Multi-Group Latent Class Analysis and Measurement Equivalence

Gungor D., KORKMAZ M. , SOMER O.

TURK PSIKOLOJI DERGISI, vol.28, no.72, pp.48-61, 2013 (Journal Indexed in SSCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 28 Issue: 72
  • Publication Date: 2013
  • Title of Journal : TURK PSIKOLOJI DERGISI
  • Page Numbers: pp.48-61
  • Keywords: Multi-group latent class analysis, measurement equivalence, discrete latent variable, MODELS


Social and behavioral research relies heavily on group comparison. Empirical demonstration of measurement equivalence is necessary when the attributes are compared. Latent class models are used when attributes are conceptualized as having discrete distributions and when discrete observed variables are used to estimate those distributions. This study illustrates the measurement equivalence in multi-group latent class analysis. Heterogeneous model imposes the same number of latent classes on two or more groups without imposing between-group parameter constraints. Homogeneous model is obtained by constraining the between-group conditional probabilities of the heterogeneous model equal. Measurement equivalence is established by demonstrating that the homogenous model fits the data as good as, if not better than, the heterogeneous model. Otherwise, the analysis moves to the exploratory mode to identify the offending equality constraints. The resultant model, if any, is called partial homogenous model. Using the Love Capacity dimension of Values in Action Inventory, the measurement invariance for latent class analysis is illustrated with a dataset involving 496 female and 237 male college students. A two-class model is chosen to represent both gender groups. Homogenous model was found to be the best fitting model. There was evidence for the equality of conditional probabilities between the groups, however, the equality constraint on unconditional probabilities was not supported, which led to the conclusion that the latent classes have the same meaning in both of the gender groups, i.e., measurement equivalence, but that the prevalence rates are gender specific.