Maximum Likelihood
for Social Science

Strategies for Analysis

By Michael Ward and John S. Ahlquist


This book has a simple goal: to introduce social scientists to the maximum likelihood principle in a practical way. This praxis includes a) being able to recognize where maximum likelihood methods are needed, b) being able to interpret results from such analyses, and c) being able to implement these methods both in terms of creating the likelihood and in terms of specifying it in a language that permits empirical analysis to be undertaken using the developed, MLE model. The book is aimed at the social sciences.


We take a resolutely applied perspective here, emphasizing core concepts, computation, and model evaluation and interpretation. While we have a chapter that builds out some of the important mathematical results we spend relatively little space discussing formal statistical properties. We made this decision for three reasons. First, we prefer to emphasize the powerful conceptual jump that likelihood-based reasoning represents in the study of statistics, one that enables us to move to a Bayesian setting relatively easily. Second, the statistics underlying the likelihood framework are well-understood and have been for decades. The requisite theorems and proofs are already collected in other excellent volumes so we allocate just a chapter for recapitulating them here. Third, and perhaps most importantly, we find that students learn more and have a more rewarding experience when the acquisition of new technical tools is directly bound up with the substantive applications motivating their study.

The things that make this book unique include a) an exclusive, applied focus on maximum likelihood procedures, b) extensive and repeated discussion of model selection and interpretation, emphasizing computational simulation and out-of-sample prediction, c) up-to-date social science examples, several of which are culled from our own applied work, d) the use of the R statistical computing environment for all examples and graphics, and a public, online repository for R code and datasets.

Book Materials


Concepts, Theory, and Implementation

This introduces Maximum Likelihood models, covering the basic theory, describes how they are implemented, and covers the application to binary variables.

1 Introduction to Maximum Likelihood


2 Theory and Properties of Maximum Likelihood Estimators


3 Maximum Likelihood for Binary Outcomes


4 Implementing MLE



Model Evaluation and Interpretation

This Part focuses on Model Evaluation and Model Selection, along with inference and the interpretation of MLE results.

5 Model Evaluation and Selection


6 Inference and Interpretation



The Generalized Linear Model

Herein we discuss the generalized linear model, and focus on ordered categorical variables, nominal data, and count data.

10 Strategies for Analyzing Count Data


7 The Generalized Linear Model


8 Ordered Categorical Variable Models


9 Models for Nominal Data



Advanced Topics

In this part, we focus on duration models and strategies for dealing with missing data.

11 Strategies for Temporal Dependence: Duration Models


12 Strategies for Missing Data



A Look Ahead

In this epilogue we briefly survey additional topics that can be attacked with a MLE perspective.



Please also see this related work: Spatial Regression Models