Semi-parametric estimation of random effects in a logistic regression model using conditional inference

Area of Science:

• Statistics
• Biostatistics
• Econometrics

Background:

• Logistic regression models are widely used for binary outcomes.
• Estimating variance components in models with multiple random effects presents challenges, especially without distributional assumptions.
• Existing methods may require strong assumptions or be computationally intensive.

Purpose of the Study:

• To develop a new estimation approach for logistic regression with two crossed random effects.
• To focus on estimating the variance of one specific random effect.
• To avoid making distributional assumptions about the other random effect.

Main Methods:

• A composite likelihood approach is investigated.
• Conditional likelihoods are used for each term in the composite likelihood to eliminate random effects.
• This results in a composite conditional likelihood involving only one-dimensional integrals.
• Numerical methods are employed to solve these integrals.

Main Results:

• The proposed method provides an effective way to estimate variance components.
• The composite conditional likelihood simplifies the estimation process.
• A simulation study demonstrates favorable properties of the resulting estimator.

Conclusions:

• The developed composite likelihood method offers a flexible and robust approach for logistic regression with random effects.
• It is particularly useful when distributional assumptions for all random effects cannot be made.
• The method shows promise for various applications in statistics and related fields.