Development and estimation of a semicompensatory residential choice model with a
flexible error structure
Sigal Kaplan, Shlomo Bekhor, Yoram Shiftan
Faculty of Civil and Environmental Engineering, Technion
The Annual Meeting of the RSAI – The Israeli Branch, Tel-Aviv University, January 10, 2010
Motivation
When faced with
many alternatives,
people apply a
sequence of non-
compensatory
heuristics followed
by a compensatory
evaluation
(Payne , 1976).
Motivation
Residential choice models:
•
•
•
are mostly Multinomial logit
necessitate exogenous choice set formation
choice set formation independent of individual characteristics
Semi-compensatory models:
•
are based on Manski’s (1977) formula
P i G q 
•
•
•
•
Pq i S  Pq S G 

S G

have 2J-1 theoretical choice sets for J alternatives
are estimated only for a few alternatives
involve thresholds that are independent of individual characteristics
do not account for correlation patterns and population heterogeneity
Research objectives
To develop a semi-compensatory model for
residential choice
To accommodate correlations across alternatives and
random taste heterogeneity in the model
Model formulation
Universal realm of alternatives
Conjunctive
heuristic
Choice set
formation
stage
No
Viable
choice set
Choice
stage
Overtly specified
criteria thresholds
Unmanageable
choice set
Utility
maximization
Chosen
alternative
No choice
Preference
structure
Abort?
Yes
Model formulation
Proposed model:
Pq  i | G   Pq i | S q  Pq S q | G 
Observed choice i
Observed choice set S
Nested logit or random
coefficients logit
Observed combination of
criteria thresholds that yield
the choice set S
Multidimensional mixed
ordered-response model
Model formulation
MMOP-NL model:
d qi
r 1




 ' X j / r  
 ' X i / r 




e

  e

Q


j S q , j B r



LL  k , k ,  , s    ln   
 
s 1
N 
q 1

i S q 
  ' X j / s  


    e


 l 1  j S q , j B s


d m1q
 Mk 
'
'

 ...    m 1  1 Z 1q  1q   m1  1 Z 1q  1q


Kq
1q
1
 mk 1 

Mk




...   m 1   K' Z Kq  Kq

K
mk 1 
K 1q ,
    

, Kq d 1q

mK



  K Z Kq  Kq
d Kq
'




d mK q



Model formulation
MMOP-RCL:
d qi




 'X
Q


e i 

LL  k , k ,  , s    ln    
f  |  d   
 'X j 

q 1

i S q   e
 j S q


d m1q
 Mk 
'
'

 ...    m 1  1 Z 1q  1q   m1  1 Z 1q  1q


1q
Kq
1
 mk 1 

Mk




...   m 1   K' Z Kq  Kq

K
mk 1 
K 1q ,
    

, Kq d 1q

mK



  K Z Kq  Kq
d Kq
'




d mK q



Empirical context
Regional impact of students:
Positive
•
•
•
•
Demand for public transport
Revitalization of city center
Local economic growth
Local employment generation
Negative
• Demand for private cars
• Formation of seasonal communities
• Competition with low income groups
in the rental market
Survey design
Product: rental apartments
Population: Technion’s students
Survey type: stated preference
Survey duration: 1 month
Survey method: web-based
Incentive: 23 prizes ($1000)
Technion campus
Survey design
Respondent’s
information
Yes
Database
Synthetically
generated
apartment
dataset
Verification
No
SQL query
3 < j <100
No
Questionnaire
socio-economic, price perceptions,
travel attitudes and study preferences
Conjunctive choice set formation
Criteria thresholds specification (e.g.,
price, rooms, noise level, parking)
Yes
Respondent’s
criteria
thresholds and
chosen
apartment
Yes
Verification
Utility-based choice stage
Rank three most preferred
apartments from the choice set
No
Survey design
Model specification
Three criteria are represented in the estimated model:
•
•
•
apartment sharing
neighborhood
monthly rent price
Universal realm of alternatives: 200 apartments
•
•
adjacent to campus with little employment or leisure
far from campus with leisure activities, shopping and jobs
Explanatory variables:
•
•
personal characteristics
apartment attributes
Nested structure: floor number
Taste variation: renovation status, view and security bars.
Model estimation results
Variable description
MMOP-MNL
est. t-stat.
Apartment sharing threshold
Married
1.823
8.88
Male
-0.775
-5.85
Age (years)
0.026
2.75
Daily car availability
0.537
3.91
Daily trip frequency to campus
-0.635
-5.04
Study on-campus for better communication
-0.155
-3.95
$ 750 - 1000
0.756
3.71
$1000 - 1750
0.931
5.18
Roommates
-0.918
-5.13
Alone
1.073
4.47
Spouse
1.354
8.25
Haifa suburbs
-0.851
-2.96
-1.266
-6.59
Haifa outskirts
Location threshold
Price-quality ratio consciousness (factor)
-0.395
-7.55
Age (years)
0.055
4.37
Daily car availability
0.696
5.51
Medical campus
0.774
3.40
$ 750 - 1500
0.637
4.26
> $1500
0.995
5.76
Part-time job
-0.558
-3.46
Difference in job opportunities
0.113
3.36
Difference in green space availability
0.299
7.33
Study on-campus to improve efficiency (factor) -0.187
-5.68
Daily trip frequency to campus
-0.461
-3.74
MMOP-NL
est. t-stat.
MMOP-RCL
est. t-stat.
1.823
-0.775
0.026
0.537
-0.634
-0.155
0.756
0.930
-0.918
1.073
1.353
-0.851
-1.267
8.88
-5.83
2.75
3.91
-5.04
-3.95
3.70
5.18
-5.13
4.46
8.24
-2.96
-6.59
1.822
-0.773
0.026
0.539
-0.633
-0.154
0.753
0.93
-0.922
1.07
1.351
-0.852
-1.265
8.86
-5.83
2.74
3.92
-5.02
-3.93
3.69
5.17
-5.15
4.45
8.22
-2.96
-6.59
-0.395
0.055
0.696
0.774
0.637
0.995
-0.558
0.113
0.299
-0.188
-0.461
-7.54
4.36
5.50
3.40
4.25
5.76
-3.46
3.36
7.32
-5.68
-3.74
-0.395
0.055
0.698
0.776
0.636
0.994
-0.558
0.113
0.299
-0.188
-0.460
-7.53
4.36
5.51
3.40
4.23
5.75
-3.45
3.36
7.30
-5.68
-3.74
Model estimation results
Variable description
Price
Married
Male
Age (years)
$ 500-750
$ 750-1500
Part-time job
Daily car availability
Price-knowledge (factor)
> 4 apartment changes
Daily trip frequency to campus
currently reside with roommates
currently reside with alone/parents
currently reside with spouse
Haifa – upper class neighborhoods
Center of Israel
Non-motorized modes preference (factor)
Travel minimization preference (factor)
Cut-off point 200 a
250
350
350
400
450
500
550
600
650
700
MMOP-MNL
est. t-stat.
threshold
0.928
7.30
-0.393
-4.87
0.052
3.82
0.362
3.51
0.854
7.05
0.148
1.76
0.337
3.61
0.160
6.07
-0.547
-3.24
-0.533
-5.82
-0.330
-2.72
0.258
2.13
0.847
6.63
0.210
1.74
0.754
6.52
-0.038
-1.66
-0.083
-3.12
-0.295
-0.70
0.330
0.79
0.735
1.75
1.051
2.49
1.691
3.99
2.353
5.54
3.239
7.61
3.583
8.39
4.115
9.66
4.328
10.14
MMOP-NL
est. t-stat.
0.928
-0.393
0.052
0.361
0.853
0.149
0.337
0.160
-0.548
-0.533
-0.330
0.258
0.847
0.210
0.755
-0.038
-0.083
-0.296
0.329
0.733
1.049
1.689
2.351
3.236
3.580
4.111
4.325
7.29
-4.86
3.81
3.51
7.04
1.77
3.61
6.07
-3.24
-5.80
-2.71
2.12
6.62
1.73
6.53
-1.66
-3.11
-0.71
0.78
1.74
2.49
3.98
5.53
7.59
8.38
9.64
10.13
MMOP-RCL
est. t-stat.
0.926
-0.393
0.052
0.361
0.853
0.148
0.337
0.161
-0.547
-0.533
-0.329
0.260
0.847
0.208
0.754
-0.038
-0.083
-0.297
0.328
0.732
1.048
1.688
2.349
3.232
3.577
4.108
4.321
7.28
-4.85
3.81
3.5
7.02
1.76
3.61
6.06
-3.24
-5.79
-2.70
2.13
6.62
1.72
6.52
-1.66
-3.09
-0.71
0.78
1.74
2.48
3.97
5.52
7.59
8.37
9.63
10.12
Model estimation results
Correlation across thresholds
Rent price and neighborhood
0.415
fixed
Rent price and apartment sharing
0.674
fixed
0.313
fixed
Neighborhood and apartment sharing
Utility function
Rent price (monthly)
-0.001
-2.04
Number of rooms
0.584
12.00
Number of roommates
-0.394
-4.64
Walking time to campus
-0.083 -15.95
Quiet apartment
1.475 25. 90
Parking
0.298
4.43
Floor
-0.071
-3.09
Smoking allowed
-0.385
-5.16
Security bars (mean)
0.185
3.63
Security bars (standard deviation)
Stunning view (mean)
0.377
6.65
Stunning view (standard deviation)
Renovated (mean)
0.565
9.49
Renovated (standard deviation)
Air conditioner
0.290
5.01
Solar water heater
0.442
5.43
λ1 Non ground floor apartment
λ2 Ground floor apartment
Number of observations
1893
Number of parameters
68
Log-likelihood at zero
-20431.414
Log-likelihood at estimates
-10710.708
2
McFadden’s adjusted R
0.472
0.415
0.674
0.313
fixed
fixed
fixed
0.415
0.674
0.313
-2.19
8.81
-5.03
-10.55
11.52
4.70
-2.78
-5.05
2.51
4.79
7.88
4.77
5.30
14.19
8.30
1893
70
-20431.414
-10700.996
0.473
-0.001
0.634
-0.363
-0.089
1.507
0.346
-0.067
-0.412
0.209
0.213
-1.369
4.517
0.356
2.19
0.321
0.453
-
-0.001
0.453
-0.364
-0.062
1.134
0.257
-0.073
-0.31
0.104
0.267
0.468
0.223
0.348
0.802
0.638
fixed
fixed
fixed
-2.62
12.04
-3.76
-15.91
24.3
4.89
-2.74
-5.26
3.58
0.23
-1.71
3.02
2.82
4.70
5.27
5.36
1893
71
-20431.414
-10692.686
0.473
Conclusions
The proposed semi-compensatory model:
•
•
•
is applicable to large universal realms
includes a probabilistic choice set formation dependent on individual
characteristics
includes a flexible error structure
The model estimation results shows the importance of incorporating a
flexible error structure into semi-compensatory models
The proposed model is a viable option for real-world applications and it can
be readily incorporated within activity-based models and joint residential
and transportation models.
Thank you!
The Annual Meeting of the RSAI – The Israeli branch, Tel-Aviv University, January 10, 2010