Probit model

About: Probit model is a research topic. Over the lifetime, 4213 publications have been published within this topic receiving 129386 citations.

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 regression model using maximum likelihood, and inferences about the model are based on the associated asymptotic theory. The accuracy of classical confidence statements is questionable for small sample sizes. In this article, exact Bayesian methods for modeling categorical response data are developed using the idea of data augmentation. The general approach can be summarized as follows. The probit regression model for binary outcomes is seen to have an underlying normal regression structure on latent continuous data. Values of the latent data can be simulated from suitable truncated normal distributions. If the latent data are known, then the posterior distribution of the parameters can be computed using standard results for normal linear models. Draws from this posterior are used to sample new latent data, and t...

Some statistical models for limited dependent variables with application to the demand for durable goods

Abstract: THIS PAPER DEVELOPS some models for limited dependent variables.2 The distinguishing feature of these variables is that the range of values which they may assume has a lower bound and that this lowest value occurs in a fair number of observations. This feature should be taken into account in the statistical analysis of observations on such variables. In particular, it renders invalid use of the usual regression model. The second section of this paper develops several models for such variables. Like Tobin's [10] model, they are extensions of the multiple probit analysis model.3 They differ from that model by allowing the determination of the size of the variable when it is not zero to depend on different parameters or variables from those determining the probability of its being zero. Estimation and discrimination in the models are considered in Section 3. The models, like their prototypes, seem particularly intractable to exact analysis and large sample approximations have to be used. The adequacy of inferences based on these procedures is explored in Section 4 through a small sampling experiment. Limited dependent variables arise naturally in the study of consumer purchases, particularly purchases of durable goods. When a durable good is to be purchased, the amount spent may vary in fine gradations, but for many durables it is probably the case that most consumers in a particular period make no purchase at all. In Section 5 we apply the models to the demand for durable goods to provide an application of the techniques.

A statistical model for the analysis of ordinal level dependent variables

Abstract: This paper develops a model, with assumptions similar to those of the linear model, for use when the observed dependent variable is ordinal. This model is an extension of the dichotomous probit model, and assumes that the ordinal nature of the observed dependent variable is due to methodological limitations in collecting the data, which force the researcher to lump together and identify various portions of an (otherwise) interval level variable. The model assumes a linear eflect of each independent variable as well as a series of break points between categories for the dependent variable. Maximum likelihood estimators are found for these parameters, along with their asymptotic sampling distributions, and an analogue of R 2 (the coefficient of determination in regression analysis) is defined to measure goodness of fit. The use of the model is illustrated with an analysis of Congressional voting on the 1965 Medicare Bill.