LATENT GROWTH MIXTURE MODELING: A SIMULATION STUDY

Latent growth curve modeling (LGM) combined with the latent classes (LGMM) in the SEM context, is the method under investigation in this study. This dynamic way of analyzing longitudinal data takes an increasingly central position in the social sciences, e.g. in psychology. Despite twenty years development of the theory behind the LGM and LGMM, these are novel methods in analyzing data in practice. With limited sample size the functionality of the model is unknown. The aim of this dissertation was to examine the functionality of the linear LGM model with four repeated measurements, which is a typical case in longitudinal research. LGMM parameters were estimated using maximum likelihood estimation with robust standard errors (MLR). The effect of differences between latent classes in mean values of latent components with varying sample sizes is examined in this study. Other affecting factors examined are reliability of observed variables, number of repeated measures, model construct and additional measurement points. The functionality of LGMM was approached from three different viewpoints: 1) problems in estimation of model parameters expressed as number of failed estimations and as the number of negative variance estimates, 2) the ability of AIC, BIC and aBIC information criteria and VLMR, LMR and BLRT statistical tests to decide the number of latent classes, and 3) good parameter estimation, which was evaluated using four different criteria: MSE, proportion of bias in MSE, bias of standard error, and 95 % coverage. The results of Monte Carlo simulations suggest that from information criteria AIC, BIC aBIC and VLMR and LMR tests, BIC is most useful with small sample sizes ( ) and aBIC with large sample sizes ( ). The few results suggest that the BLRT test could be useful in any situation. More investigation is needed to further support the functionality of this test. The study reveals that the estimation of LGMM fails only in a few cases, and problems in estimation appear mainly in the negative variance estimates. The results of the simulations suggest that it is possible to identify the true two-latent classes when SMD is at least 2, in which case reliability of observed variables should be high and the sample size should be relatively large. In that case estimation produce good parameter estimates. When SMD is 4 or 5, the probability in identifying the right two-latent-class solution instead of the wrong one-class solution is greater than .70 with the smallest sample size (n=50) using BIC in models with high reliability. To achieve reliable results in estimation, the sample size should be greater than 50. 500 < n 500 ≥ n

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