R: Fit Gamma Generalized Linear Model by Fisher Scoring with...

glmgam.fit {statmod} | R Documentation

## Fit Gamma Generalized Linear Model by Fisher Scoring with Identity Link

### Description

Fit a generalized linear model with secure convergence.

### Usage

    glmgam.fit(X, y, coef.start = NULL, tol = 1e-6, maxit = 50, trace = FALSE)

### Arguments

`X` | design matrix, assumed to be of full column rank. Missing values not allowed.
`y` | numeric vector of responses. Negative or missing values not allowed.
`coef.start` | numeric vector of starting values for the regression coefficients
`tol` | small positive numeric value giving convergence tolerance
`maxit` | maximum number of iterations allowed
`trace` | logical value. If `TRUE` then output diagnostic information at each iteration.

### Details

This function implements a modified Fisher scoring algorithm for generalized linear models, similar to the Levenberg-Marquardt algorithm for nonlinear least squares. The Levenberg-Marquardt modification checks for a reduction in the deviance at each step, and avoids the possibility of divergence. The result is a very secure algorithm that converges for almost all datasets.

`glmgam.fit` is in principle equivalent to `glm.fit(X,y,family=Gamma(link="identity"))` but with much more secure convergence.

### Value

List with the following components:

`coefficients` | numeric vector of regression coefficients
`fitted` | numeric vector of fitted values
`deviance` | residual deviance
`iter` | number of iterations used to convergence. If convergence was not achieved then `iter` is set to `maxit+1`.

### Author(s)

Gordon Smyth and Yunshun Chen

### References

Dunn, PK, and Smyth, GK (2018). Generalized linear models with examples in R. Springer, New York, NY. doi: 10.1007/978-1-4419-0118-7

### See Also

`glmgam.fit` is called by `mixedModel2Fit`.

`glm` is the standard glm fitting function in the stats package.

### Examples

    y <- rgamma(10, shape=5)
    X <- cbind(1, 1:10)
    fit <- glmgam.fit(X, y, trace=TRUE)

[Package statmod version 1.4.36 Index]