Fitting Latent Growth Models with Small Sample Sizes and Non-normal Missing Data.

Area of Science:

• Statistics
• Psychometrics
• Machine Learning

Background:

• Latent growth models (LGM) are crucial for analyzing developmental trajectories.
• Small sample sizes and non-normal missing data pose significant challenges in LGM analysis.
• Robust maximum likelihood (ML) estimators offer potential solutions for these data complexities.

Purpose of the Study:

• To evaluate the performance of robust ML estimators in small sample LGM with non-normal missing data.
• To identify the most suitable robust ML estimator for such conditions.
• To assess the impact of sample size on model fit indices.

Main Methods:

• Simulation study comparing robust ML estimators (MLR, MLMV) under various small sample sizes (N < 100) and non-normal missing data conditions.
• Evaluation of parameter estimates, standard errors, p-values, and goodness-of-fit indices (CFI, RMSEA, SRMR).

Main Results:

• Robust ML methods successfully accounted for non-normality even with very small sample sizes (N < 100).
• MLR demonstrated robustness to non-normality and missing data, providing accurate standard errors and parameter coverage.
• MLMV yielded the most accurate p-values for the Chi-square test statistic.
• Goodness-of-fit indices (CFI, RMSEA, SRMR) showed poorer performance as sample size decreased, potentially misindicating model fit for N < 60.

Conclusions:

• Robust ML estimators are viable for small sample LGM with non-normal missing data.
• MLR is recommended for overall parameter estimation accuracy and robustness.
• MLMV is preferred for accurate Chi-square test p-values.
• Caution is advised when interpreting fit indices in very small samples (N < 60).