Statistical Methods for Discrete Response, Time-Series, and Panel Data

This course covers a range of statistical techniques to model cross-sectional data with unordered and ordered categorical response, count response, univariate time-series data, multivariate timeseries data, longitudinal (or panel) data, and multi-level data from data science perspective. It teaches how to choose from a set of statistical techniques for a given question and to make tradeoffs between model complexity, ease of interpreting results, and implementation complexity in real-world applications.

In this class, you will:

• Discrete Response Models

  • Bernoulli, Binomial, Multinomial, and Poisson probability distributions
  • Maximum likelihood estimation
  • Profile likelihood ratio test
  • Inference for the probability of an event and the use of Wald, Wilson, Agresti-Coull, and Clopper-Pearson confidence intervals
  • Odds, relative risks, and odd ratios
  • Binary logistic regression model
  • Multinomial logistic regression model
  • Poisson regression model
  • Hypothesis testing for regression parameters
  • Log-odds of an event and its relationship to binary logistic regression models
  • Probability of an event in the context of binary logistic regression models
  • Variable (nonlinear) transformation and interactions
  • Contingency tables and the associated inference procedures
  • Test for independency
  • Model specification
  • Model evaluation
  • Model selection

• Time Series Models

  • Common time series patterns
  • Autocorrelation and partial autocorrelation
  • Notions and measures of stationarity
  • Exploratory time series data analysis
  • Time series regression
  • Akaike’s Information Criterion (and its bias corrected version) and Bayesian Information Criterion (BIC)
  • Model selection based on out-of-sample forecast error
  • Time series smoothing and filtering techniques
  • Stationary and non-stationary time series processes
  • Stationary Autoregressive (AR), Moving Average (MA), and Mixed Autoregressive Moving Average (ARMA) processes
  • ARIMA model
  • Seasonal ARIMA model
  • Estimation, diagnostic checking of model residuals, assumption testing, statistical inference, and forecasting
  • Regression with autocorrelated errors
  • Autoregressive Integrated Moving Average (ARIMA) Model
  • Unit roots, Dickey-Fuller (ADF) test, and Phillips-Perron tests
  • Spurious regression and Co-integration
  • Vector Autoregressive (VAR) Models

• Statistical Models for Panel (or Longitudinal) Data

  • Exploratory panel data analysis
  • Pooled OLS regression model
  • First-differenced regression model
  • Distributed lag model
  • Fixed-effect regression model
  • Random-effect regression model
  • Linear mixed-effect model

• Passing DataSci W203 with at least a B+ and having a very solid understanding of the probability and mathematical statistic concepts and techniques and linear regression modeling

• Hands-on experience in R

• Working knowledge of calculus and linear algebra

Syllabus