Multivariate probit regression using simulated maximum likelihood

We discuss the application of the GHK simulation method to maximum likelihood estimation of the multivariate probit regression model, and describe and illustrate a Stata program mvprobit for this purpose.

Locally Adaptive Nonparametric Binary Regression

A nonparametric and locally adaptive Bayesian estimator is proposed for estimating a binary regression. Flexibility is obtained by modeling the binary regression as a mixture of probit regressions with the argument of each probit regression having a thin plate spline prior with its own smoothing parameter and with the mixture weights depending on the covariates. The estimator is compared to a single spline estimator and to a recently proposed locally adaptive estimator. The methodology is illustrated by applying it to both simulated and real examples.Comment: 31 pages, 10 figure

Variational Bayesian multinomial probit regression with Gaussian process priors

It is well known in the statistics literature that augmenting binary and polychotomous response models with Gaussian latent variables enables exact Bayesian analysis via Gibbs sampling from the parameter posterior. By adopting such a data augmentation strategy, dispensing with priors over regression coefficients in favour of Gaussian Process (GP) priors over functions, and employing variational approximations to the full posterior we obtain efficient computational methods for Gaussian Process classification in the multi-class setting. The model augmentation with additional latent variables ensures full a posteriori class coupling whilst retaining the simple a priori independent GP covariance structure from which sparse approximations, such as multi-class Informative Vector Machines (IVM), emerge in a very natural and straightforward manner. This is the first time that a fully Variational Bayesian treatment for multi-class GP classification has been developed without having to resort to additional explicit approximations to the non-Gaussian likelihood term. Empirical comparisons with exact analysis via MCMC and Laplace approximations illustrate the utility of the variational approximation as a computationally economic alternative to full MCMC and it is shown to be more accurate than the Laplace approximation

Interpreting interaction terms in linear and non-linear models: A cautionary tale

Interaction terms are often misinterpreted in the empirical economics literature by assuming that the coefficient of interest represents unconditional marginal changes. I present the correct way to estimate conditional marginal changes in a series of non-linear models including (ordered) logit/probit regressions, censored and truncated regressions. The linear regression model is used as the benchmark case.interaction terms; ordered probit; ordered logit; truncated regression; censored regression; nonlinear models

Categorical Data

A very brief survey of regression for categorical data. Categorical outcome (or discrete outcome or qualitative response) regression models are models for a discrete dependent variable recording in which of two or more categories an outcome of interest lies. For binary data (two categories) probit and logit models or semiparametric methods are used. For multinomial data (more than two categories) that are unordered, common models are multinomial and conditional logit, nested logit, multinomial probit, and random parameters logit. The last two models are estimated using simulation or Bayesian methods. For ordered data, standard multinomial models are ordered logit and probit, or count models are used if ordered discrete data are actually a count.binary data, multinomial, logit, probit, count data

Predicting birth-rates through German micro-census data: a comparison of probit and Boolean regression

This paper investigates the complex interrelationships of qualitative socio-economic variables in the context of Boolean Regression. The data forming the basis for this investigation are from the German Micro-census waves of 1996 2002 and comprise about 400 000 observations. Boolean Regression is used to predict how birth events depend on the socio-economic characteristics of women and their male partners. Boolean Regression is compared to Probit. The data set is split into two halves in order to determine which method yields more accurate predictions. It turns out that Probit is superior, if a given socio-economic type is substantiated by less than about 30 observations, whereas Boolean Regression is superior to Probit, if a given socio-economic type is verified by more than about 30 observations. Therefore a "hybrid" estimation method, combining Probit and Boolean Regression, is proposed and used in the remainder of the paper. Different methods of interpreting the results of the estimations are introduced, relying mainly on simulation techniques. With respect to the reasons for the prevailing low German fertility rates, it is evident that these could be decisively higher if people had higher incomes and earned more with relative ease. From a methodological perspective, the paper demonstrates that Scientific Use Files of socio-economic data comprising hundred thousands or even millions of observations, and which have been made available recently, are the natural field of application for Boolean Regression. Possible consequences for future social and economic research are discussed. --

Probit regression in prediction analysis

To avoid diagnostic surgery, the probability of nodal involvement of prostate cancer is modeled using the probit link function to determine whether the lymph nodes of a patients are infected. X-ray status and level of acidphosphatase in the blood serum of patients are considered as preoperative explanatory variables with the number of patients having nodal involvement as response variable. Within the framework of the probit regression model, the level of nodal involvement is predicted and the probability of nodal involvement obtained