# Combining binomial data using the logistic normal model

Research output: Contribution to journalArticle

9 Citations (Scopus)

### Abstract

Combining binomial data from multiple sources has often been done using normal linear mixed effect models. In this paper we propose to combine binomial data using a two-stage logistic normal model. This model formulation will allow coherent interpretation of parameter estimates and homogeneity tests. We discuss parameter estimation for the proposed model using the approximate maximum likelihood method with Gauss quadrature points and the penalized quasi-likelihood approach. We also describe several tests for the homogeneity of studies to be combined. Simulation results demonstrate that the penalized quasi-likelihood approach is preferred because it provide better parameter estimates and coverage probabilities.

Original language English 293-306 14 Journal of Statistical Computation and Simulation 74 4 https://doi.org/10.1080/0094965031000151169 Published - Apr 2004

### Fingerprint

Penalized Quasi-likelihood
Logistics
Homogeneity Test
Linear Mixed Effects Model
Maximum Likelihood Method
Coverage Probability
Homogeneity
Estimate
Parameter Estimation
Model
Parameter estimation
Maximum likelihood
Formulation
Demonstrate
Simulation
Quasi-likelihood

### Keywords

• Homogeneity test
• Penalized quasi-likelihood
• Variance components

### ASJC Scopus subject areas

• Applied Mathematics
• Statistics and Probability
• Modeling and Simulation

### Cite this

In: Journal of Statistical Computation and Simulation, Vol. 74, No. 4, 04.2004, p. 293-306.

Research output: Contribution to journalArticle

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AB - Combining binomial data from multiple sources has often been done using normal linear mixed effect models. In this paper we propose to combine binomial data using a two-stage logistic normal model. This model formulation will allow coherent interpretation of parameter estimates and homogeneity tests. We discuss parameter estimation for the proposed model using the approximate maximum likelihood method with Gauss quadrature points and the penalized quasi-likelihood approach. We also describe several tests for the homogeneity of studies to be combined. Simulation results demonstrate that the penalized quasi-likelihood approach is preferred because it provide better parameter estimates and coverage probabilities.

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