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.

Figures

Figure 1

Figure 1a. Data in Multivariate Format (SPSS) Figure 1b. Data in Univariate Format (SPSS)

Figure 2

Spaghetti plots of a Random Sample with 20 Participants

Figure 3

Figure 3a. The Visual Demonstration of τ00, τ11, and τ01 (τ00 > 0 and τ11 > 0) Figure 3b. The Visual Demonstration of τ00, τ11, and τ01 (τ00 = 0 and τ11 > 0) Figure 3c. The Visual Demonstration of τ00, τ11, and τ01 (τ00 > 0 and τ11 = 0) Figure 3d. The Visual Demonstration of τ00, τ11, and τ01 (τ00 > 0, τ11 > 0, and τ10 = τ01 > 0)

Figure 3

Figure 3a. The Visual Demonstration of τ00, τ11, and τ01 (τ00 > 0 and τ11 > 0) Figure 3b. The Visual Demonstration of τ00, τ11, and τ01 (τ00 = 0 and τ11 > 0) Figure 3c. The Visual Demonstration of τ00, τ11, and τ01 (τ00 > 0 and τ11 = 0) Figure 3d. The Visual Demonstration of τ00, τ11, and τ01 (τ00 > 0, τ11 > 0, and τ10 = τ01 > 0)

Figure 3

Figure 3a. The Visual Demonstration of τ00, τ11, and τ01 (τ00 > 0 and τ11 > 0) Figure 3b. The Visual Demonstration of τ00, τ11, and τ01 (τ00 = 0 and τ11 > 0) Figure 3c. The Visual Demonstration of τ00, τ11, and τ01 (τ00 > 0 and τ11 = 0) Figure 3d. The Visual Demonstration of τ00, τ11, and τ01 (τ00 > 0, τ11 > 0, and τ10 = τ01 > 0)

Figure 3

Figure 3a. The Visual Demonstration of τ00, τ11, and τ01 (τ00 > 0 and τ11 > 0) Figure 3b. The Visual Demonstration of τ00, τ11, and τ01 (τ00 = 0 and τ11 > 0) Figure 3c. The Visual Demonstration of τ00, τ11, and τ01 (τ00 > 0 and τ11 = 0) Figure 3d. The Visual Demonstration of τ00, τ11, and τ01 (τ00 > 0, τ11 > 0, and τ10 = τ01 > 0)

Figure 4

Decomposing the c_Agei*Timeti Interaction Effect