Simulation

Random stuff: Rademacher distribution A month or two ago, I saw this comic on xkcd: This just shows how folks might use different ways to say the same thing (something simple can appear complex and vice versa). And then, in that same week, I was reading an article that mentioned drawing a random variable from a Rademacher distribution– which was a distribution I had not heard of (w/c has a M = 0, SD = 1) and somehow the name alone made it sound complicated.

Introduction Logistic regression is often used to analyze experiments with binary outcomes (e.g., pass vs fail) and binary predictors (e.g., treatment vs control). Although appropriate, there are other possible models that can be run that may provide easier to interpret results. In addition, some of these models may be quicker to run. Some may say that this point is moot given the availability of computing power today but if you’ve ever tried to run a hierarchical generalized linear model with a logit link function and a binary outcome, you know that when using R (using glmer or nlme) this may take quite a long time (and cross your fingers that you don’t have convergence issues).

The other day in class, while talking about instances (e.g., analyzing clustered data or heteroskedastic residuals) where adjustments are required to the standard errors of a regression model, a student asked: how do we know what the ‘true’ standard error should be in the first place– which is necessary to know if it is too high or too low. This short simulation illustrates that, over repeated sampling from a specified population, the standard deviaton of the regression coefficients can be used as the true standard errors.