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Preface

The purpose of this course is to introduce students to advanced techniques in regression, statistical computation, and techniques in scientific reproducibility and transparency. Students in this course should be very familiar with linear regression, as well as the Gauss-Markov assumptions underlying the classical linear model (i.e., POL 682). In this course, we will consider a variety of regression techniques for categorical and limited data. It is essential to remain up-to-date on the readings, as well as apply the reviewed methods to existing data.

The course will progress through several related sections. The first part will focus on several theoretical factors pertaining to statistical inference. We will start by considering two fundamental approaches underlying inference, the likelihood principle and Bayes’ rule. We will also re-consider the linear model, the Gauss-Markov assumptions, and we will review several concepts and statistical distributions. In this section we will also consider the practical trade off researchers encounter pertaining to efficiency and bias.

In the second section, we will move to discrete dependent and limited variables. In practice, it is quite rare to encounter dependent variables that are continuous and normally distributed. In circumstances with binary, ordinal, and other multicategory dependent variables, the Gauss-Markov assumptions will be violated, thus rendering OLS an inappropriate choice. At this juncture, we will use both maximum likelihood (ML) and Bayesian methods to estimate logit, probit, multinomial logit/probit, and ordinal logit/probit models.

Political scientists often encounter datasets that involve event counts (e.g., war casualties, number of conflict events, elections won by a candidate). These variables rarely follow a normal distribution; instead, they are heavily skewed. After the logit/probit weeks, we’ll consider several type of count-oriented regression models, including the Poisson, Negative Binomial, and “Hurdle” models. We will then transition to censored and sample selection models.

In the final section, we will consider a variety of topics that extend the models from the previous weeks. For instance, “endogeneity” is a common problem to arise in applied settings – an independent variable is correlated with the error term. We’ll look this problem in several ways, followed with several common solutions. We will examine two-stage least squares, three-stage least squares, and matching methods.Finally, we will examine hierarchical models.

Three major points need to be emphasized. First, many of the statistical methods build on models discussed in previous weeks. It is essential to keep up-to-date on readings, and if there is something that confuses you, please see me as soon as possible. Second, I find that the best way to learn these techniques is to implement them. I strongly recommend you find a dataset and work with this dataset throughout the semester. Even if your analysis is not always substantively interesting, at the very least, you will have the code for future use. Third, I strongly encourage you to give yourself sufficient time to complete the course requirements. One of the worst ways to learn statistics is through cramming and completing assignments at the very last minute. As you likely know, I am flexible with due dates and generally accept late assignments. Don’t take advantage of this policy! Handing things in late and consistently placing other obligations before this class has the potential to adversely impact what you learn.