Family function for Negative Binomial GLMs

Specifies the information required to fit a Negative Binomial generalized linear model, with known theta parameter, using glm().

negative.binomial(theta = stop("'theta' must be specified"), link = "log")

Arguments

theta

The known value of the additional parameter, theta.

The link function, as a character string, name or one-element character vector specifying one of log, sqrt or identity, or an object of class "link-glm".

Value

An object of class "family", a list of functions and expressions needed by glm() to fit a Negative Binomial generalized linear model.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S-PLUS. Fourth Edition. Springer.

Examples

# Fitting a Negative Binomial model to the quine data
#   with theta = 2 assumed known.
#
glm(Days ~ .^4, family = negative.binomial(2), data = quine)
#> 
#> Call:  glm(formula = Days ~ .^4, family = negative.binomial(2), data = quine)
#> 
#> Coefficients:
#>           (Intercept)                   EthN                   SexM  
#>                3.0564                -0.1386                -0.4914  
#>                 AgeF1                  AgeF2                  AgeF3  
#>               -0.6227                -2.3632                -0.3784  
#>                 LrnSL              EthN:SexM             EthN:AgeF1  
#>               -1.9577                -0.7524                 0.1029  
#>            EthN:AgeF2             EthN:AgeF3             EthN:LrnSL  
#>               -0.5546                 0.0633                 2.2588  
#>            SexM:AgeF1             SexM:AgeF2             SexM:AgeF3  
#>                0.4092                 3.1098                 1.1145  
#>            SexM:LrnSL            AgeF1:LrnSL            AgeF2:LrnSL  
#>                1.5900                 2.6421                 4.8585  
#>           AgeF3:LrnSL        EthN:SexM:AgeF1        EthN:SexM:AgeF2  
#>                    NA                -0.3105                 0.3469  
#>       EthN:SexM:AgeF3        EthN:SexM:LrnSL       EthN:AgeF1:LrnSL  
#>                0.8329                -0.1639                -3.5493  
#>      EthN:AgeF2:LrnSL       EthN:AgeF3:LrnSL       SexM:AgeF1:LrnSL  
#>               -3.3315                     NA                -2.4285  
#>      SexM:AgeF2:LrnSL       SexM:AgeF3:LrnSL  EthN:SexM:AgeF1:LrnSL  
#>               -4.1914                     NA                 2.1711  
#> EthN:SexM:AgeF2:LrnSL  EthN:SexM:AgeF3:LrnSL  
#>                2.1029                     NA  
#> 
#> Degrees of Freedom: 145 Total (i.e. Null);  118 Residual
#> Null Deviance:	    280.2 
#> Residual Deviance: 172 	AIC: 1095