Robit Regression: A Simple Robust Alternative to Logistic and Probit Regression

@inproceedings{Liu2005RobitRA,
  title={Robit Regression: A Simple Robust Alternative to Logistic and Probit Regression},
  author={Chuanhai Liu},
  year={2005},
  url={https://api.semanticscholar.org/CorpusID:3110460}
}
Logistic and probit regression models are commonly used in practice to analyze binary response data, but the maximum likelihood estimators of these models are not robust to outliers. This paper considers a robit regression model, which replaces the normal distribution in the probit regression model with a t-distribution with a known or unknown number of degrees of freedom. It is shown that (i) the maximum likelihood estimators of the robit model with a known number of degrees of freedom are… 

Figures from this paper

Convergence rates for MCMC algorithms for a robust Bayesian binary regression model

It is proved that, under certain conditions, both algorithms converge at a geometric rate, which can be used to choose an appropriate (Markov chain) Monte Carlo sample size and allow one to use the MCMC algorithms developed in this paper with the same level of confidence that one would have using classical Monte Carlo.

Robit regression in Stata

A new command is described, robit, that implements robit regression in Stata, which replaces the underlying normal distribution in the probit model with a Student’s t distribution.

Convergence properties of data augmentation algorithms for high-dimensional robit regression

This work shows that the robit DA Markov chain is trace-class for arbitrary choices of the sample size n, the number of predictors p, the design matrix X, and the prior mean and variance parameters, which implies geometric ergodicity.

Efficient estimation and prediction for the Bayesian binary spatial model with flexible link functions

A Bayesian spatial robit model for spatially dependent binomial data is introduced and the approach is doing as well as the classical models for predicting the disease severity for a root disease, as the probit link is shown to be appropriate.

On the Use of Cauchy Prior Distributions for Bayesian Logistic Regression

In logistic regression, separation occurs when a linear combination of the predictors can perfectly classify part or all of the observations in the sample, and as a result, finite maximum likelihood

Robust discrete choice models with t-distributed kernel errors

Outliers in discrete choice response data may result from misclassification and misreporting of the response variable and from choice behaviour that is inconsistent with modelling assumptions (e.g.
...

Robust Statistical Modeling Using the t Distribution

Abstract The t distribution provides a useful extension of the normal for statistical modeling of data sets involving errors with longer-than-normal tails. An analytical strategy based on maximum

Bayesian analysis of binary and polychotomous response data

Abstract A vast literature in statistics, biometrics, and econometrics is concerned with the analysis of binary and polychotomous response data. The classical approach fits a categorical response

Analysis of multivariate probit models

SUMMARY This paper provides a practical simulation-based Bayesian and non-Bayesian analysis of correlated binary data using the multivariate probit model. The posterior distribution is simulated by

Generalized linear models with random e ects: a Gibbs sampling approach

This article casts the generalized linear random effects model in a Bayesian framework and uses a Monte Carlo method, the Gibbs sampler, to overcome the current computational limitations.

Iteratively Reweighted Least Squares: Algorithms, Convergence Analysis, and Numerical Comparisons

In solving robust linear regression problems, the parameter vector x, as well as an additional parameter s that scales the residuals, must be estimated simultaneously. A widely used method for doing

The calculation of posterior distributions by data augmentation

If data augmentation can be used in the calculation of the maximum likelihood estimate, then in the same cases one ought to be able to use it in the computation of the posterior distribution of parameters of interest.

Propriety of posterior distribution for dichotomous quantal response models

In this article, we investigate the property of posterior distribution for dichotomous quantal response models using a uniform prior distribution on the regression parameters. Sufficient and

Resistant fits for some commonly used logistic models with medical application.

Logistic regression-type models are used in many applications and are fitted by the method of maximum likelihood, which, like least squares, is sensitive to atypical observations.

General linear models.

    E. Ip
    Mathematics, Psychology
  • 2007
This chapter presents the general linear model as an extension to the two-sample t-test, analysis of variance (ANOVA), and linear regression, and the F test is introduced as a means to test for the strength of group effect.

The Art of Data Augmentation

An effective search strategy is introduced that combines the ideas of marginal augmentation and conditional augmentation, together with a deterministic approximation method for selecting good augmentation schemes to obtain efficient Markov chain Monte Carlo algorithms for posterior sampling.