| residuals.probit {sampleSelection} | R Documentation |
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 |
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 ) / \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 ith residual,
y_i is the ith 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 ith observation, and
\hat{\beta} is the vector of estimated coefficients.
More details are available in Davison & Snell (1991).
Value
A numeric vector of the residuals.
Author(s)
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.
See Also
probit, residuals,
residuals.glm, and probit-methods.