Effect Size, Statistical Power and Sample Size Requirements for the Bootstrap Likelihood Ratio Test in Latent Class...

Area of Science:

• Statistics
• Psychometrics
• Social Sciences

Background:

• Determining the correct number of classes is crucial in latent class analysis (LCA).
• The bootstrap likelihood ratio test (BLRT) is a common method for class enumeration in LCA.
• Predicting statistical power and sample size for the BLRT in LCA remains a challenge.

Purpose of the Study:

• To provide practical effect size measures and power curves for the BLRT in LCA.
• To guide researchers in determining appropriate sample sizes for their studies.
• To enhance the reliability of class enumeration in LCA through data-driven power analysis.

Main Methods:

• Extensive Monte Carlo simulations were conducted to evaluate BLRT performance.
• Effect size measures and power curves were developed based on simulation results.
• Power curves and tables were generated for various population parameters and sample sizes.

Main Results:

• Practical effect size measures for the BLRT in LCA were established.
• Power curves were generated, illustrating the relationship between sample size, effect size, and power.
• Tables providing guidance for sample size selection were created.

Conclusions:

• The developed tools facilitate sample size planning for LCA studies using BLRT.
• Researchers can now proactively ensure sufficient statistical power to detect hypothesized latent classes.
• This research addresses a critical gap in the application of LCA, improving study design and interpretability.