A multi-level cross-classified model for discrete response variables

In many spatial analysis contexts, the variable of interest is discrete and there is spatial clustering of observations. This paper formulates a model that accommodates clustering along more than one dimension in the context of a discrete response variable. For example, in a travel mode choice context, individuals are clustered by both the home zone in which they live as well as by their work locations. The model formulation takes the form of a mixed logit structure and is estimated by maximum likelihood using a combination of Gaussian quadrature and quasi-Monte Carlo simulation techniques. An application to travel mode choice suggests that ignoring the spatial context in which individuals make mode choice decisions can lead to an inferior data fit as well as provide inconsistent evaluations of transportation policy measures.

[1]  C. Bhat.  A heteroscedastic extreme value model of intercity mode choice , 1995 .

[2]  Christoph W. Ueberhuber,et al.  Numerical Integration on Advanced Computer Systems , 1994, Lecture Notes in Computer Science.

[3]  Kelvyn Jones,et al.  Contextual Models of Urban House Prices: A Comparison of Fixed- and Random-Coefficient Models Developed by Expansion , 1994 .

[4]  Charles L Purvis,et al.  Incorporating Work Trip Accessibility in Nonwork Trip Generation Models in San Francisco Bay Area , 1996 .

[5]  Harald Niederreiter,et al.  Implementation and tests of low-discrepancy sequences , 1992, TOMC.

[6]  K. Jones,et al.  People and places: the multilevel model as a general framework for the quantitative analysis of geographical data , 1996 .

[7]  A. Stroud.  Approximate calculation of multiple integrals , 1973 .

[8]  Kelvyn Jones,et al.  Individuals and their ecologies: analysing the geography of chronic illness within a multilevel modelling framework , 1995 .

[9]  K. Train,et al.  Forecasting new product penetration with flexible substitution patterns , 1998 .

[10]  H. Goldstein.  Multilevel Statistical Models , 2006 .

[11]  Art B. Owen,et al.  Latin supercube sampling for very high-dimensional simulations , 1998, TOMC.

[12]  Anthony S. Bryk,et al.  Hierarchical Linear Models: Applications and Data Analysis Methods , 1992 .

[13]  H. Goldstein.  Multilevel covariance component models , 1987 .

[14]  Timothy G. Gregoire,et al.  Modelling Longitudinal and Spatially Correlated Data , 1997 .

[15]  Kelvyn Jones,et al.  Modelling Complexity: Analysing Between-Individual and Between-Place Variation—A Multilevel Tutorial , 1997 .

[16]  H. Wozniakowski.  Average case complexity of multivariate integration , 1991 .

[17]  H. Niederreiter,et al.  Tables of ( T, M, S )-Net and ( T, 5 )-Sequence Parameters , 1995 .

[18]  D. Feenberg,et al.  The Risk and Duration of Catastrophic Health Care Expenditures , 1992 .

[19]  Harald Niederreiter,et al.  Random number generation and Quasi-Monte Carlo methods , 1992, CBMS-NSF regional conference series in applied mathematics.

[20]  Henryk Wozniakowski,et al.  When Are Quasi-Monte Carlo Algorithms Efficient for High Dimensional Integrals? , 1998, J. Complex..

[21]  H. Niederreiter,et al.  Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing , 1995 .

[22]  W. J. Whiten,et al.  Computational investigations of low-discrepancy sequences , 1997, TOMS.

[23]  Chandra R. Bhat,et al.  Accommodating variations in responsiveness to level-of-service measures in travel mode choice modeling , 1998 .

[24]  K. Train,et al.  Mixed Logit with Repeated Choices: Households' Choices of Appliance Efficiency Level , 1998, Review of Economics and Statistics.

[25]  E. Braaten,et al.  An Improved Low-Discrepancy Sequence for Multidimensional Quasi-Monte Carlo Integration , 1979 .

[26]  H. Pan,et al.  A Multilevel Analysis of School Examination Results , 1993 .

[27]  Daniel McFadden,et al.  Modelling the Choice of Residential Location , 1977 .

[28]  I. Sloan.  Lattice Methods for Multiple Integration , 1994 .

[29]  M. Segal,et al.  An Assessment of Approximate Maximum Likelihood Estimators in Generalized Linear Mixed Models , 1997 .

[30]  R. Caflisch,et al.  Quasi-Monte Carlo integration , 1995 .

[31]  Paul Bratley,et al.  Algorithm 659: Implementing Sobol's quasirandom sequence generator , 1988, TOMS.

[32]  A. Owen.  Randomly Permuted (t,m,s)-Nets and (t, s)-Sequences , 1995 .

[33]  Marek J. Druzdzel,et al.  Computational Investigation of Low-Discrepancy Sequences in . . . , 2000 .

[34]  C. Bhat.  A heteroscedastic extreme value model of intercity travel mode choice , 1995 .

[35]  A. Owen.  Scrambled net variance for integrals of smooth functions , 1997 .

[36]  F. A. Seiler,et al.  Numerical Recipes in C: The Art of Scientific Computing , 1989 .

[37]  K. Fang,et al.  Number-theoretic methods in statistics , 1993 .

[38]  Harvey Goldstein,et al.  Multilevel Cross-Classified Models , 1994 .

[39]  Ita G. G. Kreft,et al.  Multilevel Analysis Methods , 1994 .

[40]  H Goldstein,et al.  Multilevel time series models with applications to repeated measures data. , 1994, Statistics in medicine.

[41]  William H. Press,et al.  The Art of Scientific Computing Second Edition , 1998 .

[42]  M. Batty,et al.  Spatial Analysis: Modelling in a GIS Environment , 1998 .