Marginal Effects: A
long-form document on using marginal effects (marginal means and marginal
slopes) to improve interpretation of regression coefficients, especially
in the presence of an interaction. Presents as a Rosetta stone for Stata’s
margins command and several R packages including emmeans,
ggeffects, marginaleffects, and
interactions. Software: Stata and R.
Interpreting log transformations in regression: Interpreting coefficients from a linear regression model (or linear
mixed model) when the predictor and/or the outcome have been log
transformed. Software: R, though concepts could transfer to other
Moderation and Mediation via Regression: Although moderation and mediation typically arise in SEM/path analysis
frameworks, moderation can be addressed in regression, and mediation can
be conceptualized through regression.
IRR and ICC: Some notes on intra-class
correlation vs inter-rater reliability, as well as how to obtain the ICC.
Software: R, though concepts could transfer to other software.
The issue of collinear predictors: A visualization to see the potential negative effect of including
highly collinear variables in a model. Software: R, though
concepts could transfer to other software.
Stata, xt versus mixed model:
Econometricians usually use the xt framework to address
repeated measures. This document shows how to fit the equivalent of fixed
effects regression, between effects regression, and random effects
regression using linear regression (regress) and linear mixed
models (mixed). Software: Stata.
Nested versus crossed random effects:
Multiple random effects in a mixed model are typically defined as either
“nested” or “crossed”. This document shows that this is a false dichotomy
(nested random effects aren’t real!), as well as showing some nice
visualization. Software: R, though concepts could transfer to
Linear splines versus interactions: Models such as interrupted time series or diff-in-diff are often
considered special analyses. This document attempts to show that these are
just regression models with particular interactions. Software:
Stata, though concepts could transfer to other software.
Mediation with Survey data: To fit a
mediation model in Stata using complex survey data requires using
gsem. Unfortunately, the gsem command does not
support directly estimating direct, indirect and total effects. This
documents how to compute them. Software: Stata.
The “Divide by 4” rule: An additional tool in
interpreting logistic regression coefficients is the “Divide by 4” rule.
Software: Stata, though concepts could transfer to other
Response Surface Model Plotting: An
example of visualization after running a “response surface model”, aka
just regression with an interaction. Software: R.