User:Sjcphd/sandbox Latent growth modeling
Latent growth modeling (LGM, also called latent growth curve analysis) is a statistical technique in the structural equation modeling (SEM) framework. Its primary aim is to estimate longitudinal trajectories of change over time. It is widely used in the field of behavioral science, education, and social science. Since LGMs are a type of SEM, general purpose SEM software may be used to estimate LGMs.
Under certain conditions, the LGM is equivalent to a multilevel model or mixed model, so some similar questions can also be answered using these approaches [citation needed].
SEM background
[edit]Latent Growth Models [1] [2] [3] [4] represent repeated measures of dependent variables as a function of time and other measures. Such longitudinal data share the features that the same subjects are observed repeatedly over time, and on the same tests (or parallel versions), and at known times. In latent growth modeling, the relative standing of an individual at each time is modeled as a function of an underlying growth process, with the best parameter values for that growth process being fitted to each individual.
These models have grown in use in social and behavioral research since it was shown that they can be fitted as a restricted common factor model in the structural equation modeling framework.[4]
The methodology can be used to investigate systematic change, or growth, and inter-individual variability in this change. A special topic of interest is the correlation of the growth parameters, the so-called initial status and growth rate, as well as their relation with time varying and time invariant covariates. (See McArdle and Nesselroade (2003)[5] for a comprehensive review)
Although many applications of latent growth curve models estimate only initial level and slope components, these models have unusual properties such as indefinitely increasing variance. [citation needed] Models with higher order components, e.g., quadratic, cubic, do not predict ever-increasing variance, but require more than two occasions of measurement. It is also possible to fit models based on growth curves with functional forms, often versions of the generalised logistic growth such as the logistic, exponential or Gompertz functions. Though straightforward to fit with versatile software such as OpenMx, these more complex models cannot be fitted with SEM packages in which path coefficients are restricted to being simple constants or free parameters, and cannot be functions of free parameters and data.
Software packages
[edit]LGMs can be estimated using any statistical software package that can estimate SEMs, including OpenMx, lavaan (both open source packages based in the R), AMOS, SAS CALIS, Mplus, LISREL, or EQS.
References
[edit]- ^ Tucker, L.R. (1958) Determination of parameters of a functional relation by factor analysis. Psychometrika 23, 19-23.
- ^ Rao, C.R. (1958) Some statistical methods for the comparison of growth curves. Biometrics. 14, 1-17.
- ^ Scher, A.M., Young, A.C. & Meredith, W.M. (1960) Factor analysis of the electrocardiogram. Circulation Research 8, 519-526.
- ^ a b Meredith, W., & Tisak, J. (1990). Latent curve analysis. Psychometrika, 55, 107–122.
- ^ McArdle, J.J., & Nesselroade, J.R. (2003). Growth curve analysis in contemporary psychological research. In J. Schinka & W. Velicer (Eds.), Comprehensive handbook of psychology: Research methods in psychology (Vol. 2, p. 447–480). New York: Wiley.
- McArdle, 1989
- Willet & Sayer, 1994
- Curran, Stice, & Chassin 1997
- Muthén & Curran 1997
- Su & Testa 2005
- Bollen, K. A., & Curran, P. J. (2006). Latent curve models: A structural equation perspective. Hoboken, NJ: Wiley-Interscience.
- Curran, P. J., & Hussong, A. M. (2003). The use of latent trajectory models in psychopathology research. Journal of Abnormal Psychology, 112(4), 526 - 544.
- Curran, P. J., Obeidat, K., & Losardo, D. (2010). Twelve frequently asked questions about growth curve modeling. Journal of Cognition and Development, 11 (2), 121 - 136.
- Fitzmaurice, G. M., Laird, N. M., & Ware, J. W. (2004). Applied longitudinal analysis. Hoboken, NJ: Wiley.
- Preacher, K. J., Wichman, A. L., MacCallum, R. C., & Briggs, N. E. (2008). Latent growth curve modeling (No. 157). Sage.
- Singer, J. D., & Willett, J. B. (2003). Applied longitudinal data analysis: Modeling change and event occurrence. New York: Oxford University Press.