residuals.probit: Residuals of probit models

Description

Calculate residuals of probit models.

Usage

## 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).

Value

A numeric vector of the residuals.

Details

The residuals are calculated with following formulas:

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

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

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

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

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

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.