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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 2015

Class meets:
TTh 4:30—5:50 pm
Savery Hall 264


Aaron Erlich
(Political Science)

Section meets:
F 4:00—5:00 pm
Savery 117

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 Thursday 15 October 2015

Problem Set 2

Due in class Tuesday 27 October 2015

Problem Set 3

Due in class Thursday 5 November 2015

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

Problem Set 4

Due in class Tuesday 17 November 2015

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

Problem Set 5

Due in class Tuesday 24 November 2015

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 Tuesday 8 December 2015

Supplementary material: Data will be provided.

Poster Presentations

1 December 2015 to 10 December 2015

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

Final Paper

Due Tuesday 15 December 2015, 3:00 pm, both in my Gowen mailbox and by email

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

University of Washington link

CSSS Center for Statistics and the Social Sciences link

Chris Adolph & Erika Steiskal

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Jefferson (2007-2011)