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Conditional Logit Models

Course Dates and Times

Monday 17 – Friday 21 February 2020, 09:00–12:30
15 hours over five days

Paul Thurner

paul.thurner@gsi.uni-muenchen.de

Ludwig-Maximilians-Universität München – LMU

Discrete choice models are the workhorse in consumer research, transport economics, and electoral research. This course offers an introduction to discrete choice modelling using appropriate statistical software packages.

Starting with binary as well as multinomial logit and probit models, the core objective of this course is the application of so-called conditional logit models, where attributes of the alternatives and characteristics of decision makers are taken into account.

You will learn a formal as well as an intuitive outline of the models. We will pay special attention to the verbal interpretation and visualisation of ‘Quantities of Interest’, e.g., conditional choice probabilities, (cross/direct) elasticities, willingness to accept, etc. Main application cases are electoral choices in multi-party systems. A wide range of exercises provide easy-to-imitate routines.

Tasks for ECTS Credits

2 credits (pass/fail grade) Attend at least 90% of course hours, participate fully in in-class activities, and carry out the necessary reading and/or other work prior to, and after, classes.

3 credits (to be graded) As above, plus complete daily assignments consisting of applications in STATA; to be handed in and graded on a daily basis.

4 credits (to be graded) As above, plus complete a take-home paper applying the methodology learned on this course to your own research question and data. Submission deadline: two weeks after the end of the course.


Instructor Bio

Paul W. Thurner is Professor of Political Science at the Geschwister-Scholl-Institut für Politikwissenschaft, Ludwigs-Maximilians-Universität München, where he directs the Chair for Empirical Political Science and Policy Analysis.

His main research interest is the statistical analysis of political choice behaviour (electoral choices, strategies of negotiation, network choices).

For more than fifteen years he has provided knowledge transfer workshops on Applied Discrete Choice Modelling (Conditional Logit, Nested Logit, Random Utility Models, Mixed Logit) and on Applied Political Network Analysis.

Discrete choice models are meanwhile the work horse in consumer research, transportation economics, and in electoral research. Conditional logit and probit models allow the researcher to use attributes of the choice alternatives as independent variables. As applied to electoral research, we are now able to specify candidates’ and parties’ policy positions and other attributes – beyond the usually used attributes of voters (sex, age, income etc). A major advantage of the underlying theory of these models is that it systematically connects demand side and supply side of electoral competition. A prominent example in electoral research is the position-taking efforts of parties/candidates on issues. In the context of the Downsian spatial theory of voting it is assumed that voters react to these positions by calculating the distance of their own position to the parties’ position. Comparing over all distances to all parties the voters are conceived to choose the party with the least distance. In the probabilistic setting of the discrete choice models, we can reformulate this expectation as follows: the lower the distance of voter i to a party j’s position in an issue k, the higher the probability that the voter chooses this party. Thus, contrary to case-specific variables like sex and age which are constant for a case, these variables vary across choice alternatives. We call them, therefore, alternative-specific variables.

When attributes of the alternatives are part of the theoretical model, theorizing as well as data handling and specification are more complex. On the theoretical side, we will outline the underlying random utility approach in order to capitalize on the enormous flexibility of these models. Their power lies especially in the consistent decision-theoretical foundation of the statistical model. Therefore, we familiarize attendants with the respective terminology and assumptions. We demonstrate how to derive substantially interesting research questions and hypotheses from this approach for electoral research in general, and for the spatial theory of voting more in particular. E.g., it will be shown how issue and / or idelogical distances (left-right dimensions) can be specified in different ways: issue-by-issue, quadratic or non-quadratic, city-block, euclidean, saliency-weighted or unweighted etc. We will also highlight features of these models so far rather neglected by the electoral research community – e.g. nested multinomial logit models, specification of alternative-specific issue and ideological distances etc. Finally, we will give an outlook to the potentials of advanced models like random coefficient (mixed logit) and rank-ordered logit models (for cases where respondents indicate a rank-order of alternatives).

As data handling is more demanding, we will spend sufficient time for acquainting participants with setting up data in the required way and to program their own hypotheses. Starting with binary logit and probit in a rather short warm-up part, we quickly turn to multinomial regression (MNL) considering individual voter attributes only. An in-depth understanding of the MNL is a prerequisite of the conditional logit model. We will provide a formal as well as an intuitive outline of these models. During the whole week, lectures and exercises in the lab will be combined. We demonstrate the application of these models mainly with Stata 12 or 13 . Therefore, Long/Freese (2014) is a good starting point for the preparation of the exercise sessions – but will be expanded substantially by using new features of Stata 13 and 14 (e.g., margins, marginsplot). Special attention will be given to the verbal interpretation and visualization of ‘Quantities of Interest’ (e.g., conditional choice probabilities, (cross/direct) elasticitiesetc.). Easy-to-imitate routines will be provided by a wide range of exercises. In the last days we also demonstrate how to specify discrete choice models with R and Limdep/Nlogit.

Basic knowledge of regression analysis and Stata is required. I suggest you use your own laptop with the suggested software installed. You will also have extensive opportunities to present, discuss and develop your own projects and datasets.

Basic knowledge of methodology and statistics is required.

You should be able to use Stata and to perform linear regression and binary logit.

See, e.g., Kohler/Kreuter (2012): Data Analysis Using Stata, Third Edition. Stata Press.

Day Topic Details
1 Introduction to Discrete Choice Modeling and Application Case

Lecture Introduction to Data Sets and Software

2 Random Utility Theory and the Logit and Probit Model (Binary and Multinomial)

Lecture Model Formulations, Methods of Interpretation

Lab Exercises, Stata Applications

3 Conditional Logit Model I

Lecture Model Formulation, Data Setup, Data Management in Stata, etc

Lab Exercises, Stata Applications

4 Conditional Logit Model II

Lecture Methods of Interpretation, Model Assumptions and Implications

Lab Exercises, Stata Applications

5 Special Features: Nested and Mixed Logit, Alternative-Specific Attribute Reactions, Rank-Ordered Logit etc.

Lecture Discussion of Model Extensions

Lab Exercises, Applications in R (and Limdep/Nlogit), etc

Day Readings
1

Train (2009), Chapters 1 and 2

Davis/Hinich/Ordeshook (1970)

Alvarez/Nagler (1998)

Thurner (2000)

2

Long / Freese (2014), Chapters 3–6

Stata Manual: ‘Margins’

3

Long / Freese (2014), Chapter 8

Thurner/Eymann (2000)

King et al. (2000)

Stata Manual: ‘Margins’

McFadden (1974)

Alvarez/Nagler (1998)

Dow/ Endersby (2004)

4

Long / Freese (2014), Chapter 8 [2006: Chapter 7]

Thurner (2000)

Adams / Merrill / Grofman (2005)

Mauerer / Thurner / Debus (2015)

Stata Manual: ‘Margins’

5

Glasgow (2001)

Heiss (2002)

Shikano / Herrmann / Thurner (2009)

See 'Literature' below for detailed references

Software Requirements

Stata 14

Hardware Requirements

None

Literature


Adams, James, Samuel Merrill, Bernard Grofman (2005)
A unified theory of party competition. A cross-national analysis integrating spatial and behavioral factors
Cambridge: Cambridge University Press

Agresti, Alan (2002)
Categorical data analysis (2nd ed.)
New York: Wiley-Interscience

Alvarez, R. Michael, Jonathan Nagler (1998)
When politics and models collide: Estimating models of multiparty elections
American Journal of Political Science 42(1): 55–96

Borooah, Vani K. (2002)
Logit and Probit. Ordered and Multinomial Models
Thousand Oaks: Sage (QASS 138)

Davis, O., M.J. Hinich, P.C. Ordeshook (1970)
An expository development of a mathematical model of the electoral process
American Political Science Review 64: 426–448

Dow, J.K., J.W. Endersby (2004)
Multinomial probit and multinomial logit: a comparison of choice models for voting research
Electoral Studies 23 (1): 107–122

Downs, A. (1957)
An Economic Theory of Democracy
Harper & Row, New York

Glasgow, Garrett (2001)
Mixed logit models for multiparty elections
Political Analysis 9 (2): 116–136

Greene, William H. (2008)
Econometric Analysis (6th ed.)
Upper Sadle River, NJ: Prentice Hall

Greene, William H., David A. Hensher (2010)
Modeling Ordered Choices: A Primer
Cambridge / New York: Cambridge University Press

Heiss, Florian (2002)
Structural choice analysis with nested logit models
Stata Journal 2(3): 227–252

Hensher, David A., John M. Rose, William H. Greene (2005)
Applied Choice Analysis: A Primer
Cambridge: Cambridge University Press

King,G., M. Tomz, J. Wittenberg (2000)
Making the most of statistical analyses: Improving interpretation and presentation
American Journal of Political Science 44: 347–61

Long, J. Scott, Jeremy Freese (2006)
Regression Models for Categorical Dependent Variables Using Stata (2nd ed.)
Stata Press

Long, J. Scott, Jeremy Freese (2014)
Regression Models for Categorical Dependent Variables Using Stata (3rd ed.)
Stata Press

Louviere, Jordan J., David A. Hensher, Joffre D. Swait (2000)
Stated Choice Methods: Analysis and Applications
Cambridge / New York: Cambridge University Press

Manski, C.F. (1977)
The structure of random utility models
Theory and Decision 8, 229–254

McFadden, D. (1974)
Conditional logit analysis of qualitative choice behaviour
In: Zarembka, P. (Ed.) Frontiers in Econometrics
Academic Press, New York

Mauerer, Ingrid, Thurner, Paul W., and Marc Debus (2015)
Under Which Conditions do Parties Attract Voters’ Reactions to Issues? Party Varying Issue Voting in German Elections 1987–2009
West European Politics, 38(6): 1251–1273

McFadden, D., K. Train (2000)
Mixed MNL models of discrete response
Journal of Applied Econometrics 15:447–470

McFadden, D. (1981)
Econometric models of probabilistic choice
In: Manski, C., McFadden, D. (Eds.): Structural Analysis of Discrete Data
MIT Press, Cambridge, MA

McFadden, D. (1974)
Conditional logit analysis of qualitative choice behaviour
In: Zarembka, P. (Ed.) Frontiers in Econometrics
Academic Press, New York

Shikano, Suzumu, Michael Herrmann, Paul W. Thurner (2009)
Strategic voting under proportional representation: Threshold insurance in German Elections
West European Politics 32,3: 630–652

Singh, Shane (2014)
Linear and Quadratic Utility Loss Functions in Voting Behavior Research
Journal of Theoretical Politics, 26:1, 35–58

Thurner, Paul W. (1998)
Wählen als rationale Entscheidung. Die Modellierung von Politikreaktionen im Mehrparteiensystem
Munich: Oldenbourg (Scientia Nova)

Thurner, Paul W. (2000)
The empirical application of the spatial theory of voting in Multiparty Systems with Random Utility Models
Electoral Studies 19, 4: 493–517

Thurner, Paul W., Angelika Eymann (2000)
Policy-Specific alienation and indifference in the calculus of voting: A simultaneous model of party choice and abstention
Public Choice 102: 51–77

Train, Kenneth (2009)
Discrete Choice Methods with Simulation
Cambridge / New York: Cambridge University Press

Tutz, Gerhard (2012)
Regression for Categorical Data
Cambridge / New York: Cambridge University Press

Recommended Courses to Cover Before this One

Summer School

Introduction to STATA

Advanced Topics in Applied Regression

Basics of Inferential Statistics for Political Scientists

Introduction to Generalised Linear Models

Advanced Topics in Applied Regression