Modeling latent growth with multiple indicators: A comparison of three approaches.

Abstract

Latent growth curve models (LGCMs) are widely used methods for analyzing change in psychology and the social sciences. To date, most applications use first-order (single-indicator) LGCMs. These models have several limitations that can be overcome with multiple-indicator LGCMs. Currently, almost all multiple-indicator applications use the so-called second-order growth model (SGM; McArdle, 1988). In this article, we review the SGM and discuss 2 alternative, but less well-known, multiple-indicator LGCMs that overcome some of the limitations of the SGM: the generalized second-order growth model (GSGM) and the indicator-specific growth model (ISGM). In contrast to the SGM, the GSGM does not involve a proportionality constraint on the ratio of general to specific variance. The ISGM allows researchers to model indicator-specific growth. Both of these alternative models allow testing measurement invariance across time for state-variability components. We also present an empirical application regarding changes in self-reported levels of anxiety and discuss implications of the differences between the 3 models for applied research.

Oxytocin receptor gene (OXTR) variant rs1042778 moderates the influence of family environment on changes in perceived social support over time

“…We used multiple indicators Latent Growth Curve Modeling (LGCM) (Bishop, Geiser, & Cole, 2015) to examine inter-individual variability in the initial levels, i.e., intercept, of perceived social support and the rate of change, i.e., slope, in participants' perception of social support when growing 18 years older. A good fit of the data to the model is indicated by a CFI value ≥ 0.95 and an RMSEA value ≤ 0.05 (Hu & Bentler, 1999).…”

Distinguishing state variability from trait change in longitudinal data: The role of measurement (non)invariance in latent state-trait analyses

“…In Appendix C, we included a sample Mplus script showing the proper specification of the hybrid linear growth model presented in this paper. Different hybrid models were also discussed in detail by Bishop et al (2013).…”

“…In this case, the researcher should first assess whether some or all indicators show non-invariant parameters across time. The MTMS model can be extended to include growth factors for some or all indicators, depending on whether non-invariance is partial or concerns all indicators (see Figure 7B for a linear growth model with indicator-specific growth factors for all indicators; a sample Mplus script is available from Appendix C; for a more detailed description of indicator-specific LGC models, see Bishop et al, 2013). In addition to linear growth, researchers may try more complex growth or hybrid models that either specify more complex forms of growth (e.g., quadratic) or estimate the form of growth freely from the data (e.g., Tisak & Tisak, 2000).…”

“…(A formal derivation of this model based on concepts of LST theory is provided in Appendix A as well as in Bishop, Geiser, & Cole, 2013. ) It can be seen that as in standard (single-indicator) linear LGC models, there is an intercept factor (ξ 1 ) that reflects individual differences in the initial (time 1) trait scores and a slope factor (ξ 2 − ξ 1 ) that reflects individual differences in linear trait change across time.…”

“…Here, we show how this model can be formally defined based on concepts of LST theory to illustrate its mathematical relationship to the STMS model. For more details, see Bishop, Geiser, and Cole (2013). In the first step, we assume that all latent trait variables measured at the same time point t are congeneric: $${\xi }_{it}={\alpha }_{it}+{\lambda }_{it}{\xi }_t.$$…”