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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 2016

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


Daniel Yoo
(Political Science)

Section meets:
F 3:30—4:50 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    

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    

The R code to simulate heteroskedastic data and model that data using a heteroskedastic normal maximum likelihood is here.

There are additional mini-lectures on two topics. The first is a review of Bayes Rule. The second presents the Monty Hall problem in color and printable pdf formats. Three versions of the Monte Hall simulation code are available: the first uses a loop and many small steps, the second uses a loop and more compact code, and the third uses lapply() to avoid looping.

Topic 3

Models of Binary Data    

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 predicted-versus-actual plots and ROC plots, which you should place in your working directory. An example trio of plots showing actual versus predicted probabilities, error versus predicted probabilities, and the ROC curve can be seen here.

Topic 4

Models of Ordered Data    

R code and data for an ordered probit, which produces graphics for expected value plots and first difference plots.

Topic 5

Models of Nominal Data    

R code for a multinomial logit, which produces graphics for expected value plots, first difference plots, and relative risk plots.

Topic 6

Models of Count Data    

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  

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    

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 13 October 2016

Problem Set 2  

Due in class Tuesday 25 October 2016

Problem Set 3  

Due in class Thursday 3 November 2016

Data for problem 1 in comma-separated variable format.

Problem Set 4  

Due in class Thursday 15 November 2016

Data for problem 1 in comma-separated variable format.

Problem Set 5  

Due in class Tuesday 29 November 2016

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

Problem Set 6  

Due in class Thursday 8 December 2016

Data will be provided.

Poster Presentations

29 November 2015 to 8 December 2016

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

Final Paper

Due Tuesday 13 December 2016, 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.


Lab 1

Review of Probability and Introduction to R Programming

Please take a look at this handout and data, especially if you are new to R or need a refresher. We will be going over a list of commands that are important to know for the course, using this as a starting point. You can also check out this reference by former TA, Aaron Erlich. If you're already comfortable in R, that's great. You may want to take a look at the tile and simcf packages that we will be using for most the course. Here is the code from Lab 1.

Lab 2

Introduction to Maximum Likelihood Estimation

Please take a look at this handout. Here is the code from Lab 2. Next week, I'll post the code earlier so you can have a chance to look at it before Friday. We'll then go over it in detail and cover as much ground as possible. For those of you having trouble installing simcf, there should be an updated version on Chris's website soon.

Lab 3

Maximum Likelihood Estimation in R

Here is the lab code and data for this week. Please take a look at it before Friday to get an idea of what we'll be covering. Since we did not cover logistic regression during Thursday's lecture, we will be spending more of our time finishing up our discussion from last week.

University of Washington link

CSSS Center for Statistics and the Social Sciences link

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