Abstract
Growth curve modeling is a widely used technique in psychological, educational, and social science research. While mainstream estimators for growth curve modeling are based on normal theory, real-world data are often not perfectly normally distributed. To enhance estimation and inference under non-normal data conditions, various estimators have been developed. Among them, the asymptotically distribution-free (ADF) estimator does not require any distributional assumptions but performs inefficiently with small or modest sample sizes. To address this, we propose a distributionally weighted least squares (DLS) estimator within the growth curve modeling framework. The DLS approach integrates normal theory-based and ADF-based generalized least squares estimations, effectively balancing the data-driven information and normality assumptions. Simulation results reveal that the model-implied covariance-based DLS (DLSM) estimator provides more accurate and efficient estimates than the alternative methods examined, irrespective of the data distribution. Furthermore, the relative biases in standard error estimates and Type I error rates of the Satorra–Bentler test statistic (TSB) under DLSM are competitive with classical methods, such as maximum likelihood and generalized least squares estimation. Finally, we demonstrate the practical implementation of DLSM and the selection of an optimal tuning parameter through a bootstrap procedure, using a real data example.
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