Binary logistic regression is one of the most widely used statistical tools. The method uses odds, log odds, and odds ratios, which are difficult to understand and interpret. Understanding of logistic regression tends to fall down in one of three ways: (1) Many students and researchers come to believe that an odds ratio translates directly into…

We consider the problem of bias arising from conditioning on a post-outcome collider. We illustrate this with reference to Elwert and Winship (2014) but we go beyond their study to investigate the extent to which inverse probability weighting might offer solutions. We use linear models to derive expressions for the bias arising in different kinds…

Subjects with initially extreme observations upon remeasurement are found closer to the population mean. This tendency of observations toward the mean is called regression to the mean (RTM) and can make natural variation in repeated data look like real change. Studies, where subjects are selected on a baseline criterion, should be guarded against…

A linear model is often used to find the effect of a binary treatment D on a noncontinuous outcome Y with covariates X. Particularly, a binary Y gives the popular "linear probability model (LPM)," but the linear model is untenable if X contains a continuous regressor. This raises the question: what kind of treatment effect does the…

The latent growth model (LGM) is a popular tool in the social and behavioral sciences to study development processes of continuous and discrete outcome variables. A special case are frequency measurements of behaviors or events, such as doctor visits per month or crimes committed per year. Probability distributions for such outcomes include the…

Causal inference involves determining whether a treatment (e.g., an education program) causes a change in outcomes (e.g., academic achievement). It is well-known that causal effects are more challenging to estimate than associations. Over the past 50 years, the potential outcomes framework has become one of the most widely used approaches for…