Behavior Research Methods

, Volume 51, Issue 1, pp 172–194 | Cite as

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

  • Hsien-Yuan HsuEmail author
  • John J. H. Lin
  • Susan Troncoso Skidmore
  • Minjung Kim


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 RMSEAT_S_COV, TLIT _ S _ COV, and SRMRB maximizes the capacity to detect misspecifications in the between-covariance structure. Moreover, the use of RMSEAPS _ B, CFIPS _ B, and TLIPS _ 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 (RMSEAPS _ W, CFIPS _ W, TLIPS _ W, and SRMRW) had a practically significant sensitivity.


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


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Copyright information

© Psychonomic Society, Inc. 2018

Authors and Affiliations

  • Hsien-Yuan Hsu
    • 1
    Email author
  • John J. H. Lin
    • 2
  • Susan Troncoso Skidmore
    • 3
  • Minjung Kim
    • 4
  1. 1.Children’s Learning InstituteUniversity of Texas Health Science CenterHoustonUSA
  2. 2.Office of Institutional ResearchNational Central UniversityTaoyuan CityTaiwan
  3. 3.Department of Educational LeadershipSam Houston State UniversityHuntsvilleUSA
  4. 4.Department of Educational StudiesOhio State UniversityColumbusUSA

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