Generalized linear mixed models for binary data: are matching results from penalized quasi-likelihood and numerical...

Area of Science:

• Statistics
• Biostatistics
• Computational Statistics

Background:

• Adaptive Gaussian Hermite quadrature (QUAD) is preferred for generalized linear mixed models with binary outcomes.
• Penalized quasi-likelihood (PQL) remains a frequently used alternative estimation method.
• Systematic evaluation is needed to compare bias between PQL and QUAD estimations.

Purpose of the Study:

• To evaluate if matching PQL and QUAD results indicates less bias in regression coefficients and variance parameters.
• To assess the impact of data characteristics on the bias of PQL and QUAD estimations.
• To determine if similarity between PQL and QUAD estimates predicts reduced bias.

Main Methods:

• A simulation study was conducted, varying dataset size, outcome probability, random effect variance, and cluster/subject numbers.
• Bias in regression coefficients, odds ratios, and variance parameters was estimated using both PQL and QUAD.
• The predictive power of estimate similarity for reduced bias was investigated.

Main Results:

• Absolute percent bias of the odds ratio increased with greater discrepancy between PQL and QUAD estimates.
• Results varied significantly based on specific dataset characteristics.
• No universal threshold for discrepancy indicating bias could be established.

Conclusions:

• Comparing PQL and QUAD estimates for generalized linear mixed models is valuable.
• Discrepancies between PQL and QUAD results can signal bias, but interpretation depends on data characteristics.
• QUAD is recommended when PQL is known to yield reasonable results, highlighting the importance of comparative analysis.