# residuals.probit: Residuals of probit models In sampleSelection: Sample Selection Models

## Description

Calculate residuals of probit models.

## Usage

 1 2  ## S3 method for class 'probit' residuals( object, type = "deviance", ... ) 

## Arguments

 object an object of class probit. type the type of residuals which should be returned. The alternatives are: "deviance" (default), "pearson", and "response" (see details). ... further arguments (currently ignored).

## Details

The residuals are calculated with following formulas:

Response residuals: r_i = y_i - \hat{y}_i

Pearson residuals: r_i = ( y_i - \hat{y}_i ) / √{ \hat{y}_i ( 1 - \hat{y}_i ) }

Deviance residuals: r_i = √{ -2 \log( \hat{y}_i ) } if y_i = 1, r_i = - √{ -2 \log( 1 - \hat{y}_i ) } if y_i = 0

Here, r_i is the ith residual, y_i is the ith response, \hat{y}_i = Φ( x_i' \hat{β} ) is the estimated probability that y_i is one, Φ is the cumulative distribution function of the standard normal distribution, x_i is the vector of regressors of the ith observation, and \hat{β} is the vector of estimated coefficients.

More details are available in Davison & Snell (1991).

## Value

A numeric vector of the residuals.

Arne Henningsen

## References

Davison, A. C. and Snell, E. J. (1991) Residuals and diagnostics. In: Statistical Theory and Modelling. In Honour of Sir David Cox, edited by Hinkley, D. V., Reid, N. and Snell, E. J., Chapman & Hall, London.

probit, residuals, residuals.glm, and probit-methods.