Calculate residuals of probit models.
# S3 method for probit
residuals( object, type = "deviance", ... )an object of class probit.
the type of residuals which should be returned. The alternatives are: "deviance" (default), "pearson", and "response" (see details).
further arguments (currently ignored).
A numeric vector of the residuals.
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).
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.