Table 4.

Extensions of the Basic Random Coefficients Model for Change and Complementary Approaches: Purposes and Examples

Model/Approach	Purpose	Example
Time-varying Covariates	To estimate the effects of an individual’s changing status on trajectory parameters	Harrison, T., Blozis, S., & Stuifbergen, A. (2008). Longitudinal predictors of attitudes towards aging among women with multiple sclerosis. Psychology & Aging, 23, 823-832. doi: 10.1037/a0013802
Trajectories in Context	To estimate the effects of contextual factors on trajectory parameters	Black, M. M., & Krishnakuman, A. (1999). Predicting longitudinal growth curves of height and weight using ecological factors for children with and without early growth deficiency. Journal of Nutrition, 129, 539-543.
Latent Class Growth Model	To identify latent classes based on similar trajectories, without variation within class	Gill, T. M., Gahbauer, E. A., Han, L., & Allore, H. G. (2010). Trajectories of disability in the last year of life. New England Journal of Medicine, 362, 1173-1180.
Growth Mixture Model	To identify latent classes based on similar trajectories, allowing individual variation within class	Stoddard, S. A., Henly, S. J., Sieving, R. E., & Bolland, J. (2010). Social connections, trajectories of hopelessness and serious violence in impoverished urban youth. Journal of Youth and Adolescence. doi: 10.1007/s10964-010-9580-z
Parallel Process Model	To estimate multiple trajectories and relationships among growth parameters for each trajectory	Taylor, M. G., & Lynch, S. M. (2004). Trajectories of impairment, social support, and depressive symptoms in later life. Journal of Gerontology: Social Sciences, 59B, S238-S246. doi: 10.1093/geronb/59.4.S238
Categorical Responses	To estimate trajectories based on categorical responses by incorporating a link function into the model	Hedeker, D., & Mermelston, R. J. (2000). Analysis of longitudinal substance use outcomes using ordinal random-effects regression models. Addiction, 95 (Supp. 3), S381-S394. doi: 10.1080.09652140020004296
Generalized Estimating Equations	To estimate a population average model for longitudinal data using a semiparametric regression approach	Bohl, A. A., Fishman, P. A., Ciol, M. A., Williams, B., LoGerfo, J., & Phelas, E. A. (2010). A longitudinal analysis of total 3-year healthcare costs for older adults who experience a fall requiring medical care. Journal of the American Geriatrics Society, 58, 853-860. doi: 10.1111/j.1532-5415.2010.02816.x
Dynamic Process Models	To estimate parameters of dynamic systems using coupled differential equations models	Boker, S. M., & Laurenceau, J.-P. (2006). Dynamical systems modeling: An application to the regulation of intimacy and disclosure in marriage. In T. A. Walls & J.L. Schafer, Models for intensive longitudinal data (pp. 195-218). Oxford: University Press.