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Biometrika 1992 79(3):441-461; doi:10.1093/biomet/79.3.441
© 1992 by Biometrika Trust
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Response models for mixed binary and quantitative variables

D. R. COX1 and NANNY WERMUTH2

1Nuffield College Oxford OX1 1NF, U.K.
2Psychological Institute, University of Mainz 6500 Mainz, Germany

A number of special representations are considered for the joint distribution of qualitative, mostly binary, and quantitative variables. In addition to the conditional Gaussian models and to conditional Gaussian regression chain models some emphasis is placed on models derived from an underlying multivariate normal distribution and on models in which discrete probabilities are specified linearly in terms of unknown parameters. The possibilities for choosing between the models empirically are examined, as well as the testing of independence and conditional independence and the estimation of parameters. Often the testing of independence is exactly or nearly the same for a number of different models.

Key Words: Conditional Gaussian model • Graphical chain model • Linear model • Logistic function • Multivariate normal distribution • Probit model


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