Latent growth modeling is a statistical technique used in the structural equation modeling (SEM) framework to estimate growth trajectories. It is a longitudinal analysis technique to estimate growth over a period of time. It is widely used in the field of psychology, behavioral science, education and social science. It is also called latent growth curve analysis. The latent growth model was derived from theories of SEM. General purpose SEM software, such as

OpenMx OpenMx is an open source program for extended structural equation modeling. It runs as a package under R. Cross platform, it runs under Linux, Mac OS and Windows.S. Boker, M. Neale, H. Maes, M. Wilde, M. Spiegel, T. Brick, J. Spies, R. Estabroo ...

, lavaan (both open source packages based in R),

AMOS Amos or AMOS may refer to: Arts and entertainment * Amos Records, an independent record label established in Los Angeles, California, in 1968 * Amos (band), an American Christian rock band * ''Amos'' (album), an album by Michael Ray * ''Amos' ...

, Mplus,

LISREL LISREL (linear structural relations) is a proprietary statistical software package used in structural equation modeling (SEM) for manifest and latent variables. It requires a "fairly high level of statistical sophistication". History LISREL was ...

, or EQS among others may be used to estimate growth trajectories.

Background

Latent Growth Models Tucker, L.R. (1958) Determination of parameters of a functional relation by

factor analysis Factor analysis is a statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved variables called factors. For example, it is possible that variations in six observed ...

. ''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. Meredith, W., & Tisak, J. (1990). Latent curve analysis. ''Psychometrika'', 55, 107–122. 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. 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)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. for a comprehensive review) Although many applications of latent growth curve models estimate only initial level and slope components, more complex models can be estimated. 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 Exponential may refer to any of several mathematical topics related to exponentiation, including: *Exponential function, also: **Matrix exponential, the matrix analogue to the above * Exponential decay, decrease at a rate proportional to value *Exp ...

or Gompertz functions. Though straightforward to fit with versatile software such as

, 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. Discontinuous models where the growth pattern changes around a time point (for example, is different before and after an event) can also be fit in SEM software. Similar questions can also be answered using a

multilevel model Multilevel models (also known as hierarchical linear models, linear mixed-effect model, mixed models, nested data models, random coefficient, random-effects models, random parameter models, or split-plot designs) are statistical models of parame ...

approach.{{Cite book , last=Grimm , first=Kevin J. , url=https://www.worldcat.org/oclc/926062148 , title=Growth modeling : structural equation and multilevel modeling approaches , date=2017 , others=Nilam Ram, Ryne Estabrook , isbn=978-1-4625-2606-2 , location=New York, NY , oclc=926062148

References

* 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. * Singer, J. D., & Willett, J. B. (2003). Applied longitudinal data analysis: Modeling change and event occurrence. New York: Oxford University Press. * Fitzmaurice, G. M., Laird, N. M., & Ware, J. W. (2004). Applied longitudinal analysis. Hoboken, NJ: Wiley.

External links

OpenMxlavaanAMOSMPlusSemoPy
Structural equation models