Topics and activities covered in the advanced statistics course

Week Number / Topics / Lectures and Tutorials / Assignments
1 /
  • Refresher of prerequisites: types of variables, descriptive statistics, sampling distributions and the ‘bootstrap’, hypothesis testing, significance and statistical power
  • Commentary on core statistical applications used across disciplines compared to applications that are mostly discipline-specific
/
  • Orientation lecture: discussion of course objectives, syllabus, textbook, topics covered, course evaluation, posting questions in the discussion boards, communicating with the instructor via course email, and office hours for consultation in person or via telephone
  • Two topic lectures
/
  • Submit a picture and a small biography to be shared with the other students, using as example a short biography posted by the instructor ( 7 days to submit)

2 /
  • Basics of Linear Algebra
  • Dealing with Missing Data: an introduction to multiple imputation
/
  • Two topic lectures
  • Computer tutorial on inspecting data, conducting univariate and bivariate analyses, and plotting of histograms, boxplots, barplots, and scatterplots

3 /
  • General Linear Model Revisited: unifying framework encompassing two-sample t-tests, analysis of variance (ANOVA), analysis of covariance (ANCOVA), and simple and multiple regression.
  • How the model parameters are actually estimated using matrix algebra
  • Assumptions and strategies to deal with violations of these assumptions
  • Issues of multiple predictors and model selection
  • Basic discussion on how linear models are used in ‘causal’ modeling (i.e. mediation and moderation)
/
  • Three topic lectures

4 /
  • General Linear Model Revisited (cont'd)
/
  • Computer tutorial that illustrated fitting models with combinations of continuous and categorical predictors, as well as identifying problems such as multicollinearity
/
  • Homework 1: Analyze a dataset in several steps that include inspecting the variables, conducting univariate and bivariate analyses, fitting some linear models, and writing results (7 days to submit)

5 /
  • Logistic Regression: proportions, odds, odds ratios, the binomial distribution, the likelihood function. Interpretation of model parameters as odds ratios. Extensions to ordinal and multinomial outcomes
  • Additional applications: classification and propensity scores in 'causal' modeling
/
  • Three topic lectures
/
  • Group assignment: peer-review of homework 1 (7 days to complete)

6 /
  • Generalized Linear Models: Introduction to poisson, negative binomial, zero-inflated, gamma, and beta-regression models
/
  • One topic lecture
  • Computer tutorials for fitting logistic models (both binary and binomial) and count models using poisson and negative binomial models

7 /
  • Linear Models Under Non-Independence: justification, marginal models (GEE), ‘multilevel’ or ‘hierarchical’ models (Linear Mixed Models)
  • Longitudinal or repeated measure analysis
/
  • Two topic lectures
/
  • Midterm exam: True/False/It depends questions; model interpretation questions; and analyses of three datasets using general linear, binary logistic, and binomial logistic models, respectively (7 days to submit)

8 /
  • Linear Models Under Non-Independence (cont'd): Using the Linear Mixed Model in the presence of 'nesting' in cross-sectional data, and in situations classically referred to as multivariate analysis of variance (MANOVA)
/
  • One topic lecture
  • Computer tutorial for fitting models with one and two levels of ‘nesting’
/
  • Group assignment: peer-review of midterm data analyses (7 days to complete)

9 /
  • Principal Components Analysis (PCA) and Exploratory Factor Analysis (EFA)
  • Commentary on statistical techniques used in survey instrument development
/
  • Midterm discussion lecture
  • One topic lecture

10 /
  • PCA and EFA (cont'd)
/
  • Computer tutorial illustrating an example of Exploratory Factor Analysis and computation of Cronbach's alpha
/
  • Homework 2: conduct a longitudinal analysis using either GEE or a linear mixed model. With a second dataset, conduct an EFA. Write up results (7 days to submit)

11 /
  • Structural Equation Models (SEM):
  • Introduction to the technique, advantages and limitations, and comparison of different software packages for it
  • Steps in SEM model fitting: model specification, identification, estimation, evaluation of fit, model modification, and interpretation
/
  • Two topic lectures
/
  • Group assignment: peer-review of homework 2 (7 days to complete)

12 /
  • Structural Equation Models (cont'd)
/
  • Computer tutorial with three examples: a confirmatory factor analysis; a path model with indirect effects; and a complex model with latent variables as well as indirect effects
/
  • Final exam: (7 days to submit): fitting of a confirmatory factor analysis model, and fitting of a path model. Write up results.

Notes:

Group assignments at Weeks 5, 8, and, 11 were implemented in the third iteration of the course (Summer 2012)

GEE (Generalized Estimating Equations): a robust technique to estimate regression-type models for situations with typically one level of nesting