Unit 1: GLM and regression
Topic: Introduction to the General Linear Model and bivariate
regression refresher
Objectives:
- Characterize a bivariate relationship along five dimensions
(direction, linearity, outliers, strength and magnitude)
- Describe how statistical models differ from deterministic
models
- Mathematically represent the population model and interpret its
deterministic and stochastic components
- Formulate a linear regression model to hypothesize a population
relationship
- Estimated a fitted regression line using Ordinary-Least Squares
regression
- Describe residuals and how they can describe the degree of our OLS
model fit
- Explain \(R^{2}\), both in terms of
what it tells us and what it does not
- Conduct an inference test for a regression coefficient and our
regression model
- Calculate a correlation coefficient \((r)\) and describe its relationship to
\(R^{2}\)
- Distinguish between research designs that permit correlational
associations and those that permit causal inferences
Readings:
Lectures:
Assignment 1: get started!!! (see below)
Unit 2: Assumptions & diagnostics
Topic: Regression assumptions and diagnostics
Objectives:
- Articulate the assumptions of the General Linear Model broadly and
least squares estimation and inference particularly
- Describe sources of assumption violation in the regression model
including: measurement error, non-linearity, heteroscedasticity,
non-normally distributed residuals, correlated errors, and
outliers.
- Articulate properties of residuals and describe their centrality in
understanding the regression model assumptions
- Conduct diagnostic tests on regression model assumption
violations
- Implement a consistent screening protocol to identify regression
model assumption violations
- Implement solutions to regression model assumption violations, when
appropriate
Readings:
Lecture:
Assignment 1:
Unit 3: Multiple regression
Topic: Multiple Regression
Objectives:
- Articulate the concepts of multiple regression and “statistical
adjustment”
- Distinguish between the substantive implications of the terms
“statistical control” and “statistical adjustment”
- Estimate the parameters of a multiple regression model
- Visually display the results of multiple regression models
- State the main effects assumption and what the implication would be
if it is violated
- Conduct statistical inference tests of single predictors ( \(t\)-test) and full model ( \(F\)-test) in multiple regression
- Decompose the total variance into its component parts (model and
residual) and use the \(R^2\) statistic
to describe this decomposition
- Describe problems for regression associated with the phenomenon of
multicollinearity
- Use visual schema (e.g., Venn diagrams) to assess regression models
for the potential of multicollinearity
- Use statistical results (e.g., correlation matrices or heat maps) to
assess regression models for the potential of multicollinearity
- Describe and implement some solutions to multi-collinearity
Readings:
Lecture:
Assignment 2:
Unit 4: Categorical predictors
Topic: Categorical predictors and ANOVA
Objectives
- Describe the relationship between dichotomous and polychotomous
variables and convert variables between these forms, as necessary
- Conduct a two-sample \(t\)-test
- Describe the relationship between a two-sample \(t\)-test and regressing a continuous
outcome on a dichotomous predictor
- Estimate a regression with one dummy variable as a predictor and
interpret the results (including when the reference category
changes)
- Estimate a multiple regression model with several continuous and
dummy variables and interpret the results
- Estimate an ANOVA model and interpret the within- and between-group
variance
- Do the same for an ANCOVA model, adjusting for additional continuous
predictors
- Describe the similarities and differences of Ordinary-Least Squares
regression analysis and ANOVA/ANCOVA, and when one would prefer one
approach to another
- Describe potential Type I error problems that arise from multiple
group comparisons and potential solutions to these problems, including
theory, pre-registration, ANOVA and post-hoc corrections
- Describe the relationship between different modeling approaches with
the General Linear Model family
Readings:
Lecture:
Assignment 3:
Unit 5: Interactions and non-linearity
Topic: Interactions and non-linearity
Objectives
- Describe in writing and verbally the assumptions we violate when we
fit a non-linear relationship in a linear model
- Transform non-linear relationships into linear ones by using
logarithmic scales
- Estimate regression models using logarithmic scales and interpret
the results
- Describe in writing and verbally the concept of statistical
interaction
- Estimate and interpret regression models with interactions between
categorical and continuous predictors
- Visualize interaction effects graphically
- Describe statistical power and Type II error challenges resulting
from interactions
- Estimate models with quadratic and higher-order polynomial
terms
Readings:
Lecture:
Assignment 4:
Unit 6: Model building
Topic: Model building
Objectives
- Translate research questions into question predictors, covariates,
outcomes and rival hypothesis predictors
- Develop work processes to address real life data which contain large
number of predictors
- Build a logical and sequential taxonomy of fitted regression
models
- Distinguish between model building and reporting, including best
practices for research transparency, replicability and integrity
- Present results in publication-ready tables and figures
- Write compelling and scientifically accurate interpretation of
results
- Describe power and limits of quantitative research
Readings:
Lecture:
Class cancelled on March 13 (David in Baltimore for
AEFP Conference)