Linear and Non-Linear Mixed Models in Longitudinal Studies and Complex Survey Data

Correlated data are fairly common in health and social sciences. For example, clustered data arise when subjects are nested in clusters such as classrooms, hospitals, and neighborhoods; while longitudinal data result from multiple measures for the same subject over long period of time; whereas repeated measures data are involved in multiple measurements for the same subject over time or other dimension. Observations for the same cluster/subject are likely to be correlated (non-independent). Mixed models (also known as multilevel models or hierarchical models) including both fixed effects and random effects have been developed to deal with correlated data [1-3]. The random effect of one variable has a prior distribution with variance and varies randomly within the population; whereas the fixed effect of the variable is the average effect in the entire population, expressed by the regression coefficient.