Generalized linear mixed models to analyze longitudinal data related to general health

Abstract

Generalized Linear Models (GLMs) overcome the limitations of traditional regression models by relaxing the assumption of normality. Although these models have been used extensively in research they still rely on the assumption that the responses are independent. Two models that relax the assumption of independence are Generalized Estimating Equations (GEE) models and Multilevel models. Both models are extensions of GLMs because they relate the predicted values to a linear predictor through an invertible link function. To accommodate the longitudinal correlated data, GEE models use quasi-likelihood estimation instead of the maximum likelihood approach used in GLMs. On the other hand, multilevel models are more appropriate to analyze data that has a hierarchical nested structure assuming the distribution of the responses to be a member of the exponential family. The 2-level random intercept and coefficient models and the 3-level random intercept model will be used to relate general health rating scores to seventeen demographic, recreational, behavioral and psychographic predictors. The health rating scores from the Add Health study were recorded for 3342 American participants in four cycles over a period of twelve years. The 3342 American participants are nested in the four health rating scores, which in turn are nested in 132 regional clusters.