POLS 606: Fall 2016
Maximum Likelihood Procedures
Course Description and Syllabus

 

 

 

B. Dan Wood

Time: 18:30-21:20 R

Office: 2098 Allen Building

Room: 2064 Allen Building

Office Hours: 2:30-3:00 T

Phone: 845-1610

 Course Description: This course is about the underlying theory and application of maximum likelihood (ML) procedures to social science research. There will be strong emphasis on the statistical theory of maximum likelihood, particularly during the first five weeks or so when we develop principles of specification, estimation, inference, measures of fit, and properties of the ML model. We shall strongly emphasize in this course that good social science involves an appropriate fit between substantive theory and the statistical model of uncertainty that is chosen to represent that theory. Maximum likelihood offers a range of possible models of uncertainty. Among the specific models to be discussed are the normal general linear model, models for non-normal disturbances (such as with logged data or rare events), logit and probit models for binary choice, discrete choice models for multiple nominal and ordinal alternatives (such as voting for multiple parties as in any system with more than two parties), event count models for dependent variables which are counts of the number of times an event occurs in some period of time (such as wars in a decade, coups in a year, court appointments in a presidential term, or incumbents defeated in an election), models for non-random selection (as when you observe the preferences of voters but not non-voters), and duration models (where the dependent variable is a period of time between start and end of a process). The applications are almost endless.

Course Requirements: The background required for the course is a good introduction to probability and statistical inference and at least one good regression course, preferably with emphasis on the matrix perspective. Additionally, some familiarity with linear algebra and calculus is assumed. If you lack these tools, then you should consider another course.

Readings: Readings for each of the topics covered will be assigned from the following.

Eliason, Scott R. 1993. Maximum Likelihood Estimation: Logic and Practice. Newbury Park: Sage. (This is one of the fairly inexpensive green Sage publications).

Long, J. Scott. 1997. Regression Models for Categorical and Limited Dependent Variables. Newbury Park.: Sage. (This provides an introduction to the theory of likelihood, as well as nice discussions of interpretation and applications of various methods).

Forbes, Catherine, Merran Evans, Nicholas Hastings, and Brian Peacock. 2010. Statistical Distributions, Fourth Edition. New York: John Wiley. (This is available online at http://onlinelibrary.wiley.com/book/10.1002/9780470627242 .)

Greene, William C. 2012. Econometric Analysis, 7th Edition. New York: Prentice Hall.

Many of the recommended articles cited in the course outline below can be printed from JSTOR at http://www.jstor.org . Those which cannot be printed from JSTOR will be provided for Xeroxing.

Obtain data to replicate the analyses in the Long book by clicking here.  Obtain data for the project assignments by clicking here.  Obtain lecture notes in PDF format by clicking here.

Course Grade: The course grade will be based on three components:

Homework- 1/10
Midsemester Examination- 3/10
Final Examination- 3/10
Research Project- 3/10

All homework assignments will be graded on a good faith effort basis, and receive full credit (95) if this seems apparent from the work. An empirical research paper using one of the methods taught in this class is due electronically on December 6th. We shall discuss the research paper in more detail later. However, a synopsis of the proposed work is due prior to the midsemester exam. The midsemester and final examinations will be take home. The midsemester will be given out via email on the first Monday after topic 5 below and is due the following Tuesday. Homework for topic 5 is due on the Monday the exam is distributed. There will be no class during the period of the exam. The final exam will be given out via email on December 5th and is due on December 9th.

Course Outline: The following topics will be covered in the order specified at a pace consistent with your understanding. You should complete the assigned reading prior to the class in which it will be discussed. 

  1. Introduction to Probability Models and Likelihood

    Read Eliason, chapter 1; Long, chapter 1

    RECOMMENDED:
    --King. 1989. Unifying Political Methodology. The Likelihood Theory of Statistical Inference.  Chapters 1 and 2

    DO: Fundamentals of STATA.  Click here for STATA Assignment 1. Fundamentals of R. Click here for R Assignment 1.


  2. Review of Probability Distributions and Likelihood (continued)

    Read Forbes, Evans, Hastings, and Peacock, chapters 1-3; browse Forbes, Evans, Hastings, and Peacock, chapters 4-45; Greene, chapter 14, pp. 509-522 (look over Greene Appendix B).

    --King. 1989. Unifying Political Methodology. The Likelihood Theory of Statistical Inference.  Chapter 3

    DO    : Probability distributions and estimating a mean and variance using MLE. Click here for STATA Assignment 2. Click here for R Assignment 2.


  3. Maximum Likelihood Estimation: The Normal General Linear Model

    ASSIGNED- Eliason, chapters 1-3; Long chapter 2, 4; Greene, remainder of chapter 14 (look over Greene, Appendix E)

    RECOMMENDED-
    --King. 1989. Unifying Political Methodology. The Likelihood Theory of Statistical Inference.  Chapters 4.1-4.5
    --Kmenta. 1986. Elements of Econometrics (2nd edition), Chapter 6-2
    --Judge et al. 1988. Introduction to the Theory and Practice of Econometrics, Chapter 6
    --Davidson and MacKinnon. 1993. Estimation and Inference in Econometrics. Chapter 8.
    --Cramer. 1986. Econometric Applications of Maximum Likelihood Methods. Chapter 2.

    DO: Estimating a linear regression using MLE. Click here for STATA Assignment 3. Click here for R Assignment 3.


  4. Maximum Likelihood Estimation: The Heteroskedastic and Autocorrelated General Linear Models

    ASSIGNED- Eliason, chapter 2; King, chapter 4.6-4.8; Greene, pp. 548-557.

    RECOMMENDED-
    --King. 1989. Unifying Political Methodology. The Likelihood Theory of Statistical Inference.  Chapters 4.6-4.8
    --Franklin. 1991. Eschewing Obfuscation? Campaigns and the Perception of Senate Incumbents. American Political Science Review, 85:1193-1214
    --White. 1980. A Heteroskedastic-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity. Econometrica 48:817--838

    DO: Estimating the heteroskedastic/autocorrelated linear regression using MLE. Click here for STATA Assignment 4. Click here for R Assignment 4.


  5. Continuous Distributions with Truncation: Gamma, Exponential, Weibull, Log Normal, Beta, and Truncated Normal Distributions

    ASSIGNED- Eliason, chapters 4-6; Greene, 1024-1025, 74-75, 165-167, 460-461, 1107; Forbes, Evans, Hastings, and Peacock, chapters 5, 14,19, 26,42.

    RECOMMENDED-
    --Brehm and Gates. 1993. Donut Shops and Speed Traps: Evaluating Models of Supervision on Police Behavior. American Journal of Political Science. 37: 555-81.
    --McDonald. 1984. Some Generalized Functions for the Size Distribution of Income. Econometrica. 52: 647-62.
    --Cameron and White. 1990. Generalized Gamma Family Regression Models for Long Distance Telephone Call Durations. In A. de Fontenay, M. Shugard, and D. Sibley, eds. Telecommunications Demand Modeling.     Amsterdam: North Holland.
    --    Salem and Mount. 1974. A Convenient Descriptive Model of Income Distribution. Econometrica. 42: 1115-28.

    ---DO: Models with non-normal disturbances. Click here for STATA Assignment 5. Click here for R Assignment 5.


  6. Models for Binary Choice: Logit and Probit

    ASSIGNED- Long, chapter 3; Greene, 681-715.
    Click here for Scott Long’s XPOST Excel Interpretation Tools 
    Scott Long has also developed interpretation tools for use in STATA. See http://www.indiana.edu/~jslsoc/spost13.htm . Simply install the SPOST module into STATA to use them. You might also be interested in Long’s other book which uses these tools extensively. Go to the following link for a description. http://www.stata-press.com/books/regression-models-categorical-dependent-variables/ 
    Click here for Gary King’s Clarify  interpretation tools for STATA. These can be installed from within STATA.
    Click here for the Zelig website which contains full documentation for interpretational tools in Zelig and R. It is installed as a package in R.
    Note also that STATA’s “margins” command adds considerable flexibility for interpretation.

    RECOMMENDED-
    --King. 1989. Unifying Political Methodology. The Likelihood Theory of Statistical Inference.  Chapters 5.1-5.3
    --Aldrich and Nelson. 1984. Linear Probability, Logit and Probit Models. Sage. Entire.
    --Maddala. 1983. Limited-Dependent and Qualitative Variables in Econometrics.     Cambridge: Cambridge University Press. Chapter 2.1--2.5.
    --Hosmer and Lemeshow. 1989. Applied Logistic Regression.     New York: John Wiley and Sons.
    --Ragsdale. 1984. The Politics of Presidential Speechmaking, 1949-1980. American Political Science Review. 78: 971-984.
    --Franklin and Kosaki. 1995. Media, Knowledge and Public Evaluations of the Supreme Court, in Lee Epstein, (ed), Contemplating Courts,     Washington DC: Congressional Quarterly Press.
    --McCarthy, McPhail, and Smith. 1996. Images of Protest: Dimensions of Selection Bias in Media Coverage of     Washington Demonstrations, 1982 and 1991. American Sociological Review. 61:478-499.
    --Zaller. 1992. The Nature and Origins of Mass Opinion.     New York: Cambridge University Press. Chapter 7. (Read the entire chapter, but focus on pp. 132-150).
    --Brooks and Manza. 1997.     U.S. Middle-Class Political Realignment, 1972 to 1992. American Sociological Review. 62: xxx-xxx.

    DO: Binary logit/probit. Click here to download examples of interpreting Probit and Logit using XPOST.  Click here for STATA Assignment 6.  Click here for examples of interpretation of Probit and Logit using Clarify. Click here for R Assignment 6 which includes interpretational tools using Zelig.


  7. Models with Multiple Choices: Multinomial Logit, Probit, and Ordered Probit

    ASSIGNED- Long, chapter 5, 6; Greene, 760-801.

    RECOMMENDED-
    --King. 1989. Unifying Political Methodology. The Likelihood Theory of Statistical Inference.  Chapters 5.4
    --Maddala. 1983. Limited Dependent and Qualitative Variables in Econometrics, pp. 34-46 and 62-64.
    --Whitten, Guy D. and Harvey D. Palmer. 1996. Heightening Comparativists' Concern for Model Choice: Voting Behavior in     Great Britain and the Netherlands. American Journal of Political Science 40:231-260.
    --Alvarez and Nagler. 1995. Economics, Issues and the Perot Candidacy: Voter Choice in the 1992 Presidential Election. American Journal of Political Science, 39:714-744.
    --Entwisle et al. 1995. Gender and Family Businesses in Rural     China. American Sociological Review. 60:36-57.
    --Hao and Brinton. 1997. Productive Activities and Support Systems of Single Mothers. American Journal of Sociology. xx (March): xxx-xxx.
    --Franklin and Kosaki. 1989. Republican Schoolmaster: The Supreme Court, Public Opinion and Abortion. American Political Science Review. 83:751-771.
    --Franklin and Jackson. 1983. The Dynamics of Party Identification. American Political Science Review. 77: 957-973.
    --Expensade and Fu. 1997. An Analysis of English Language Proficiency among U.S.     Immigrants. American Sociological Review. 62:xxx-xxx.

    DO: Multinomial Models for Discrete Outcomes. Click here for STATA Assignment 7.  Click here for examples of interpretation of Multinomial Logit, Ordered Probit, and Ordered Logit using Clarify. Click here for R Assignment 7 which includes interpretation in Zelig.


  8. Models for Count Data: Poisson and Negative Binomial Estimators

    ASSIGNED- Long, chapter 8 ; Greene, 802-829.

    RECOMMENDED-
    --King. 1989. Unifying Political Methodology. The Likelihood Theory of Statistical Inference.  Chapters 5.5-5.10
    --King. 1987. Presidential Appointments to the Supreme Court: Adding Systematic Explanation to Probabilistic Description. American Politics Quarterly. 15: 373--386.
    --King. 1989. Event Count Models for International Relations: Generalizations and Applications. International Studies Quarterly. 33: 123-147.
    --Sampson and Laub. 1996. Socioeconomic Achievement in the Life Course of Disadvantaged Men: Military Service as a Turning Point, Circa 1940-1965. American Sociological Review. 61:347-367.
    --Rasler, Karen. 1996. Concessions, Repression and Political Protest in the Iranian Revolution. American Sociological Review. 61:132-152.

    DO: Models for count data. Click here for STATA Assignment 8. Click here for examples of interpretation of Poisson and Negative Binomial regression using Clarify. Click here for R Assignment 8.


  9. Limited Dependent Variables: Censoring and Truncation

    ASSIGNED- Long, chapter 7; Greene, 833-860, 872-898.

    RECOMMENDED-
    --King. 1989. Unifying Political Methodology. The Likelihood Theory of Statistical Inference.  Chapters 9.1-9.3
    --Maddala. 1983. Limited-Dependent and Qualitative Variables in Econometrics.     Cambridge: Cambridge University Press. Chapter 9.
    --Heckman. 1979. Sample Selection Bias as a Specification Error. Econometrica. 47:153-161.
    --Dubin and Rivers. 1989/90. Selection Bias in Linear Regression, Logit and Probit Models. Sociological Methods and Research. November 1989/February 1990: 360-390.
    --Nakosteen and Zimmer. 1980. Migration and Income: The Question of Self-Selection. Southern Economic Journal. 46: 840-51.
    --Willis and Rosen. 1979. Education and Self-Selection. Journal of Political Economy. 87: S7-S36.
    --Tobin. 1958. Estimation of Relationships for Limited Dependent Variables. Econometrica. 26: 24-36.
    --Nakamura and Nakamura. 1983. Part-Time and Full Time Work Behavior of Married Women: A Model with a Doubly Truncated Dependent Variable. Canadian Journal of Economics. 229-57.
    --Rosett and Nelson. 1975. Estimation of the Two Limit Probit Regression Model. Econometrica. 43: 141-46.
    --Fair. 1978. A Theory of ExtrAssigned- Marital Affairs. Journal of Political Economy. 86: 45-61.
    --Quester and Greene. 1982. Divorce Risk and Wives' Labor Supply Behavior. Social Science Quarterly. 63: 16-27.
    --Witte. 1980. Estimating an Economic Model of Crime with Individual Data. Quarterly Journal of Economics. 94: 57-84.

    DO: Censoring and Truncation. Click here for STATA Assignment 9. Click here for R Assignment 9.


  10. Parametric Duration Models

    ASSIGNED- Greene, 861-869.

    RECOMMENDED-
    --Hosmer, David W. and Stanley Lemeshow. 1999. Applied Survival Analysis.     New York: Wiley.
    --    Cleves, Mario A., William W. Gould, and Roberto Gutierrez. 2002. An Introduction to Survival Analysis Using STATA. College Station, TX: STATA Press.
    --Box-Steffensmeier and Jones. 1997.  Time is of the Essence: Event History Models in Political Science.  American Journal of Political Science.  41: 1414-1461.
    --Box-Steffensmeier and Zorn.  2001.  Duration Models and Proportional Hazard Models in Political Science.  American Journal of Political Science.  45: 972-88.
    --Kieffer, N. 1988. Economic Duration Data and Hazard Functions. Journal of Economic Literature. 26: 646-79.
    --Heckman, J. and B. Singer. 1984. Econometric Duration Analysis. Journal of Econometrics. 24: 63-132.

    Do: Duration Models. Click here for STATA Assignment 10. Click here for R Assignment 10.