We discuss fixed and random effects models in the context of educational research and set out the assumptions behind the two approaches. To illustrate the issues, we analyse the determinants of pupil achievement in primary school, using data from the Avon Longitudinal Study of Parents and...

We report the results of a Mendelian randomization study in which multiple genetic variants are used as instrumental variables to estimate the causal effect of body mass index on personal income in the presence of unobserved confounding. The data come from Understanding Society, a large-scale...

Structural mean models (SMMs) were originally formulated to estimate causal effects among those selecting treatment in randomised controlled trials affected by non-ignorable non-compliance. It has already been established that SMM estimators identify these causal effects in randomised...

Using data from the British Household Panel Survey, we illustrate how longitudinal repeated measures of binary outcomes are analysed using population average and subject specific logistic regression models. We show how the autocorrelation found in longitudinal data is accounted for by both...

Structural mean models (SMMs) are used to estimate causal effects among those selecting treatment in randomised controlled trials affected by non-ignorable non-compliance. These causal effects can be identified by assuming that there is no effect modification, namely, that the causal effect is...