Binary probit regression with I-priors

Abstract

An extension of the I-prior methodology to binary response data is explored. Starting from a latent variable approach, it is assumed that there exists continuous, auxiliary random variables which decide the outcome of the binary responses. Fitting a classical linear regression model on these latent variables while assuming normality of the error terms leads to the well-known generalised linear model with a probit link. A more general regression approach is considered instead, in which an I-prior on the regression function, which lies in some reproducing kernel Hilbert space, is assumed. An I-prior distribution is Gaussian with mean chosen a priori, and covariance equal to the Fisher information for the regression function. By working with I-priors, the benefits of the methodology are brought over to the binary case - one of which is that it provides a unified model-fitting framework that includes additive models, multilevel models and models with one or more functional covariates. The challenge is in the estimation, and a variational approximation is employed to overcome the intractable likelihood. Several real-world examples are presented from analyses conducted in R.

Date
8 May 2017 12:00 pm — 12:35 pm
Event
LSE Department of Statistics PhD Presentation Event
Location
LSE
Houghton Street, London, WC2A 2AE
Haziq Jamil
Haziq Jamil
Assistant Professor in Statistics

My research interests include statistical theory, methods and computation, with applications towards the social sciences.

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