After the foundational material is presented (roughly the first third of the class), I will introduce a large variety of statistical models and methods. I will choose these based on what makes sense from a pedagogical perspective at first, but as the semester goes on I will choose more and more material based on students interest and class projects.
For more information on the content of the class, see the detailed lecture notes online, which gives a general outline. Here's another version of some of the material:
Foundations
- What is statistics?
- What is political methodology?
- Models and a language of inference
- The role of simulation
- To solve probability problems
- to evaluate estimators
- to compute features of probability distributions
- to transform statistical results into quantities of interest
- Stochastic components (normal, log-normal, Bernoulli, Poisson, etc)
- The relationship between stochastic and systematic components and data generation processes
- Systematic components (linear, logit, etc.)
- Uncertainty and Inference
- Probability as a model of uncertainty
- Probability distributions, theory, discrete, continuous, examples
- Inference
- Inverse probability problems
- The likelihood theory of inference
- The Bayesian theory of inference
- Detailed example: Forecasting presidential elections
- Properties of maximum likelihood estimation (finite sample, asymptotic, etc.)
- Precision of likelihood estimates
Specific Topics
We will not get to all these topics, and the list of topics we do cover will likely include others than those listed here, depending on student interest.
- Discrete regression models
- Binary variables
- Interpreting functional forms
- Ordinal variables
- Grouped uncorrelated binary variables
- Event count models --- Correlated and uncorrelated events; over and under dispersion.
- Basic time series models
- Basic multiple equation models, including identification
- Multinomial choice models
- Models for selection bias, censoring, and truncation
- Models for duration
- Hurdle models
- Case-control designs
- Model dependence
- Matching as nonparametric preprocessing
- Rare events
- Neural network models
- An overview of MCMC methods
- Compositional data
- Missing data (item and unit nonresponse) problems
- Ecological inference (avoiding aggregation bias)
- Models for reciprocal causation and endogenity
- Empirical and hierarchical Bayesian analysis
- Time series cross-sectional data
- Models for interpersonal incomparability in surveys
- Text Analysis