived.
Bu t , a s m en t ioned a bove, wit h crim e t r ips , t h is is ver y difficu lt , if not im possib le, t o
do. Con sequ en t ly, for t h e t im e bein g, we’r e st u ck wit h a n a ggr ega t e a ppr oa ch t owa r ds
m odeling t h e u t ilit y of t r a vel by offen der s.
R e l a t i v e Access ib ility
F or t h is ver s ion of Crim eS tat, a n a pp r oxima t ion t o a u t ilit y fun ction wa s cr ea t ed.
Th e a p pr oa ch is t o es t im a t e a relative accessibility fu n ct ion a n d t h en a pp ly t h a t fu n ct ion t o
t h e pr edict ed t r ip dis t r ibu t ion . Th e r ela t ive a ccessibilit y fu n ct ion is a m a t h em a t ica l
a pp r oxima t ion t o a u t ilit y fun ction , r a t h er t h a n a m ea su r ed u t ilit y fun ction by it se lf.
Beca u s e t h e cos t com p on en t s ca n n ot be m ea s u r ed , a t lea s t for offen d er s , we u s e a n
in du ctive a pp r oach . Rea son a ble a ss u m pt ion s a r e m a de a n d a m a t h em a t ical fun ction is
foun d th at fits th ese assu mpt ions.
It is a pla u sible m odel, n ot a n a n a lyt ical one . Th e pla u sibilit y comes by m a k in g
reasonable assu mpt ions a bout actu al tr avel beha vior. One can assu me th at walking tr ips
will occu r for sh or t t r ip s, s a y u n der t wo m iles. Bicycle t r ip s, on t h e ot h er h a n d, cou ld occu r
over lon ger dis t a n ces, bu t will s t ill be r ela t ively sh or t (a ls o, t h er e is a lwa ys t h e r is k of
t r a ffic on t h e sa fet y of bicycle t r ip s). Tr a n sit t r ip s (bu s a n d t r a in ) will be u sed for
moderat ely long dista nces but require an a ctu al tr an sit network . Finally, driving tr ips ar e
t h e m ost flexible becau se t h ey can occur over a n y size dis t a n ce an d r oad n et wor k . Th ey a r e
less likely to be u sed for very sh or t t r ips, on t h e ot h er h a n d, du e t o r ea sons d iscu ssed
a bove.
Hierarch ical Approac h to Es timatin g Mode Acce ssibility
Usin g t h is a pp r oach , sp ecific st eps ca n be defined t o pr odu ce a p la u sible
a ccessibilit y model. To h elp in est a blishin g a m odel, an E xcel spr ea dsh eet h a s been
develop ed for m a k in g t h ese ca lcu la t ion s (Estim ate m od e split im ped an ce valu es.xls). It ca n
a lso be down loa ded from t h e Crim eS tat downloa d pa ge. The s pr ea dsh eet h a s been defin ed
wit h r espect t o dis t a n ce, bu t it ca n be a da pt ed for a n y t yp e of im peda n ce (t r a vel t im e or
15.9
cost). A spreadsh eet h as been used becau se it is more flexible th an incorpora ting it a s a
r ou t in e in Crim eS tat t o est im a t e t h e pa r a m et er s. Th er e is n ot a sin gle solu t ion t o t h e
pa r a m et er s est ima t es, an d t h e differ en t ch oices can be seen m or e ea sily in a spr ea dsh eet .
D efi n e t a r g et p r op o r ti on s
F irs t , define t h e m od es. In t h e Crim eS tat m ode sp lit r ou t ine, u p t o five differ en t
m odes a r e a llowed. Th es e h a ve defa u lt n a m es of “Wa lk ”, “Bik e”, “Dr ive”, “Bu s”, a n d
“Train”. The user is not r equired to use th ese na mes nor all five modes. Clearly, if th ere
is n ot a t r a in s yst em in t h e st u dy ar ea , th en t h e “Tr a in” m ode does not a pply. Tr a vel
m odeler s u se va r ia t ion s on t h ese, su ch a s “dr ive a lon e”,”ca r pool”, “a u t om obile”,
“m ot or cycle”, a n d so for t h .
D efi n e t a r g et p r op o r ti on s
Secon d, define t h e target proportion s. These a r e t h e expect ed pr oport ion s of t r a vel
for ea ch m ode. Wher e wou ld su ch pr oport ion s com e fr om ? Ther e h a ve been m a n y st u dies
of dr iving a n d t r a n sit beh a vior , bu t r ela t ively few s t u dies of bicycle a n d p edest r ia n u se
(Tu r n er , Shu n k, a n d H ot t en st ein, 1998; Schwa r t z et a l, 1999; P or t er , Suh r bier a n d
Schwa r t z, 1999). Ther e a r e n ot sim ple t a bles t h a t on e ca n look u p defau lt va lues .
To solve t h is p r oblem , exa m ple s w er e sough t from differ en t size m et r opolita n a r ea s.
E st ima t es of t r a vel m ode sh a r e for a ll t r ip pu r poses (wor k a n d n on -wor k) were obta ined
fr om 1) Ot t a wa (Ot t a wa , 1997); 2) P or t la n d (P or t la n d, 1999); a n d H ou st on 4 . Ta ble 15.1
sh ows t h e es t im a t ed sh a r es. Th e H ous t on d a t a does n ot in clud e wa lkin g a n d bik in g
sha res, and tr an sit tr ips ar e not distinguished by mode in t he Port land an d Otta wa dat a.
Ta ble 15.1
E s t im a t e d Mo d e S h a r e fo r Th r e e Me t r o p o li t a n Ar e a s
Al l Tr ip P u r p o s e s
Ot t aw a
P o rt la n d
Houston
P o p u la ti on :
725 t h ou s a n d
(1995)
2.0 m illion
(2001)
4.6 m illion
(2000)
P e r c e n t o f t ri p s b y:
Dr ivin g
Tr a n sit
(1995)
73.5%
15.2%
(1994)
88.6%
3.0
(2025 forecast )
98.3%
1.7%
(bu s 1.1%; r a il 0.6%)
-
Wa lkin g
Bicycle
Ot h er
9.6%
1.7%
-
4.6%
1.0%
2.8%
Wh ile it ’s difficu lt t o gen er a lize, wa lk in g is ver y m u ch depen den t on t h e exist en ce of
a n exten sive tr a n sit syst em . In H ou st on , th e t r a n sit syst em is pr ima r ily a com m u t er
15.10
sys t em wh er ea s in P or t la n d a n d Ot t a wa , it ser ves m u lt ip le pu r poses. Clea r ly, t h e m or e
com p a ct t h e u r ba n a r ea , t h e m or e lik ely t h a t t r ip s will occu r by t r a n s it , wa lk in g or bik in g.
Bu t , even in t h e ca se of Ot t a wa wh er e a lm ost 10% of t r ip s a r e by wa lk in g, t h e m a jor it y of
t r ips a r e by pr iva t e veh icle. In t h e U n it ed St a t es a n d Ca n a da , for m et r opolit a n a r ea s wit h
ext en sive t r a n sit fa cilit ies (New York , Ch ica go, Bos t on , Mon t r ea l), a m a jor it y of r egion a l
t r ips a r e st ill by au t om obile.
Ba sed on t h is, som e defau lt va lues wer e select ed a n d pu t int o t h e spr ea dsh eet . The
sp r ea ds h eet r equ ir es t h a t t h ey a r e en t er ed a s p r opor t ion s (n ot p er cent a ges). Th e defau lt s
va lu es wer e (t a ble 15.2):
Ta ble 15.2
D e fa u lt Mo de S h are Va lu e s
P r op or t ion s
Mo d e
Sh are
Wa lk
.04
Bicycle
.01
Dr ivin g
.90
Bu s
.04
Tr a in
.01
Th e u ser ca n m odify t h ese in t h e spr ea dsh eet . It ’s im por t a n t t h a t a u ser con t a ct t h e
loca l Met r opolit a n P la n n in g Or ga n iza t ion t o fin d ou t wh a t wou ld be r ea son a ble va lu es for
t h e u r ba n a r ea . Th e defa u lt va lu es a r e bu t gu es se s ba se d on a lim it ed a m oun t of da t a .
An a lt er n a t ive a p pr oa ch is t o u s e t h e J ou r n ey t o Wor k da t a of t h e U .S . Cen s u s
Bu r ea u (2004). Du r in g ever y cen su s, t h e Ce n su s Bu r ea u docu m en t s h om e-t o-wor k
‘com m u t e’ t r ips a n d br ea ks down t h ese da t a by mode sh a r e. They relea se t h ese da t a u n der
t h e t it le “J our n ey t o Work ”. In t h e U n it ed St a t es in 2000, 87.9% of all h ome-to-wor k t r ips
wer e by pr iva t e veh icle (au t omobile, va n , t r u ck), 4.7% wer e by pu blic tr a n sit (bus 2.5%; r a il
2.1%; ot h er 0.1%), 2.9% wer e by walkin g, 0.4% wer e by bicycle, 0.1% wer e by motorcycle,
0.7% wer e by ot h er m ea n s, an d 3.3% wor ked a t h om e.
Na t ion a l jou r n ey t o wor k st a t ist ics for 1990 a n d 20 00 a n d for m et r opolit a n a r ea s in
1990 can be foun d at h t t p://www.cen su s.gov/popu la t ion/www/socdem o/jou r n ey.h t m l. Dat a
on m et r opolita n a r ea s for 2000 ca n be fou n d in McGu ckin a n d Sr inivas a n (2003). In 2000,
t h e h om e-t o-wor k m ode sh a r e for a sa m ple of lar ge met r opolita n (inclu din g th e 15 lar gest )
a r ea s is sh own in Ta ble 15.3. Th ey a r e r a n k -or der ed by t h e 2000 popu la t ion of th e
m et r op olit a n a r ea .
As ca n be s een , t h e la r ger m et r op olit a n a r ea s gen er a lly h a ve a h igh er sh a r e of
t r a n sit u se a n d wa lk in g t h a n sm a ller m et r opolit a n a r ea s, bu t t h e differ en ces a r e n ot t h a t
dr a m a t ic. E ven t h e la r gest m et r opolit a n a r ea s h a ve a m a jor it y of th eir h ome-to-wor k t r ips
by priva t e vehicle.
15.11
Ta ble 15.3
Mode Sh are of J ou rn e y to Work Trips: 2000
(F r om McGu ck in a n d S r in iva s a n , 2003)
Gre a te r
Mod e Sh are
M e t r o p o li ta n
2000
Area
P op (M) Walk B ic y c le
D r iv e
B u s Ra il
Oth e r*
N e w Yor k
21 .1
5 .6 %
0 .3 %
6 5 .7 % 6 .8 % 1 7 .1 %
4 .5 %
L o s An g e l e s
16 .4
2 .6 %
0 .6 %
8 7 .6 % 4 .3 %
0 .3 %
4 .6 %
C h i ca g o
9.2
3 .1 %
0 .3 %
8 1 .5 % 4 .6 %
6 .6 %
3 .9 %
W a s h in g t on D C
7.6
3 .0 %
0 .3 %
8 3 .2 % 4 .1 %
5 .0 %
4 .4 %
S a n F r a n ci s co
7.0
3 .3 %
1 .1 %
8 1 .0 % 5 .7 %
3 .5 %
5 .4 %
P h ila d elp h ia
6.2
3 .9 %
0 .3 %
8 3 .6 % 5 .3 %
3 .3 %
3 .6 %
D et r oit
5.5
1 .8 %
0 .2 %
9 3 .4 % 1 .7 %
0 .0 %
2 .9 %
B os t on
5.8
4 .1 %
0 .4 %
8 2 .7 % 3 .2 %
5 .5 %
4 .1 %
D a lla s
5.2
1 .5 %
0 .1 %
9 2 .7 % 1 .6 %
0 .1 %
4 .0 %
H ou s t on
4.7
1 .6 %
0 .3 %
9 1 .3 % 3 .1 %
0 .0 %
3 .7 %
At la n t a
4.1
1 .3 %
0 .1 %
9 0 .6 % 2 .4 %
1 .1 %
4 .5 %
M ia m i
3.9
1 .8 %
0 .5 %
9 0 .1 % 3 .2 %
0 .5 %
3 .9 %
S ea t t le
3.6
3 .2 %
0 .6 %
8 4 .4 % 6 .2 %
0 .0 %
5 .6 %
P h oe n ix
3.3
2 .1 %
0 .9 %
9 0 .0 % 1 .9 %
0 .0 %
5 .1 %
M in n e a p olis /S t P a u l
3.0
2 .4 %
0 .4 %
8 8 .4 % 4 .4 %
0 .0 %
4 .4 %
C leve la n d
2.9
2 .1 %
0 .2 %
9 1 .1 % 3 .1 %
0 .3 %
3 .2 %
Sa n D ieg o
2.8
3 .4 %
0 .6 %
8 6 .9 % 3 .1 %
0 .2 %
5 .8 %
S t L ou is
2.6
1 .6 %
0 .1 %
9 2 .5 % 2 .1 %
0 .2 %
3 .5 %
Den ver
2.6
2 .4 %
0 .7 %
8 7 .1 % 4 .2 %
0 .1 %
5 .5 %
P itt sbu r gh
2.4
3 .6 %
0 .1 %
8 7 .1 % 6 .0 %
0 .1 %
3 .1 %
P or t la n d
2.3
3 .0 %
0 .8 %
8 5 .2 % 5 .1 %
0 .5 %
5 .4 %
C in cin n a t i
2.0
2 .3 %
0 .1 %
9 1 .4 % 2 .8 %
0 .0 %
3 .4 %
S a cr a m e n t o
1.8
2 .2 %
1 .4 %
8 8 .9 % 2 .4 %
0 .3 %
4 .8 %
K a n s a s C it y
1.8
1 .4 %
0 .1 %
9 3 .2 % 1 .2 %
0 .0 %
4 .1 %
Milwa u kee
1.7
2 .8 %
0 .2 %
9 0 .0 % 3 .9 %
0 .0 %
3 .1 %
I n d i a n a p o lis
1.6
1 .7 %
0 .2 %
9 3 .3 % 1 .2 %
0 .0 %
3 .6 %
Orlando
1.6
1 .3 %
0 .4 %
9 2 .7 % 1 .6 %
0 .0 %
4 .0 %
S a n An t on io
1.6
2 .4 %
0 .1 %
9 0 .9 % 2 .8 %
0 .0 %
3 .8 %
N or folk
1.6
2 .7 %
0 .3 %
9 1 .0 % 1 .7 %
0 .0 %
4 .3 %
L a s Ve g a s
1.6
2 .4 %
0 .5 %
8 9 .5 % 3 .9 %
0 .0 %
3 .7 %
C h a r l ot t e
1.5
1 .2 %
0 .1 %
9 3 .8 % 1 .3 %
0 .0 %
3 .6 %
N e w O r le a n s
1.3
2 .7 %
0 .6 %
8 7 .7 % 5 .2 %
0 .0 %
3 .8 %
S a lt L a k e C it y
1.3
1 .8 %
0 .4 %
9 0 .3 % 2 .7 %
0 .3 %
4 .5 %
M em p h is
1.1
1 .3 %
0 .1 %
9 3 .9 % 1 .6 %
0 .0 %
3 .1 %
R o ch e s t e r
1.1
3 .5 %
0 .2 %
9 0 .9 % 1 .9 %
0 .0 %
3 .5 %
O k la h om a C it y
1.1
1 .7 %
0 .2 %
9 3 .8 % 0 .5 %
0 .0 %
3 .8 %
Lou isv ille
1.0
1 .7 %
0 .2 %
9 2 .9 % 2 .2 %
0 .0 %
3 .0 %
-----------------------------------------------------------------------------------------------------------------* In clu des t a xi, fer r y, a n d wor kin g a t h om e
Th e pr oblem wit h t h es e da t a , h owever , is t h a t t h ey only exa m in e wor k t r ips .
Na t ion a lly, home-to-wor k t r ips r epr esen t on ly about 15% of all da ily tr ips (BTS, 2002). On
t h e oth er h a n d, 45% of da ily tr ips a r e for sh oppin g a n d er r a n ds a n d 27 % ar e socia l a n d
15.12
r ecr ea t iona l. Fu r t h er , n on-wor k t r ips a r e even m ore likely t o occu r by a u t omobile, a n d a r e
gen er a lly s h or t er . F or exa m ple, in H ou st on , for h om e-ba sed n on -wor k t r ip s, on ly 1% of
t r ip s a r e by t r a n sit com pa r ed t o 3.1% for h om e-t o-wor k t r ip s. Th ese h om e-ba sed n on -wor k
t r ips m a y be a bet t er a n a logy to cr im e t r ips t h a n work t r ips sin ce th ey t en d t o be of sim ila r
tr ips lengths a s crime tr ips.
Th u s, u n less t h e u ser is willin g t o as su m e t h a t a crim e t r ip is like a work t r ip
(which is qu est ion a ble), th en t h e J our n ey t o Work t a bles a r e pr obably not t h e bes t guide
for t h e t a r get pr opor t ion s. N ever t h eless, a n exa m in a t ion of t h em is va lu a ble t o see h ow
work tr ips ar e split am ong the various t ra vel modes.
S el ec t m o d e fu n ct i on s
Th ir d, s elect m a t h em a t ical fun ctions t h a t a pp r oxim a t e a ccessibilit y ut ilit y. Aga in ,
some plau sible assu mpt ions n eed to be made. In Crim eS tat, t h e u se r can select a m ong five
differe n t m a t h em a t ical fun ctions (linea r , nega t ive expon en t ia l, norm a l, logn orm a l,
t r u n ca t ed n ega t ive expon en t ia l). Th e defa u lt fu n ct ion s a r e (Ta ble 15.4):
Ta ble 15.4
D e fa u lt Mo de S h are F u n ct io n s
Mo d e
Wa lk
Bicycle
Dr ivin g
Bu s
Tr a in
Function
Nega t ive expon en t ia l
Nega t ive expon en t ia l
Logn or m a l
Logn or m a l
Logn or m a l
The reasoning behind th is is th at walking and biking are r elat ively short tr ips,
wh er ea s t r a n sit m odes a r e u sed for in t er m edia t e len gt h t r ip s wh ile dr ivin g ca n be u sed for
a n y len gt h t r ip. Th u s, it ’s u n likely t h a t a n a u t omobile will be u sed for ver y sh ort t r ips
(less t h a n a qu a r t er m ile) an d it ’s ver y un likely t h a t t r a n sit will be u sed for sh ort t r ips
(less t h a n a h a lf m ile or m or e). Nevert h eless, th e u ser ca n m odify th ese choices a n d
exam ine t h e a ppr opr iat e colum n in t h e spr ea dsh eet .
S elect m od el p r ior it ies
F ou r t h , s elect t h e pr ior it ies for m odelin g t h e t a r get . U n for t u n a t ely, t h er e m a y n ot
be a s ingle solut ion t h a t will yield t h e t a r get pr oport ion s. Ther efor e, a decision n eeds t o be
m a d e on wh ich o rd e r t h e spr ea dsh eet will be ca lcu la t ed. Th e defa u lt or der is (t a ble 15.5 ):
15.13
Ta ble 15.5
D e fa u lt Mo de S h are F u n ct io n s
Mo d e
Wa lk
Bicycle
Dr ivin g
Bu s
Tr a in
Or d e r o f
It e r a ti o n
1
2
3
4
5
Th e r ea son in g is t h a t t h e offend er fir st m a k es a decision on t h e len gt h of t h e t r ip
(sh or t , med ium , lon g, or t h e equiva lent in t r a vel t ime). Then , wit h in ea ch ca t egor y, m a kes
a decis ion on wh ich m ode t o ch oose. F or ver y s h or t t r ip s, t h e defa u lt m ode is wa lk in g. F or
in t er m edia t e t o long t r ips , t h e defau lt choice is d r iving. However , t h e u ser can cha n ge t h is
or der .
It er a t i v el y es ti m a t e p a r a m e t er s
F ift h , in t h e spr ea dsh eet , it er a t ively a djus t t h e pa r a m et er s u n t il t h e t a r get
pr opor t ion is r ea ch ed. Do t h is in t h e or der select ed in t h e a bove st ep. Aga in , t h er e is n ot a
sin gle solu t ion t h a t will p r odu ce t h e t a r get pr opor t ion . F or exa m ple, ea ch of th e
ma th emat ical fun ctions h as t wo or t hr ee par am eters t ha t can be adjusted:
1.
2.
3.
4.
5.
F or t h e n egat ive expon en t ial, th e coefficient a n d expon en t
F or t h e n or m a l d is t r ibu t ion , t h e m ea n dis t a n ce, s t a n da r d devia t ion a n d
coefficient
F or logn or m a l d is t r ibu t ion , t h e m ea n dis t a n ce, s t a n da r d devia t ion a n d
coefficient
For t he linear distr ibut ion, an int ercept an d slope
F or t h e t r u n ca t ed n ega t ive exp on en t ia l, a pea k dis t a n ce, p ea k lik elih ood,
in t er cept , a n d expon en t .
Th e t a r get pr oport ion ca n be a chieved by a dju st in g a n y or a ll of t h e pa r a m et er s.
F or exa m ple , t o ach ieve a t a r get pr oport ion of 0.05 (i.e., 5%) u sin g t h e n ega t ive
expon en t ial, an infin ite n u m ber of m odels can yield t h is, for exam ple coefficient =0.0366,
exp on en t =-2.63; coefficien t =0.0459 or expon en t =-5; coefficien t =0.01966, exp on en t =-1; a n d
so for t h . Ther efor e, th er e m u st be ad dit ion a l cr iter ia t o con st r a in t h e ch oices.
On e crit er ia is t o set a n a pp r oxim a t e m ea n dis t a n ce. For exa m ple, wit h wa lkin g
t r ips, th e m ea n dist a n ce ca n be set t o a h a lf m ile or for dr iving, th e m ea n dist a n ce ca n be
set t o 6 m iles. Th en , ch eck t h e a ppr oxim a t e m ea n dis t a n ce of t h e select ed fu n ct ion .
Th ou gh r a r ely will t h e exa ct m ea n dis t a n ce be r eplica t ed, t h e ca lcu la t ed m ea n dis t a n ce
sh ould be close t o th e ide a l. Th e one except ion is for ver y sh ort t r ips . Sin ce th e in t er va ls
in t h e spr ea dsh eet a r e a h a lf m ile ea ch , th er e is con sider a ble err or for very sh or t dist a n ces.
15.14
Exa m in e th e gr a p h s in th e sp r ea d sh eet
An ot h er is t o exa m in e t h e gr a p h of t h e fu n ct ion in t h e s pr ea d sh eet (below t h e
ca lcu la t ion s ). Does t h e t yp ica l t r ip a pp r oxim a t e t h e exp ect ed m ea n d is t a n ce? Does t h e
select ed fun ct ion pr odu ce somet h ing t h a t looks int u itive? Adm itt edly, t h ese a r e su bject ive
decision s. But , if t h e fu n ct ion looks st r a n ge, it can be ca u ght a n d r e-ca lcu lat ed.
In sh or t , th e a im s h ou ld be to pr odu ce a fu n ct ion t h a t n ot on ly ca pt u r es t h e t a r get
pr opor t ion , but looks plau sible. Severa l exa m ples ar e sh own below. Figu r e 15.1 sh ows t h e
defau lt wa lkin g m odel u sin g a n ega t ive expon en t ia l. Figu r e 15.2 s h ows t h e defau lt bik in g
m odel, a ls o u sin g a n ega t ive exp on en t ia l. F igu r e 15.3 sh ows t h e defa u lt dr ivin g m ode
u sin g a lognor m a l fun ction . Figu r e 15.4 sh ows t h e defa u lt bu s m ode, a lso u sin g a
logn or m a l fu n ct ion a n d figu r e 15.5 s h ows t h e d efa u lt t r a in m od e u s in g a logn or m a l
fu n ct ion .
F igu r e 15.6 shows t h e cu m u lat ive r esu lts of t h e defau lt va lues . This is a lso gra ph ed
in t h e spr ea ds h eet , st a r t in g in cell I1. N otice h ow t h e r ela t ive a cces sib ilit y fun ction wor k s.
As dista nce increases, the mode proport ions cha nge. At very short dista nces, walking tr ips
pr edomin a t e with biking t r ips a lso gett ing a m oder a t e sh a r e. As t h e dist a n ce increa ses,
t h e pr opor t ion s in crea sin gly sh ift t owar d d r iving. Even t h ough t h e lik elih ood of dr iving
declines w it h dis t a n ce, th e oth er m odes decline even fas t er . In oth er wor ds , t h e r ela t ive
a cces sibilit y fu n ct ion is es t im a t in g t h e r ela t ive sh a r es of ea ch m ode a s a fu n ct ion of th e
im peda n ce (in t h is ca se , dis t a n ce).
Ad a p ti ng sp rea d sheet for t ra vel t im e or tr a vel cost
Th e illus t r a t ion s t o t h is poin t h a ve used dist a n ce a s a n imp eda n ce u n it. H owever,
oth er im peda n ce un it s, s u ch a s t r a vel t im e a n d gen er a lized t r a vel cost , can a lso be u se d.
Th ese gener a lly r equ ire a n et wor k (see below) in t h a t weigh t s h a ve to be ass ign ed t o
segm en t s. N ever t h eles s, t h e sa m e logic ap plies . For ea ch t r a vel m ode, a sp ecific
im peda n ce fu n ction is est im a t ed a n d t h en a pp lied t o th e t r ip d ist r ibu t ion m a t r ix.
Em p ir ica lly est im a ti ng th e m od e-sp ecific im p ed a nce
As m en t ion ed a t t he begin n in g of t h is ch a p t er , t h e la ck of in for m a t ion a bou t
offen d er t r a vel m od es h a s n eces sit a t ed t h e u s e of m a t h em a t ica l ‘gu es ses ’ a bou t t r a vel
beh a vior . However , if it wer e possible t o obt a in a ct u a l in for m a t ion on t r a vel m odes by
offen der s, t h en t h is in for m a t ion cou ld be u t ilized dir ect ly t o est im a t e a m u ch m or e
a ccu r a t e im peda n ce fu n ction . If t h is da t a ba se existed , th en t wo a ppr oa ch es a r e possible:
1.
F it t h e da t a wit h t h e va r iou s m a t h em a t ical fun ctions t o see wh ich ones fit
best a nd t o estimat e the par am eters.
2.
Use t h e k er n el de n sit y fu n ction t o est im a t e a n on-linea r im peda n ce valu e
wit h t h e specific in for m a t ion .
15.15
Figure 15.1:
Negative Exponential Function: Walk Mode
Impedance proportion
0.020
0.015
0.010
0.005
0.000
0.0
2.5
5.0
7.5
10.0
12.5
Distance
15.0
17.5
20.0
22.5
25.0
Figure 15.2:
Negative Exponential Function: Bike Mode
Impedance proportion
0.002
0.001
0.000
0.0
2.5
5.0
7.5
10.0
12.5
Distance
15.0
17.5
20.0
22.5
25.0
Figure 15.3:
Lognormal Function: Drive Mode
0.07
Impedance proportion
0.06
0.05
0.04
0.03
0.02
0.01
0.00
0.0
2.5
5.0
7.5
10.0
12.5
Distance
15.0
17.5
20.0
22.5
25.0
Figure 15.4:
Lognormal Function: Bus Mode
Impedance proportion
0.005
0.004
0.003
0.002
0.001
0.000
0.0
2.5
5.0
7.5
10.0
12.5
Distance
15.0
17.5
20.0
22.5
25.0
Figure 15.5:
Impedance proportion
Lognormal Function: Train Mode
0.002
0.001
0.000
0.0
2.5
5.0
7.5
10.0
12.5
Distance
15.0
17.5
20.0
22.5
25.0
Figure 15.6:
Default Relative Accessibility by Mode
0.0500
Impedance proportion
0.0400
Walk
Bike
Drive
Bus
Train
0.0300
0.0200
0.0100
0.0000
0 0. 1 1. 2 2. 3 3. 4 4. 5 5. 6 6. 7 7. 8 8. 9 9. 10
Distance (miles)
Th ese a ppr oa ch es wer e discuss ed in cha pt er 9 (J ou r n ey to Crim e) a n d in ch a pt er 14
(Tr ip Dis t r ibu t ion ). Th e “Ca libr a t e im peda n ce fu n ct ion ” r ou t in e in t h e Tr ip Dis t r ibu t ion
m odu le ca n be u sed for t h is pu r pose. Th e a dva n t a ge wou ld be en or m ou s. In st ea d of
gues ses a bou t likely imp eda n ce fu n ct ion s of specific t r a vel m odes, t h e u ser wou ld h a ve a
fun ction t h a t wa s ba sed on r ea l da t a . Th er e sh ould be a su bst a n t ia l im pr ovem en t in
m odeling a ccu r a cy th a t wou ld r esu lt. H owever, t h ese da t a h a ve to be firs t collect ed.
Cr i m eS t a t III Mode Sp lit To ols
Th e Crim eS tat m ode sp lit m odu le allows t h e r elat ive a ccessibilit y fu n ct ion t o be
calcu la t ed. Figu r e 15.7 sh ows t h e set u p p a ge for t h e m ode s plit r out in e a n d figu r e 15.8
sh ows t h e set u p for m odes 1 a n d 2, in t h e exa m ple “Wa lk ” a n d “Bicycle”. Th e set u p for
m odes 3, 4, a n d 5 a r e sim ila r .
Mo de S pli t S e tu p
On t h e m ode sp lit set u p pa ge, t h e pr edict ed origin a n d pr edict ed des t ina t ion files
m u st be inpu t a s t h e pr ima r y an d secon da r y files. If t h e or igin a n d des t ina t ion files ar e
iden t ica l (i.e., a ll t h e or igin zon es a r e inclu ded in t h e dest ina t ion zon es), t h en t h e file m u st
be in pu t a s t h e pr im a r y file.
In a dd it ion , t h e u ser m u st in pu t a pr edicted origin -dest in a t ion t r ip file fr om t h e t r ip
dist r ibut ion m odu le. Fin a lly, an a ssu m ed im peda n ce valu e for t r ips from t h e “E xter n a l
zone” mu st be specified. The defau lt is 25 miles. Ch oos e a va lu e t h a t wou ld rep res en t a
‘t yp ica l’ t r ip fr om ou t sid e t h e st u dy r egion .
F or ea ch m ode, th e u ser m u st pr ovide a label for t h e n a m e a n d define t h e
m a t h em a t ical fun ction wh ich is t o be app lied a n d s pecify t h e pa r a m et er s. Th e firs t t im e
t h e r ou t ine is opened , th e defau lt va lues a r e list ed. H owever, t h e u ser ca n ch a n ge th ese.
H in t : On ce t h e pa r a m et er s a r e en t er ed, t h ey ca n be sa ved on t h e Opt ion s
pa ge. Then , th ey ca n be re-ent er ed by loa din g th e sa ved pa r a m et er s file.
Con stra in Cho ice to N e tw ork
Th e imp eda n ce will be ca lcu lat ed eit h er dir ect ly or is con st r a ined t o a n et wor k. Th e
defa u lt im peda n ce is defin ed wit h t h e t yp e of dis t a n ce m ea su r em en t specified on t h e
Mea su r em en t P a r a m et er s p a ge (un der Da t a set u p). On t h e oth er h a n d, if th e im peda n ce is
t o be con st r a in ed t o a n et wor k , t h en t h e n et wor k h a s t o be define d.
D e fa u l t
The defau lt impedan ce is th at specified on t he Measu rem ent par am eters page. If
d ir ect d is t a n ce is t h e d efa u lt d is t a n ce (on t h e m ea s u r em en t p a r a m et er s pa ge), t h en a ll
15.22
Figure 15.7:
Mode Split Module
Figure 15.8:
Set Up for Individual Modes
im peda n ces a r e calcu la t ed a s a dir ect dis t a n ce. If in dir ect dis t a n ce is t h e defau lt , t h en a ll
im peda n ces a r e calcu la t ed a s in dir ect (Man h a t t a n ) dist a n ce. If n et work dis t a n ce is t h e
defau lt, t h en a ll imp eda n ces a r e ca lcu lat ed u sin g th e specified net wor k a n d it s pa r a m et er s;
t r a vel im peda n ce will a u t om a t ica lly be con st r a in ed t o t h e n et wor k u n der t h is con dit ion .
C on st r a i n t o n et w o r k
An im p ed an ce ca lcu la t ion sh ou ld be con st r a in ed to a n et wor k wh en t h er e a r e
lim it ed ch oices. F or exa m ple, a bu s t r ip r equ ir es a bu s r ou t e; if a pa r t icu la r zon e is n ot
n ea r a n exist in g bu s r out e, t h en a dir ect dis t a n ce ca lcula t ion will be m islea din g sin ce it
will pr oba bly u n der est ima t e t r u e dist a n ce. Similar ly, for a t r a in t r ip, th er e n eeds t o be an
exist in g t r a in r ou t e. Ot h er wis e, t h e r ou t in e will a ssign t r a n sit t r ip s wh er e t h ose a r e n ot
possib le (i.e., it will a ss ign t r a in t r ips wh er e t h er e a r e n o tr a in st a t ions a n d it will a ss ign
bu s t r ips wh er e t h er e a r e n o bus r ou t es). The r ou t ine does n ot ‘kn ow’ wh et h er t h er e a r e
t r a n sit r out es a n d m u st be t old wh er e t h ey a r e. E ven for wa lkin g, bicyclin g a n d d r iving
t r ips , an exist in g net work m ight pr odu ce a m ore r ea list ic t r a vel im peda n ce th a n sim ply
a ss u m in g a dir ect t r a vel pa t h .
If t h e im peda n ce ca lcu la t ion is t o be con st r a in ed t o a n et wor k , t h en t h e n et wor k
m u st be defined . A m or e exten sive discu ssion of a n et wor k is p r ovided in ch a pt er 3 (u n der
Type of dis t a n ce mea su r em en t on t h e Mea su r em en t P a r a m et er s p a ge) an d in cha pt er 16 in
t h e dis cu ssion of t h e Tr ip Assign m en t m odu le. E ssen t ia lly, a n et wor k is a ser ies of
conn ected segment s th at specify possible rout es. Ea ch segment h as t wo end nodes (in
Crim eS tat, t h ey a r e ca lled ‘F r om Node’ a n d “ToNode). Depen din g on t h e t yp e of n et wor k ,
t h e segm en t s ca n be bi-dir ection a l (i.e., tr a vel is a llowed in eit h er dir ection ) or sin gle
dir ect iona l (i.e., tr a vel is a llowed only fr om t h e “F r omN ode” t o th e “ToNode”).
A cr it ica l com p on en t of a n et wor k for t h e m od e s plit r ou t in e is t h a t t r a vel ca n on ly
pa ss t h r ough n odes. Th is m ea n s t h a t t wo segm en t s t h a t a r e con n ected can a llow a t r ip t o
pa ss over t h ose t wo segmen t s wh erea s t wo segmen t s t h a t ar e not con n ect ed ca n n ot allow a
t r ip t o pa ss dir ectly fr om on e t o th e oth er . Fr om ou t sid e t h e n et work , a t r ip con n ects t o it
a t a n ode. For a t r a n sit n et wor k, t h is ca n be cr itical. For a bus r ou t e, it m a y or m a y not be
im p or t a n t . A p recis e bu s n et wor k defin es nod es by bu s s top s s o t h a t a tr ip ca n ‘en t er ’ or
‘leave’ t h e bus syst em a t a r ea l st op. A less pr ecise bus n et wor k d efines n odes by t h e end s
of segm en t s (e.g., th e end n odes of a TIGE R segmen t ). The r ou t ine will not k n ow wh et h er
t h e n ode it en t er s or lea ves fr om is a r ea l bu s s t op or n ot. In t h e cas e of bu s r out es, it
pr oba bly doesn’t m a t t er sin ce t h ey gen er a lly m a ke ver y regu lar st ops (ever y two or t h r ee
block s).
Ac cu r a t e ly d e fi n ed t r a n s i t n et w o r k s
F or t r a in n et wor ks , however , it is abs olut ely cr itical th a t t h e n et wor k be d efined
a ccu r a t ely. Th e n odes m u st be legit im a t e st a t ion s; a t r ip ca n only en t er or lea ve t h e t r a in
sys t em t h r ou gh a st a t ion (i.e ., it ca n n ot en t er or lea ve a t r a in n et wor k a t t h e en d of an
a r bit r a r y segm en t n ode). Most t r a vel dem a n d m odels u se ver y pr ecise bu s a n d t r a in
n et wor ks t h a t h a ve been car efu lly ch ecked ; wh er e er r or s occu r , th e n et wor ks a r e edit ed
15.25
a n d u pd a t ed. If th e u ser does n ot h a ve a n edit ed t r a n sit n et work , on e can be m a de in t h e
t r ip a ss ignm en t m odu le. Th er e is a “Cr ea t e a t r a n sit n et work from pr im a r y file” r out in e
t h a t will d r a w segm en t s bet ween in pu t pr im a r y file poin t s; t h e u ser in pu t s t h e st a t ion or
bu s s t op locat ion s a s t h e pr im a r y file a n d t h e r out in e cre a t es a n et work from one p oin t t o
t h e n ext in t h e sam e ord er a s in t h e pr im a r y file (i.e., t h e pr im a r y file n eed s t o be pr oper ly
sor t ed in ord er t o tr a vel). See cha pt er 16 for m ore in for m a t ion a bout crea t in g a t r a n sit
n e t wor k .
En t er i n g t h e n et w o r k p a r a m e t er s
Th e n et wor k is in pu t by s elect in g “Con st r a in t o n et wor k ” a n d click on t h e
‘P a r a m et er s’ bu t t on . A dia logu e is br ou gh t u p t h a t a llows t h e u ser t o specify t h e n et wor k
t o be u sed. Th e n et wor k file ca n be eit h er a sh a pe lin e or polylin e file (t h e defa u lt ) or
a n ot h er file, eith er dBa se IV ‘dbf’, Micr osoft Access ‘m db’, Ascii ‘da t ’, or a n ODBCcom plia n t file. If th e file is a sh a pe file, th e r out in e will k n ow t h e loca t ions of t h e n odes .
All t h e u ser n eeds t o do is ident ify a weight ing var iable, if u sed, a n d possible on e wa y
r ou t es (‘flags’). For a dBa se IV or ot h er file, t h e X a n d Y coor din a t e var iables of t h e end
n odes m u st be defined . These a r e ca lled th e “F r om ” n ode a n d t h e “E n d” n ode, th ou gh t h er e
is n o pa r t icula r ord er .
An opt ion a l weigh t va r ia ble is a llowed for both a sh a pe or d bf file. Th e r out in e
iden t ifies n odes a n d s egm en t s a n d fin ds t h e sh ort est pa t h . By defa u lt , t h e sh ort est pa t h is
in t er m s of dis t a n ce t h ou gh ea ch segm en t ca n be weigh t ed by t r a vel t im e, t r a vel s peed, or
genera lized cost; in th e lat ter case, th e units a re minu tes, hour s, or u nspecified cost u nits.
F in a lly, t h e n u m ber of gr a ph segm en t s t o be ca lcu la t ed is defin ed a s t h e n et wor k
limit . The defau lt is 50,000 segmen t s. This can be ch a n ged, but be su r e t h a t t h is n u m ber
is gr e a t er t h a n t h e n u m be r of s egm e n t s in you r n e t wor k .
Mini m um a bsolu te im p ed a nce
If a m ode is con st r a ined t o a n et wor k, a n a ddit ion a l con st r a int is need ed t o en su r e
r ea listic a lloca t ion s of t r ips. This is t h e m inim u m a bsolu t e imp eda n ce bet ween zon es. The
defau lt is 2 m iles. F or a n y zon e pa ir t h a t is closer t oget h er t h a n t h e m in im u m sp ecified (in
dis t a n ce, tim e in t er va l, or cost ), n o tr ips will be a llocat ed t o th a t m ode. Th is con st r a in t is
t o pr event u n r ea listic t r ips being a ssign ed t o int r a -zon a l tr ips or t r ips bet ween n ea r by
zones.
Crim eS tat u ses t h r ee im peda n ce com pon en t s for a const r a in ed n et wor k :
1.
Th e im peda n ce fr om t h e origin zone t o th e n ea r es t n ode on t h e n et wor k (e.g.,
n ea r es t r a il s t a t ion );
2.
Th e im peda n ce a lon g t h e n et wor k t o t h e n ode n ea r est t o t h e dest in a t ion ; a n d
3.
Th e im peda n ce fr om t h a t n ode t o th e dest in a t ion zon e.
15.26
Sin ce m ost imp eda n ce fu n ct ion s for a m ode con st r a ined t o a n et wor k will ha ve th e
h igh est likelih ood some d ist a n ce fr om t h e or igin, it’s possible th a t t h e m ode would be
a ss igned t o, essen t ia lly, very sh ort t r ips (e.g., th e dist a n ce fr om a n origin zon e t o a r a il
n et wor k a n d t h en ba ck a gain m igh t be m odeled a s a h igh likelih ood of a t r a in t r ip even
t h ough su ch a t r ip is ver y u n lik ely).
F or ea ch m ode t h a t is con st r a in ed t o a n et work , sp ecify t h e m in im u m a bsolu t e
imp eda n ce. The u n its will be th e sa m e a s t h a t specified by th e m ea su r em en t u n its . The
defa u lt is 2 m iles. If t h e u n it s a r e dis t a n ce, t h en t r ip s will on ly be a lloca t ed t o t h ose zon e
pairs t ha t a re equal to or great er in dista nce tha n t he minimu m specified. If th e units a re
t r a vel t ime or s peed, t h en t r ips will on ly be alloca t ed t o t h ose zon e pa irs t h a t a r e fa r t h er
a pa r t t h a n t h e dis t a n ce t h a t wou ld be t r a veled in t h a t t im e a t 30 m iles per h ou r . If t h e
u n it s a r e cost , t h en t h e r ou t in e ca lcu la t es t h e a ver a ge cost per m ile a lon g t h e n et wor k a n d
on ly a lloca t es t r ip s t o t h os e zon e p a ir s t h a t ar e fa r t h er a p a r t t ha n t h e d is t a n ce t h a t wou ld
be t r a veled a t t h a t a ver a ge cost .
Ap p l y in g t h e R e l a ti v e Ac c e s s i b i li t y F u n c t i o n
To a pply th e r elat ive a ccessibilit y fu n ct ion , th e pa r a m et er ch oices for ea ch m ode a r e
en t er ed int o t h e m ode sp lit r ou t ine. All t r a n sit m odes a r e t h en con st r a ined
Once the mode split setup h as been defined and all tr an sit modes have been const ra ined to
a pr oper n et wor k , t h e m ode s plit r out in e can be r u n .
F igu r e 15.9 shows t h e t op 300 wa lkin g cr ime t r ips in Ba ltim or e Cou n t y est ima t ed
wit h t h e defau lt a ccessibilit y fu n ctions. As se en , t h e va st m a jor it y of walkin g t r ips a r e
int r a -zon a l (loca l). Ther e a r e on ly a cou ple of int er -zon a l walk ing t r ip lin ks sh own . The
defau lt im peda n ce fu n ct ion a ssign ed a ppr oxim a t ely 4% of t h e t r ips t o t h is m ode a n d t h e
result is man y int ra -zona l tr ips.
F igu r e 15.10 sh ows t h e t op 300 bicycle cr ime t r ips in Ba ltim or e Cou n t y. Ther e a r e
fewer t r ip s by bicycle a n d t h ey a ls o t en d t o be qu it e loca l. Th e im peda n ce fu n ct ion u sed for
bicycle tr ips a lloca t ed a ppr oxim a t ely 1% of a ll t r ips t o t h is m ode. Thu s, it’s less frequ en t
t h a n wa lkin g mode. Th er e a r e pr oport ion a t ely m or e int er -zon a l tr ips a m on g th e t op 300
t h a n for wa lk in g t r ip s, bu t t h ese t en d t o be qu it e sh or t (t r a vel bet ween a dja cen t zon es).
On t h e oth er h a n d, d r iving is t h e pr edomin a n t t r a vel m ode for t h e crim e t r ips
(Figu r e 15.11). Th e im peda n ce fu n ction u sed a llocat ed a pp r oxim a t ely 90% of th e t r ips t o
dr iving. The pa t t er n a lmost per fect ly r eplica t es t h e pr edict ed t r ip dist r ibut ion (see figur es
14.12 an d 14.20 in ch a pt er 14). Fu r t h er , th e t r ips a r e a lot lon ger. Am on g th e t op 300
link s, t h er e wer e n o int r a -zon a l dr iving t r ips. The u se of a lognorm a l fu n ct ion m inim ized
in t r a -zon a l t r a vel.
To a lloca t e bu s a n d t r a in t r ip s, h owever , it wa s n ecessa r y t o con st r a in t h em t o a
n et work . Sep a r a t e bu s a n d t r a in n et work s wer e obta in ed from t h e Ba lt im ore M et r opolit a n
Cou n cil. F igu r e 15.12 sh ows t h e Ba lt im or e bu s n et wor k a n d figu r e 15.13 sh ows t h e
pr edict ed bu s t r ip s su per im posed over t h e bu s n et wor k . Over a ll, a bou t 4% of t h e t ot a l
15.27
Figure 15.9:
Mode Split: Walking Crime Trips
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Mode Split: Bicycle Crime Trips
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Figure 15.11:
Mode Split: Driving Crime Trips
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Figure 15.12:
Baltimore Bus Network
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Figure 15.13:
Mode Split: Bus Crime Trips
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t r ips wer e a lloca t ed t o t h e bus m ode by th e a ccessibilit y fu n ct ion . As seen , th e t r ips t en d t o
be m oder a t e dist a n ces a n d t en d t o be close t o t h e bus n et wor k. Con st r a inin g th ese t r ips by
t h e n et work decrea ses t h e lik elih ood t h a t t h e r out in e wou ld a ss ign a pa r t icula r t r ip lin k
t h a t wa s fa r from t h e bu s w ork t o a bu s t r ip.
F ina lly, tr a in crim e t r ips wer e con st r a ined t o t h e t r a in n et wor k. F igu r e 15.14
su per imp oses t h e a ssign ed t r a in t r ips over t h e int r a -u r ba n r a il n et wor k. Overa ll, on ly 1%
of t h e t ot a l t r ip s wer e a lloca t ed t o t r a in m od e. Th er efor e, t h e n u m ber of t r ip s for a n y zon e
pair is quite sma ll. The trips ar e genera lly longer th an th e bus t rips, as m ight be expected,
a n d t h ey a ls o t en d t o fa ll a lon g t h e m a jor r a il lin es. S om e of t h e t r ip s st a r t qu it e fa r fr om
t h e r a il line s, s o it ’s p ossible t h a t t h ese a r e n ot r ea list ic r epr esen t a t ion s. Keep in m in d
t h a t t h is is a m a t h em a t ica l m odel a n d is fa r fr om per fect .
Overa ll, t h e m ode sp lit r ou t ine h a s pr odu ced a r ea sona ble app r oxim a t ion t o t r a vel
m odes for cr im e t r ip s. Sin ce t h er e wa s n o da t a u pon wh ich t o ca libr a t e t h e fu n ct ion s,
r ea sona ble gu esses wer e m a de a bou t t h e a ccessibilit y fu n ct ion . The m a t h em a t ica l model
pr odu ced a pla u sible, t h ough n ot p er fect , r epr esen t a t ion of t h ese a ss u m pt ion s, gen er a lly
fitting int o what we kn ow about crime tr avel pat tern s.
U se fu ln e s s o f Mo de S plit Mo de lin g
Th e m ode split m odel is a logica l ext en sion of t h e t r a vel d em a n d fr a m ewor k . F or
t r a n spor t a t ion pla n n in g, it is a n im por t a n t st ep in t h e pr ocess. Bu t , it a ls o is im por t a n t for
cr im e a n a lysis . F ir st , it a ddr esses t h e com plexit y of t r a vel by s epa r a t in g t h e t r ip s fr om
specific or igin s t o specific dest in a t ion s in t o dis t in ct m odes. In t h is sen se, it a dds m or e
r ea lism t o ou r u n der st a n din g of cr imin a l tr a vel beha vior . The J ou r n ey to Crim e lit er a t u r e,
wh ich h a s been u sed by cr ime a n a lyst s a n d crim ina l ju st ice r esea r ch er s t o “u n der st a n d”
crim in a l t r a vel beh a vior, is sim plis t ic in t h is r es pect. I t a ss u m es a sin gle m ode, t h ough
t h a t is r a r ely a r t icu lat ed by th e r esea r ch er s. By poin t ing ou t t ypica l tr a vel dist a n ces by
offenders circum vents t he critical question of how they made th e trip. This was, perha ps,
n ot a s crit ica l 50-60 year s a go wh en m ost cr imes wer e com m itt ed wit h in a sm a ller
com m u n it y a n d it cou ld be a s su m ed t h a t m os t offen d er s wa lk ed t o t h e cr im e loca t ion . Bu t
in p ost - Wor ld War er a , au t om obile t r a vel h a s becom e increa sin gly dom ina t e. This m odel
a ss u m es t h a t t h e va st m a jor it y of cr im e t r ips a r e t a k en by a u t omobile. Wh ile t h er e is
cu r r en t ly n o d a t a t o p r ove t h a t a ss er t ion , it follows fr om t h e t r a n s por t a t ion p a t t er n s t h a t
h a ve becom e widespr ea d in t h e U.S. a n d elsewh er e.
Th er e is a secon d r ea son wh y a n a n a lysis of crim e t r a vel m ode ca n be im por t a n t . If
t h e lim it a t ion s of t r a vel m ode in for m a t ion cou ld be im pr oved t h r ou gh bet t er a n d m or e
car eful d a t a collection by police a n d ot h er la w en for cemen t a gen cies, t h is t ype of an a lysis
cou ld be ver y u sefu l for policin g. For on e t h in g, it cou ld a llow m or e focu sed police
deploym en t . F or n eigh bor h oods wit h a pr edom in a n ce of wa lk in g cr im e t r ip s, t h en a police
foot pa t r ol cou ld be m ost effect ive. Con ver sely, for n eigh bor h oods wit h a pr edom in a n ce of
dr iving cr im e t r ips , t h en pa t r ol car s a r e pr obably th e m ost effective. Police int u it ively
u n der st a n d t h ese cha r a cter ist ics, bu t t h e crim e m ode sp lit m odel m a k es t h is m ore e xplicit.
15.33
Figure 15.14:
Mode Split: Intra-Urban Train Trips
Baltimore County
Train trips
Less than 0.1
0.1-0.019
0.02-0.029
0.03-0.039
0.04 or more
Rail network
Baltimore County
City of Baltimore
City of Baltimore
N
W
0
10
20 Miles
E
S
F or a n ot h er t h in g, a m ode split a n a lysis of cr im e ca n bet t er h elp cr im e pr even t ion
effor t s. As th e Ba lt im or e d at a su gges t , m a n y of t h e loca l (in t r a -zon a l) cr im e t r ip s a r e
com m it t ed a r oun d h ous in g pr ojects a n d in ver y low in com e com m u n it ies. Most like ly, th is
is a by pr odu ct of pover t y, la ck of loca l em ploym en t oppor t u n it ies , det er iora t ed h ous in g,
a n d even poor su r veilla n ce. S in ce t een a ger s a r e m or e lik ely t o n ot own vehicles, it m igh t be
exp ect ed t h a t t h e m a jor it y of t h ese loca l cr im e t r ip s a r e com m it t ed by ver y you n g
offen der s . Th is ca n be u sefu l in cr im e p reven t ion . Aga in , t h e “Weed an d Seed ” a n d a ft er sch ool p r ogr a m s a r e gen er a lly t a r get ed t o you t h fr om ver y low in com e n eigh bor h oods.
Wh a t is s h own by t h e m ode sp lit a n a lysis is p r obably th e crim e pa t t er n s a ss ocia t ed wit h
t h ese n eigh borh oods . Even t h ough it is in t u it ively un der st ood, t h e m ode sp lit a n a lysis
qu a n t ifies t h ese r elat ion sh ips in a n explicit m a n n er .
In sh ort , a m ode s plit a n a lysis of crim e t r ips is a n im por t a n t t ool for crim e a n a lyst s
a n d cr im in a l ju st ice r esea r ch er s. If cor r ect ly ca libr a t ed, it ca n h elp focu s police
en for cem en t a n d cr im e pr even t ion effor t s m or e specifica lly a n d ca n im pr ove t h e t h eor y of
cr im in a l t r a vel beh a vior .
H opefully, police depa r t m en t s will st a r t t o im pr ove t h e qu a lit y of da t a in cap t u r in g
likely t r a vel m odes wh ile t a kin g in ciden t r eport s. Even t h ou gh m ost police depa r t m en t s
h a ve a n it em sim ila r t o “Met h od of depa r t u r e”, t h er e h a s n ot been a lot of em ph a sis on t h is
in for m a t ion a n d m os t cr im e d at a set s a r e d eficien t on t h is in for m a t ion . H owever , wit h
imp r oved da t a will com e m or e a ccu r a t e a ccessibilit y fu n ct ion s a n d, hopefu lly, even r ea l
u t ilit y fu n ct ion s wh er e a ct u a l cost s a r e m ea su r ed. The expecta t ion is t h a t t h is will h a ppen
an d we should work towar ds accelerat ing th e process.
Li m i t a ti o n s t o t h e Mo d e S p l i t Me t h o d o l o g y
Th er e a r e a lso lim ita t ion s t o t h e m et h od, pa r t icu lar ly t h e a ggr egat e a ppr oa ch . The
a ggr egat e a ppr oa ch does not con sider ind ividu a ls, on ly pr oper t ies a ssociat ed wit h zon es
(e.g., aver a ge t r a vel t im e bet ween t wo zon es). As m en t ion ed ea r lier , t h e a ccessibilit y
fu n ct ion u s ed (or t h e u n d er lyin g u t ilit y t h eor y) is m u ch s im p ler for zon es t h a n for
in dividu a ls. Consequ en t ly, th e a n a lysis is cru der a t a n a ggrega t e level t h a n a t a n
in dividu a l level. Policy scen a r ios a r e m u ch m ore lim it ed wit h a ggrega t e m ode sp lit t h a n
with individu a l-level models. For exam ple, if an an a lyst wan t ed t o explor e wha t was t h e
lik ely effect of in cr ea sed pu blic su r veilla n ce on wa lk in g beh a vior by p ick pocket s, it is m or e
difficult t o do with aggregate dat a t ha n with individua l dat a. For example, it could be
h yp ot h esized t h a t a ct u a l p ick pocket s a r e m or e sen sit ive t o in cr ea sed pu blic su r veilla n ce
t h a n , say, ca r t h ieves, but t h is ca n ’t be tes t ed a t t h e a ggr egat e level. In st ea d, som e gener a l
cha r a cter ist ics a r e a ss igned t o all in dividu a ls (e.g., th e n u m ber of secur it y per son n el in a
zon e).
Secon d, t h e zona l m odel for m ode sp lit (as wit h t r ip d ist r ibu t ion ) ca n n ot exp la in
in t r a -zon a l t r a vel. Th e a ccessibilit y fu n ct ion is a pplied t o in t er -zon a l t r ip s; for in t r a -zon a l
t r ip s, it is in a ccu r a t e a n d gen er a lly d efa u lt s t o sim ple ch oices (e.g., wa lk in g, bik in g or
dr iving). For exam ple, bus or t r a in m ode can r a r ely be ap plied at a n int r a -zon a l level
beca u se t h er e a r e u su a lly t oo few n et wor k segm en t s t h a t t r aver s e a zon e a n d t h e s egm en t s
15.35
r a r ely st op wit h in t h e zon e. Wh ile t h is deficien cy a ls o a pplies t o t h e t r ip dis t r ibu t ion
m odel, th e depen den ce on a n et wor k for t r a n sit m odes, pa r t icu lar ly, lea d t o
un derestimat ion of tr an sit use for very short tr ips.
Th ird , th e zon a l mode split m odel ca n n ot explain ind ividu a l differ en ces. This goes
ba ck t o th e first poin t t h a t a sin gle u t ilit y fun ction is bein g a pp lied a t t h e zona l level.
Th u s, t h e valu e of t ime t o differ en t ind ividu a ls livin g in t h e sa m e zon e ca n n ot be exam ined ;
ins t ea d, everyon e is given t h e sa m e valu e.
F ou r t h , th e a ggr egat e m ode sp lit m odel does n ot a n a lyze tim e of da y ver y well. The
pr oba bilit ies a r e a ssign ed t o a ll t r ip s, r a t h er t h a n t o t r ip s t a k en a t pa r t icu la r t im es of th e
da y. To cond u ct t h a t a n a lysis , a n a n a lyst h a s t o brea k down crim es by t im e of da y a n d
m odel t h e differ en t per iods s epa r a t ely. Aside from being a wk wa r d, th e su m m ed t r ips n eed
to be balanced to ensur e tha t t hey sum t o th e tota l nu mber of tr ips.
F ift h , a n d fin a lly, t h e m ode split m odel, bot h a ggr ega t e a n d dis a ggr ega t e, ca n n ot
expla in linked trips (somet imes called t rip ch a in in g). An offen der m igh t lea ve h om e on e
da y, go ou t t o ea t , visit a fr iend , com m it a st r eet r obber y, go t o a ‘fen ce’ t o dist r ibut e t h e
goods, bu y dru gs fr om a dr u g dealer , an d t h en fina lly go h om e. The m ode sp lit m odel
t r ea t s ea ch of t h ese a s sep a r a t e t r ips; in t h e ca se of cr ime m ode sp lit, th er e a r e t h r ee
dis t in ct cr im e t r ips - comm it t in g t h e r obber y, sellin g t h e st olen goods t o th e ‘fen ce’, a n d
bu yin g th e dr u gs fr om t h e dr u g dealer . The m odel doesn ’t u n der st a n d t h a t t h ese a r e
r ela t ed even t s, bu t in st ea d a ss igns s epa r a t e m ode pr obabilit ies t o each t r ip. Th u s, it is
possible t o pr odu ce a bsu r d ch oices, s u ch a s dr ivin g t o t h e cr im e scen e, t a k in g t h e bu s t o t h e
dr u g dea ler , an d t h en bik in g home. In t h is r espect, t h e disa ggrega t e a pp r oach is equ a lly
fla wed as th e a ggr ega t e s in ce bot h t r ea t ea ch t r ip as in dep en den t even t s. Th e s olu t ion t o
th is lies in a ‘th ird genera tion’ of tr avel modeling in which individua l tr ip ma kers a re
sim u la t ed over a da y; activity-based m od eling, a s it is k n own , is s t ill in a r es ea r ch s t a ge
(Gou lia s, 1996; Miller , 1996; P a s, 1996). But , it will even t u a lly em er ge a s t h e domin a n t
t r a vel dem a n d m odelin g a lgorit h m .
Co n clu s io n s
Never t h eles s, m ode sp lit m odelin g ca n be a ver y useful a n a lysis st ep for crim e
a n a lysis . It r epr esen t s a n ew a ppr oa ch for cr im e a n a lysis a n d one wit h m a n y u sefu l
possibilities. It will r equ ire bu ilding more s yst em a t ic da t a ba ses in or der t o docu m en t
t r a vel m odes . Bu t , t h e possibilit ies t h a t it offer s u p ca n be im por t a n t for crim e a n a lyst s
a n d crim ina l ju st ice r esea r ch er s a like.
In t h e n ext cha pt er , th e fina l st ep in t h e cr ime t r a vel dem a n d m odel will be
discuss ed, net wor k a ssign m en t .
15.36
En d n ot e s fo r Ch ap te r 15
1.
Th er e is n o r ea son t h is da t a cou ld n ot be collect ed. Typ ica lly, m a n y p olice
depa r t m en t s collect infor m a t ion on ‘Met h od of depa r t u r e’ fr om a cr ime s cen e. Wh en
a police r epor t is t a k en , t h e vict im is som et im es a sk ed h ow t h e offen der left t h e
scene. In m ost ca ses, t h e infor m a t ion is not r ecor ded on t h e police for m s, or a t leas t
t h ose t h a t h a ve been exa m in ed. Th is in for m a t ion is pr oba bly u n r elia ble in a n y ca se
sin ce m a n y offen der s will t a k e t h e bu s or lea ve t h eir ca r n ea r by wh ile t h ey wa lk /r u n
t o th e crim e scene . St ill, if police depa r t m en t s wer e t o pu t m ore e ffort in t o
collecting this inform at ion a nd, perh aps, to validat ing it with a rr ested offenders,
t h en it is possible t o bu ild u p r elia ble da t a set s t h a t ca n be u sed t o m odel m ode
split . Un t il t h en , un for t u n a t ely, we ha ve to rely on t h eor y ra t h er t h a n eviden ce.
2.
In a su r vey of t h e t r a vel beh a vior of h om eless per son s, it wa s n ot ed t h a t m ost
h omeless wa lked ver y sh ort dis t a n ces over t h e da y even t h ough t h e va lu e of t h eir
t ime wa s ver y low. For lon ger t r ips, th ey st ill t en ded t o t a ke t h e bus r a t h er t h a n
wa lk. Su r vey on t h e t r a vel beha vior of very low incom e individu a ls. Ur ba n
P la n n in g Pr ogr a m , Un iver sit y of Califor n ia a t Los Angeles , 1987 (wit h Ma r t in
Wachs).
3.
In t est s, I did fin d t h a t t h e t wo models p r odu ced sim ila r pa t t er n s. Th ey wer e off in
t er m s of t h e m a gnit u de of t h e pr edict ed t r ips, but t h e r elat ive pa t t er n wa s ver y
sim ila r .
4.
H ou st on -Ga lvest on Ar ea Cou n cil. P er sona l com m u n ica t ion . 2004.
15.37