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Abstract
Latent growth modeling (LGM) is a method commonly used for analyzing longitudinal data, derived from confirmatory factor analysis models as a special case of structural equation modeling. However, it has several limitations, such as the inability to assess measurement invariance in a longitudinal study. This study develops a longitudinal item response theory-latent growth modeling (LIRT-LGM) model, which can be viewed as a combination of a LGM model and an IRT model for the purpose of investigating growth or change in the latent variable(s). To motivate this study, an illustrative example was provided comparing the performance of the LGM and LIRT-LGM in analyzing depressive symptoms. The LIRT-LGM was used to analyze the data with both the one-parameter logistic (1PL) and the two-parameter logistic (2PL) models. A simulation study was presented to provide more detailed information about the performance of the LIRT-LGM. Test lengths, sample sizes, and effect sizes were manipulated in the simulation study. Type I error and power were compared for the LIRT-LGM to the LGM models. An analysis of a real data set from a measure of depressive symptoms indicated the performances of the LGM and LIRT-LGM were not consistent. For empirical results, the mean and variance of the slope of the LGM were statistically significant, indicating that depressive symptoms increased and individual differences increased over three time points. On the other hand, the mean of the slope of the LIRT-LGM was not significant, but the variance of the slope of the 2PL version was significant. Results of the simulation indicated that the Type I error was controlled for most conditions. When the effect size was .3 with a sample size of 100 at = .05, the power was greater than .8. The results further showed that, when sample sizes, effect sizes, and test lengths increased, the performance of LIRT-LGM model was better than the LGM model.