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Maximum Likelihood Estimation
Fall 1997
PSCI 6000
Instructor: David A. Leblang; Wooten 145; x3231; [email protected]
Office Hours: R 2-4 and by appointment
Time and Place: R 6:30-9:20pm; Wooten 130
Course Description:
This seminar covers a wide range of topics in quantitative methodology. The focus of the
course is on maximum likelihood estimation; a technique of estimation which allows us
to develop a wide variety of substantively useful models. Among the topics we cover are
models for binary and ordered outcomes, event count models, and models for durations.
The great advantage of maximum likelihood estimation is that it provides a unified
approach to estimation which spans a wide number of statistical models. We will also
discuss models for panel data where the dependent variable is dichotomous.
The course begins by introducing matrix algebra and probability theory in the context of
ordinary least squares. Explicitly laying out the foundation of OLS will help you
understand where, why, and how this estimator breaks down. In addition, it will provide
you with an opportunity to develop computer skills. We will be using two statistical
packages in this course: STATA and S-PLUS. Most of the work will be done in STATA
where you will learn how to use matrix algebra and how to write likelihood functions.
The payoffs are enormous: once you learn how to do a bit of programming, your work
will no longer be limited to the canned procedures found in statistical software.
One of the great difficulties encountered in using MLE models is that these models are
nonlinear. The result is that parameter estimates are difficult to interpret and measures of
goodness of fit for the model are not straightforward. As a result, we will spend
considerable time in class discussing how to interpret, write-up, and display empirical
results.
The requirements for this course are as follows: 1. There will be problem sets each
week. Five of these will be picked up and graded (25%). 2. You will write a
quantitative paper addressing a substantive problem. This paper can be a replication style
(AJPS style) research note suitable for publication; it can be an empirical chapter for your
thesis or dissertation; or it can be a paper you are preparing for presentation at a
conference. Further information regarding the research note will be provided at a later
date. (50%). 3. There will be a take-home final examination. (25%)
The following texts are required and are (hopefully) available at the bookstore:
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Long, J. Scott. 1997. Regression Models for Categorical and Limited Dependent
Variables. Thousand Oaks, CA: Sage Publications.
Hamilton, Lawrence C. 1998. Statistics with Stata 5. Belmont, CA: Duxbury. (SWS)
Kennedy, Peter. 1992. A Guide to Econometrics, Third Edition. Cambridge, MA:
MIT Press. (GUIDE)
We will also be making extensive use of Michael Ward’s, Statistical Models of Political
Processes, Version 2.0. A copy will be placed in Wooten 125.
The following books have been ordered and are recommended:
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Hagle, Timothy. 1996. Basic Math for Social Scientists. Thousand Oaks, CA: Sage
Publications. Math refresher; will (re)-acquaint you with matrix algebra and calculus.
Eliason, Scott. 1993. Maximum Likelihood Estimation. Thousand Oaks, CA: Sage
Publications. Introduction to the process of mle and to a variety of models that can be
estimated using this technique.
Liao, Tim Futing. 1994. Interpreting Probability Models. Thousand Oaks, CA:
Sage Publications. Useful extension of chapter four in Long.
King, Gary. 1989. Unifying Political Methodology. Cambridge: Cambridge
University Press. Broad survey of maximum likelihood methods; if you get through
this book you know quite a bit.
Maddala, G.S. 1988. Introduction to Econometrics. NY: Macmillan. Everyone
needs at least one good econometrics text on their shelves. Maddala’s is quite good.
Do not purchase the second edition, the third edition should be out by the end of
November.
Lindsey, J.K. 1995. Introductory Statistics: A Modelling Approach. Oxford: Oxford
Scientific Publications. This book is great—it will help you through the basics of
probability theory and has a terrific introduction to the method of maximum
likelihood.
There are also a number of articles and book chapters that will be available in Wooten
125B.
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OUTLINE AND READINGS
(the numbers correspond to topics, not weeks in the semester)
1. Fundamentals: Regression in scalar form; OLS estimation; Interpretation of
slope coefficients.
Long, section 1.1
Kennedy, chaps 1-2
Hamilton, chaps 1 & 2
Homework Assignment 1: Data management, graphics, and bivariate regression in
STATA
2. Matrix algebra; Multiple regression in matrix form; OLS assumptions.
Handouts on matrix algebra
Hamilton chap 13
Kennedy, chap 3.
Homework Assignment 2: OLS in matrix form in STATA
3. Basic assumptions of OLS, violations of assumptions, partial plots, residual
plots, outliers.
Long, chapter 2 (excluding maximum likelihood)
Kennedy, chaps 6,7,8,11
Hamilton, chap 6
Granato, Jim, Ronald Inglehart and David Leblang.1996. “Political Culture and
Economic Growth.” American Journal of Political Science.
REVIEW CALCULUS NOTES
Homework Assignment 3: Replicate Granato, et al.
4. Introduction to Maximum Likelihood Estimation.
Kmenta, Elements of Econometrics, section 6-2
Long, chapter 2 (maximum likelihood)
Green, Don. “Maximum Likelihood for the Masses,” The Political Methodologist
Homework Assignment 4: OLS via MLE
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5. Linear Probability, Logit, Probit.
Long, chap 3
Kennedy, chap 15
Homework Assignment 5: Comparison of linear probability, logit and probit
6. Interpretation of Coefficients, graphical techniques, residual plots.
Hamilton, chapter 10
Kaufman, Robert. 1996. “Comparing Effects in Dichotomous Logistic Regression: A
Variety of Standardized Coefficients,” Social Science Quarterly 77:90-109
Landwehr, James, Daryl Pregibon, and Anne Shoemaker. 1984. “Graphical Methods for
Assessing Logistic Regression Models.” (With discussion) Journal of the American
Statistical Association 79:61-71.
Maddala, G. S. 1995. “Specification Tests in Limited Dependent Variable Models.” In
Maddala, G.S., Peter C.B. Phillips, and T.N. Srinivasan (eds.), Advances in Econometrics
and Quantitative Economics. Oxford: Blackwell.
Homework Assignment 6: Drawing conditional effects plots in STATA; writing up
results.
7. Statistical inference and model comparison for MLE models.
Long, chapter 4
Kennedy, chapter 4
King, section 4-6
Homework Assignment 7: Testing nested and non-nested models; calculating AIC and
BIC in STATA
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8. Goodness of fit for MLE models.
Long, chapter 4
Veall, Michael and Klaus Zimmerman. 1996. “Pseudo-R2 Measures for Some Common
Limited Dependent Variable Models,” Journal of Economic Surveys 10:241-259.
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Windmeijer, Frank. 1995. “Goodness-of-Fit Measures in Binary Choice Models,”
Econometric Reviews 14:101-116.
Homework Assignment 8: Graphical Display of goodness of fit measures
9. Ordinal Outcomes: estimation, inference, interpretation, goodness of fit.
Long, chap 5
King, section 5.4
Franklin, Charles. 1992. “Measurement and the Dynamics of Party Identification,”
Political Behavior, September.
Homework Assignment: Inference and interpretation.
10. Nominal Outcomes: estimation, inference, interpretation, goodness of fit.
Long, chap 6
Palmer, Harvey and Guy Witten. 1996. “Heightening Comparativists’ Concern for
Model Choice: Electoral Behavior in Great Britain and the Netherlands.” American
Journal of Political Science
Homework Assignment: comparing nominal to ordinal outcomes
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11. Duration models (readings will be selected from).
Beck, Nathaniel. 1997. “Modelling Space and Time: The Event History Approach,” In
E. Scarbrough and E. Tanenbaum eds., Research Strategies in the Social Sciences.
Box-Steffensmeier, Janet and Bradford Jones. 1997. “Time is of the Essence: Event
History Models in Political Science,” American Journal of Political Science October.
Teachman, Jay and Mark Hayward. 1993. “Interpreting Hazard Rate Models,”
Sociological Methods and Research 21:340-71.
Petersen, Trond. 1991. “The Statistical Analysis of Event Histories,” Sociological
Methods and Research 19:270-323.
Wu, Lawrence and Nancy Brandon Tuma. 1991. “Assessing Bias and Fit of Global and
Local Hazard Models,” Sociological Methods and Research 19:354-87
Bennett, D. Scott. 1997. “Testing Alternative Models of Alliance Duration, 1816-1984,”
American Journal of Political Science.
Homework Assignment: Replication of Bennett (1997).
12. Panel designs with limited dependent variables.
Allison, Paul. 1994. “Using Panel Data to Estimate the Effects of Events,” Sociological
Methods and Research 23:174-99.
Alt, James, Gary King, and Curtis Signorino. 1997. “Estimating the Same Quantities
from Different Levels of Data: Time Dependence and Aggregation Bias in Event Process
Models.” Manuscript
Beck, Nathaniel, Jonathan Katz and Richard Tucker. 1997. “Beyond Ordinary Logit:
Taking Time Seriously in Binary Time-Series Cross-Section Models.” Manuscript
Beck, Nathaniel and Jonathan Katz. 1997. “The Analysis of Binary Time-Series Cross
Section Data and/or The Democratic Peace.” Manuscript.
Beck, Nathaniel and Richard Tucker. 1996. “Conflict in Space and Time: Time-Series
Cross-Section Analysis with a Binary Dependent Variable.” Manuscript
Homework Assignment: Comparing regular effects (estimates and standard errors) to
panel effects in logit.
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