Analyzing longitudinal data with multilevel models: An example with individuals living with lower extremity intra-articular fractures.

Abstract

The use and quality of longitudinal research designs has increased over the past two decades, and new approaches for analyzing longitudinal data, including multi-level modeling (MLM) and latent growth modeling (LGM), have been developed. The purpose of this paper is to demonstrate the use of MLM and its advantages in analyzing longitudinal data. Data from a sample of individuals with intra-articular fractures of the lower extremity from the University of Alabama at Birmingham's Injury Control Research Center is analyzed using both SAS PROC MIXED and SPSS MIXED. We start our presentation with a discussion of data preparation for MLM analyses. We then provide example analyses of different growth models, including a simple linear growth model and a model with a time-invariant covariate, with interpretation for all the parameters in the models. More complicated growth models with different between-and within-individual covariance structures and nonlinear models are discussed. Finally, information related to MLM analysis such as online resources is provided at the end of the paper. Publisher's Disclaimer:The following manuscript is the final accepted manuscript. It has not been subjected to the final copyediting, fact-checking, and proofreading required for formal publication. It is not the definitive, publisher-authenticated version. The American Psychological Association and its Council of Editors disclaim any responsibility or liabilities for errors or omissions of this manuscript version, any version derived from this manuscript by NIH, or other third parties. The published version is available at http://www.apa.org/journals/rep NIH Public Access NIH-PA Author ManuscriptNIH-PA Author Manuscript NIH-PA Author ManuscriptLongitudinal designs have recently received more attention in a variety of different disciplines of psychology including clinical, developmental, personality and health psychology . In some areas, such as developmental psychology and personality psychology, a substantial number of recently published studies have been longitudinal Khoo, West, Wu, & Kwok, 2006). For example, Khoo et al. (2006) found that slightly more than one third of articles published in Developmental Psychology in 2002 included at least one longitudinal study, defined as having at least two measurement occasions. This proportion is double the proportion of longitudinal studies published in the same journal in 1990. Furthermore, more than 70% of the longitudinal studies published in Developmental Psychology in 2002 included three or more measurement waves.In this paper, we will focus on the analyses of multiwave longitudinal data, where multiwave is defined as more than two waves.With the growing use of longitudinal research, a number of methodological and statistical sources on the analysis of multiwave longitudinal data have appeared in the past decade (e.g., Bollen & Curran, 2006;Collins & Sayer, 2001; Singer & Willet, 2003), including discussions of traditional approaches such as repeated-measures Univariate Analysis ...

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