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Maximum Likelihood Methods
for the Social Sciences


Social science data seldom meet the assumptions of the linear regression model taught in introductory statistics courses. Our data often consist of discrete categorizations or counts of events, and may be correlated across periods or clustered by groups. Students will use maximum likelihood methods to derive models appropriate for their own data, learn to communicate their findings to a broad audience, and gain familiarity with statistical programming in R.


Maximum Likelihood Methods
for the Social Sciences

Offered every Fall at the
University of Washington



Fall 2013

Class meets:
TTh 4:30–5:50 pm
Johnson Hall 111


Aaron Erlich
(UW Political Science)

Lectures                 PDFs of slides are best viewed in Adobe Acrobat, rather than in your browser.

Topic 1

Introduction to the Course, Probability, and R


Supplementary material: You may want to read through Kevin Quinn’s matrix algebra and probability distribution reviews, or consult my undergrad lectures on discrete and continuous distributions. For a more general review, you can find the lecture notes for the CSSS Math Camp here.

There are also R code and data for exploratory data analysis using histograms and boxplots, code and data for a simple bivariate linear regression, and code and data for a multiple regression example.

Finally, you’ll find detailed instructions for downloading, installing, and learning my recommended software for quantitative social science here. Focus on steps 1.1 and 1.3 for now, and then, optionally, step 1.2.

Topic 2

Introduction to Maximum Likelihood


Supplementary material: There are additional slides on the Monty Hall problem in color and printable pdf formats. The R code to simulate heteroskedastic data and model that data using a heteroskedastic normal maximum likelihood is here.

Finally, for an extended discussion of Bayes Rule, with examples, see my undergrad lecture on probability.

Topic 3

Models of Binary Data


Supplementary material: There are separate R scripts for interpreting and selecting binary logit models, as well as an example dataset. The goodness of fit code also relies on R functions for computing the percent correctly predicted and making actual-versus-predicted plots, which you should place in your working directory.

Topic 4

Models of Ordered Data


Supplementary material: R code and data for an ordered probit, which produces this output.

Topic 5

Models of Nominal Data


Topic 6

Models of Count Data


Supplementary material: R code for count data models, including the Poisson, negative binomial, zero-inflated Poisson, and zero-inflated negative binomial models. The data for these examples comes either as a complete dataset, or a dataset with zero-count observations deleted.

Advanced Topic 1

Missing Data and Multiple Imputation


Advanced Topic 2

Introduction to Multilevel Models:
Maximum Likelihood and Bayesian Approaches


Supplementary material: For the curious, the R script used to construct the example plots in the first half of this lecture is here.

Self-Study Lecture 1

Introduction to Contingency Tables


Supplementary material: This lecture and the two below it introduce log-linear models of tabular data, and will not be presented as part of POLS/CSSS 510. They are posted here for interested students, especially for the use of mosaic plots to investigate cross-tabulated data (in this lecture, and in the third lecture on multidimensional tables). Students interested in a CSSS course on log-linear models should investigate CSSS 536.

Self-Study Lecture 2

Log-linear Models of Contingency Tables: 2D tables


Self-Study Lecture 3

Log-linear Models of Contingency Tables: 3D+ tables


Student Assignments

Problem Set 1

Due in class October 10, 2013

Problem Set 2

Due in class October 17, 2013

Problem Set 3

Due in class October 29, 2013

Supplementary material: Data for problem 1 in comma-separated variable format.

Problem Set 4

Due in class November 7, 2013

Supplementary material: Data for problem 1 in comma-separated variable format.

Problem Set 5

Due in class November 21, 2013

Supplementary material: Data for problem 1 in comma-separated variable format; data for problem 2 in R data format.

Problem Set 6

Due in class December 5, 2013

Supplementary material: Data will be provided.

Poster Presentations

November 26 to December 5

Requirments and suggestions for poster presentations will be presented in class.

Final Paper

Due December 11, 2013, 3:00 pm, in my Gowen mailbox

See the syllabus for paper requirements, and see my guidelines and recommendations for quantitative research papers.


Lab 1


Supplementary material: Code and Data. Here is a file about how to think about R: Thoughts on R .

Lab 2

R-Refresher Cont'd & MLE Intro

Supplementary material: Code. Another example of basic function writing: Linear Regression .

Lab 3

Binary Data

Supplementary material: Code and Data.

Lab 4

Binary Data GOF

Supplementary material: Code and Data.

Lab 5

Ordered and Unordered Data


Lab 6

Count Data

Code and Data.

University of Washington linkDepartment of Political Science
Center for Statistics and the Social Sciences
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Jefferson (2007-2011)