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**Latent growth mixture modeling: A simulation study.**
*(English)*
Zbl 1153.65012

Report. University of Jyväskylä. Department of Mathematics and Statistics 111. Jyväskylä: University of Jyväskylä, Department of Mathematics and Statistics (Dissertation) (ISBN 978-951-39-2971-8/pbk). vii, 201 p. (2007).

Latent growth mixture 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. 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 is to examine the functionality of the linear LGM model with four repeated measurements, which is a typical case in longitudinal research. LGMM parameters are estimated using maximum likelihood estimation with robust standard error (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 is approached from three different viewpoints: 6mm

The aim of this dissertation is to examine the functionality of the linear LGM model with four repeated measurements, which is a typical case in longitudinal research. LGMM parameters are estimated using maximum likelihood estimation with robust standard error (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 is approached from three different viewpoints: 6mm

- 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)
- goog parameter estimation, which is evaluted using four different criteria: MSE, proportion of bias in MSE, bias of standard error.

Reviewer: Rózsa Horvàth-Bokor (Budapest)

### MSC:

65C60 | Computational problems in statistics (MSC2010) |

62F10 | Point estimation |

62-07 | Data analysis (statistics) (MSC2010) |

62F35 | Robustness and adaptive procedures (parametric inference) |

62J10 | Analysis of variance and covariance (ANOVA) |

62F03 | Parametric hypothesis testing |