Matching conditional and marginal shapes in binary random intercept models using a bridge distribution function

• Published in: Biometrika Vol. 90; no. 4; pp. 765 - 775
• Main Authors: Wang, Zengri, Louis, Thomas A.
• Format: Journal Article
• Language: English
• Published: Oxford Oxford University Press 01.12.2003; Biometrika Trust, University College London; Oxford University Press for Biometrika Trust; Oxford Publishing Limited (England)
• Series: Biometrika
• Subjects: Bridge distribution function; Clustered data; Cumulative distribution functions; Density distributions; Distribution functions; Eigenfunctions; Exact sciences and technology; Fourier transforms; Gaussian‐Hermite quadrature; Linear inference, regression; Logistic regression; Logistics; Marginal model; Mathematical independent variables; Mathematics; Multilevel models; Parameter estimation; Parametric models; Probability and statistics; Random effects model; Regression analysis; Sciences and techniques of general use; Statistics; Conditional distribution; Cluster analysis (statistics); Conditional inference; Binary data; Response model; Cluster; Statistical estimation; Logistic model; Random distribution; Logistic distribution; Quadrature; Statistical regression; Logistic regression; Regression model; Marginal distribution; Distribution function; Binary response; Random effect; Models; Random function; Likelihood function
• ISSN: 0006-3444; 1464-3510
• DOI: 10.1093/biomet/90.4.765

Random effects logistic regression models are often used to model clustered binary response data. Regression parameters in these models have a conditional, subject‐specific interpretation in that they quantify regression effects for each cluster. Very often, the logistic functional shape conditional on the random effects does not carry over to the marginal scale. Thus, parameters in these models usually do not have an explicit marginal, population‐averaged interpretation. We study a bridge distribution function for the random effect in the random intercept logistic regression model. Under this distributional assumption, the marginal functional shape is still of logistic form, and thus regression parameters have an explicit marginal interpretation. The main advantage of this approach is that likelihood inference can be obtained for either marginal or conditional regression inference within a single model framework. The generality of the results and some properties of the bridge distribution functions are discussed. An example is used for illustration.