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Discrete Choice Models (DCM): An Object-Oriented Package for Ox
Matias Ekl¨f o Department of Economics Uppsala University, Sweden Melvyn Weeks Faculty of Economics and Politics University of Cambridge Sidgwick Avenue Cambridge, UK

August 25, 2005
Abstract DCM v1.1 (Discrete Choice Models) is a package, written in Ox, for estimating a class of discrete choice models. DCM represents animportant development for both the OxMetric and, more generally, microeconometric computing environment in making available a broad range of discrete choice models, including standard binary response models, with notable extensions including conditional mixed logit, mixed probit, multinomial probit, and random coefficient ordered choice models. Developed as a derived class of ModelBase, users may accessthe functions within DCM by either writing Ox programs which create and use an object of the DCM class, or use the program in an interactive fashion. We demonstrate the capabilities of DCM by using a number of applications from both the discrete choice literature. This document will serve as a manual for DCM. JEL Classification: C20; C25; C87; D00. Key Words: Discrete Choice Models, mixed logit,multinomial probit, ordered probit, Ox.

Contents
1 Introduction 1.1 Disclaimer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Availability and citation . . . . . . . . . . . . . . . . . . . . . . . 1.3 Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Overview 1 4 4 4 4 5

3 Data Input and Transformation 3.1 Loading data . . . . . . . . . . . . . . .3.2 Transforming between data structures . . 3.3 Panel data . . . . . . . . . . . . . . . . . 3.4 Data manipulation and variable selection 3.4.1 Creating Variables . . . . . . . . 3.4.2 Selecting Variables . . . . . . . .

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6 8 8 9 9 9 10 12 15 16 17 17 18 21 21 22 28 31 32 33 35 36 36 37 39 39 40 50 55 55 56 59 60 60

4 Model Specification 4.1 Some comments on model specification . . . . . . . . . . . . . . . 5 Estimation 6 Post-estimation 6.1 Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Elasticities and marginal effects . . . . . . . . . . . . . . .. . . . 6.3 Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Examples 7.1 Conditional, Nested, and Mixed logit models . . . . . . . . . . . . 7.2 Multinomial probit models . . . . . . . . . . . . . . . . . . . . . . 8 Monte Carlo experiments using Generate() 8.1 Example: Ordered probit models . . . . . . . . . . . . . . . . . . 9 DCM in OxPack for GiveWin 9.1 Limitationsin OxPack implementation . . . . . 9.2 Model Type . . . . . . . . . . . . . . . . . . . . 9.3 Variable selection and setting random coefficient 9.4 Estimation and model options . . . . . . . . . . 9.5 Future plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . distributions . . . . . . . . . . . . . . . . . . . . . . . . . .

A DCM member functions A.1 Exported memberfunctions . . . . . . . . . . . . . . . . . . . . . A.2 Non-exported member functions . . . . . . . . . . . . . . . . . . . B Technical appendix B.1 Inference on data structure . . . . . . . . . . . . . . . . . . . . B.2 Covariance matrix Specification in Multinomial Probit Models. B.3 Nested Logit . . . . . . . . . . . . . . . . . . . . . . . . . . . . B.4 Elasticities . . . . . . . . . . . . . . . .. . . . . . . . . . . . . B.4.1 Logit, Mixed Logit, and Nested Logit . . . . . . . . . . . . . . . . . . . .

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List of Tables
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 First example of DCM code . . . . . . . . . . . . . . . . . . . . . Example of ”multiple rows” structured database . . . . . . . . . . Example of ”single row” structured database . . . . . . . . ....