scholarly journals Intra-class Correlation in Random-effects Models for Binary Data

2003 ◽  
Vol 3 (1) ◽  
pp. 32-46 ◽  
Author(s):  
Germán Rodríguez ◽  
Irma Elo
Keyword(s):  
Random Effects ◽  
Latent Variable ◽  
Binary Data ◽  
Binary Outcomes ◽  
Measures Of Association ◽  
Intra Class Correlation ◽  
Random Effects Models ◽  
Alternative Measures

We review the concept of intra-class correlation in random-effects models for binary outcomes as estimated by Stata's xtprobit, xtlogit, and xtclog. We consider the usual measures of correlation based on a latent variable formulation of these models and note corrections to the last two procedures. We also discuss alternative measures of association based on manifest variables or actual outcomes and introduce a new command xtrho for computing these measures for all three types of models.

Sibling Models, Categorical Outcomes, and the Intra-Class Correlation

2021 ◽  
Author(s):  
Richard Breen ◽  
John Ermisch
Keyword(s):  
Random Effects ◽  
Probability Model ◽  
Intraclass Correlation ◽  
Linear Probability Model ◽  
Intra Class Correlation ◽  
Sibling Differences ◽  
Sibling Models ◽  
Alternative Measures ◽  
Linear Probability ◽  
Parametric Estimate

Abstract In sibling models with categorical outcomes the question arises of how best to calculate the intraclass correlation, ICC. We show that, for this purpose, the random effects linear probability model is preferable to a random effects non-linear probability model, such as a logit or probit. This is because, for a binary outcome, the ICC derived from a random effects linear probability model is a non-parametric estimate of the ICC, equivalent to a statistic called Cohen’s κ. Furthermore, because κ can be calculated when the outcome has more than two categories, we can use the random effects linear probability model to compute a single ICC in cases with more than two outcome categories. Lastly, ICCs are often compared between groups to show the degree to which sibling differences vary between groups: we show that when the outcome is categorical these comparisons are invalid. We suggest alternative measures for this purpose.

scholarly journals Modeling clustered binary data with excess zero clusters

2016 ◽  
Vol 27 (9) ◽  
pp. 2641-2656
Author(s):  
John Kwagyan ◽  
Victor Apprey
Keyword(s):  
Random Effects ◽  
Binary Data ◽  
Latent Class ◽  
Marginal Likelihood ◽  
Gaussian Quadrature ◽  
Gaussian Model ◽  
Likelihood Estimation ◽  
Clustered Binary Data ◽  
Random Effects Models ◽  
Cancer Data

We establish a zero-inflated (random-effects) logistic-Gaussian model for clustered binary data in which members of clusters in one latent class have a zero response with probability one, and members of clusters in a second latent class yield correlated outcomes. Response probabilities in terms of random-effects models are formulated, and maximum marginal likelihood estimation procedures based on Gaussian quadrature are developed. Application to esophageal cancer data in Chinese families is presented.

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