The Impact of Measurement Noninvariance on Latent Change Score Modeling: A Monte Carlo Simulation Study

ABSTRACT

Measurement invariance (MI) overtime is required for meaningful interpretation of changes in the latent change score model (LCSM). In this simulation study, we investigate the impact of measurement noninvariance on the estimation of LCSM when proportional change model, dual change model, and their bivariate versions are used with mean composites or MI-assumed measurement models. The results show that even noninvariance in one item could result in severe bias in the LCSM parameter estimates and false statistical inferences (e.g., Type I error). However, the impact depends on the simulation factors, fitted models, and estimated parameters. For example, the intercept-factor mean is biased in proportional change model but not in dual change model. In bivariate LCSM the parameter estimates of only the noninvariant variable are biased except coupling effects. Model fit indices such as RMSEA and SRMR are insensitive to the ignored noninvariance. Discussions and implications of findings are presented.

KEYWORDS:

• Longitudinal data
• latent change score model
• dual change model
• longitudinal measurement invariance

Notes

¹ A supplement is available at https://www.usf.edu/education/faculty/faculty-profiles/eun-sook-kim.aspx that analytically shows the parameter estimates (e.g., proportional change coefficient and slope-factor mean) are biased under noninvariance in factor loadings and noninvariance in intercepts when mean composite scores are used in PCM and DCM.

² We reviewed 12 peer-reviewed journal articles in which LCSM was used. The list of articles is available at https://www.usf.edu/education/faculty/faculty-profiles/eun-sook-kim.aspx.

³ The Mplus code for each fitted model is presented in a supplement at https://www.usf.edu/education/faculty/faculty-profiles/eun-sook-kim.aspx.

⁴ The summary tables of the simulation results not shown in the paper (e.g., results under MI conditions; PCM, DCM, and BPCM under MNI conditions) are available as a supplement at https://www.usf.edu/education/faculty/faculty-profiles/eun-sook-kim.aspx.

Additional information

Funding

Authors received no financial support for the research.