Nonlinear mixed-effects models offer a highly flexible framework for describing longitudinal data. The model is subject-specific, meaning that a model is specified at the individual level. The model characterizes the typical response trajectory, as well as those of each individual. Popular statistical software programs used to fit these models, although flexible in the different growth functions that one can specify, do not offer an alternative residual covariance structure to the standard one that specifies independence of residuals between occasions with constant variance across occasions. Harring and Blozis (2014) provide a way to specify several alternative covariance structures using SAS PROC NLMIXED. This paper evaluates the impact of considering alternative structures when fitting these models, including an interesting problem involving data that may not be missing at random.
Blozis, S. A., & Harring, J. R. (2018). Fitting nonlinear mixed-effects models with alternative residual covariance structures. Sociological Research Methods.
Understanding individual-level change through the basis functions of a latent curve model (Blozis & Harring, 2015)
Latent curve models are widely popular for the analysis of longitudinal data. These models allow researchers to study change and development in behavior at the level of the individual. This article takes a deeper approach to understanding the individual differences that are captured by the model. By using differential calculus, psychologists can gain greater insight into a longitudinal process at the level of the individual that goes beyond the typical interpretation of the model.
Blozis, S. A., & Harring, J. (2015). Understanding individual-level change through the basis functions of a latent curve model. Sociological Methods and Research.