Evaluating fit indices in a multilevel latent growth curve model: A Monte Carlo study

Hsien Yuan Hsu*, John J.H. Lin, Susan Troncoso Skidmore, Minjung Kim

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


The multilevel latent growth curve model (MLGCM), which is subsumed by the multilevel structural equation modeling framework, has been advocated as a means of investigating individual and cluster trajectories. Still, how to evaluate the goodness of fit of MLGCMs has not been well addressed. The purpose of this study was to conduct a systematic Monte Carlo simulation to carefully investigate the effectiveness of (a) level-specific fit indices and (b) target-specific fit indices in an MLGCM, in terms of their independence from the sample size’s influence and their sensitivity to misspecification in the MLGCM that occurs in either the between-covariance, between-mean, or within-covariance structure. The design factors included the number of clusters, the cluster size, and the model specification. We used Mplus 7.4 to generate simulated replications and estimate each of the models. We appropriately controlled the severity of misspecification when we generated the simulated replications. The simulation results suggested that applying RMSEA T_S_COV , TLI T _ S _ COV , and SRMR B maximizes the capacity to detect misspecifications in the between-covariance structure. Moreover, the use of RMSEA PS _ B , CFI PS _ B , and TLI PS _ B is recommended for evaluating the fit of the between-mean structure. Finally, we found that evaluation of the within-covariance structure turned out to be unexpectedly challenging, because none of the within-level-specific fit indices (RMSEA PS _ W , CFI PS _ W , TLI PS _ W , and SRMR W ) had a practically significant sensitivity.

Original languageEnglish
Pages (from-to)172-194
Number of pages23
JournalBehavior Research Methods
Issue number1
Publication statusPublished - 2019 Feb 15
Externally publishedYes


  • Fit index
  • Model evaluation
  • Multilevel latent growth curve model
  • Multilevel structural equation modeling

ASJC Scopus subject areas

  • Experimental and Cognitive Psychology
  • Developmental and Educational Psychology
  • Arts and Humanities (miscellaneous)
  • Psychology (miscellaneous)
  • General Psychology


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