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Power Analysis for the Likelihood-Ratio Test in Latent Markov Models: Shortcutting the Bootstrap p-Value-Based Method
Dereje W Gudicha1, Verena D Schmittmann1, Fetene B Tekle1
1a Department of Methodology and Statistics , Tilburg University.
Multivariate Behavioral Research
|October 15, 2016
Summary
A new shortcut method makes power analysis for the bootstrap likelihood-ratio (BLR) test computationally feasible. This approach enables accurate sample-size determination for latent Markov models, improving statistical rigor.
Area of Science:
- Statistics
- Computational Statistics
- Psychometrics
Background:
- Latent Markov (LM) models identify unobserved states and transitions in longitudinal data.
- The bootstrap likelihood-ratio (BLR) test is rigorous for determining the number of latent states.
- Power analysis for the BLR test is crucial but computationally challenging.
Purpose of the Study:
- To develop a computationally feasible shortcut for power analysis of the BLR test.
- To enable accurate sample-size determination for LM models using the BLR test.
Main Methods:
- A novel shortcut method for power computation is presented.
- This method involves obtaining model parameters under the null hypothesis.
- Empirical distributions of the likelihood ratio are constructed via Monte Carlo simulations.
Main Results:
- The shortcut method is computationally feasible, unlike the proportion of bootstrap p values (PBP) method.
- The shortcut method's performance is evaluated against the PBP method.
- The shortcut method is demonstrated for sample-size determination.
Conclusions:
- The developed shortcut method offers a practical solution for BLR test power analysis.
- This facilitates more robust statistical inference in longitudinal studies using LM models.
- The method aids in determining appropriate sample sizes for research designs.
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