testGLMGamma {gofedf}

Apply Goodness of Fit Test to the Residuals of a Generalized Linear Model with Gamma Link Function

Description

testGLMGamma is used to check the validity of Gamma assumption for the response variable when fitting generalized linear model. Common link functions in glm can be used here.

Usage

testGLMGamma(
  x,
  y,
  fit = NULL,
  l = "log",
  hessian = FALSE,
  start.value = NULL,
  control = NULL,
  method = "cvm"
)

Arguments

x

is either a numeric vector or a design matrix. In the design matrix, rows indicate observations and columns presents covariats.

y

is a vector of numeric values with the same number of observations or number of rows as x.

fit

is an object of class glm and its default value is NULL. If a fit of class glm is provided, the arguments x, y, and l will be ignored. We recommend using glm2 function from glm2 package since it provides better convergence while optimizing the likelihood to estimate coefficients of the model by IWLS method. It is required to return design matrix by x = TRUE in glm or glm2 function. For more information on how to do this, refer to the help documentation for the glm or glm2 function.

l

a character vector indicating the link function that should be used for Gamma family. Some common link functions for Gamma family are 'log' and 'inverse'. For more details see make.link from stats package in R.

hessian

logical. If TRUE the Fisher information matrix is estimated by the observed Hessian Matrix based on the sample. If FALSE (the default value) the Fisher information matrix is estimated by the variance of the observed score matrix.

start.value

a numeric value or vector. This is the same as start argument in glm or glm2. The value is a starting point in iteratively reweighted least squares (IRLS) algorithm for estimating the MLE of coefficients in the model.

control

a list of parameters to control the fitting process in glm or glm2 function. For more details, see glm.control.

method

a character string indicating which goodness-of-fit statistic is to be computed. The default value is 'cvm' for the Cramer-von-Mises statistic. Other options include 'ad' for the Anderson-Darling statistic, and 'both' to compute both cvm and ad.

Value

A list of three containing the following components:

• Statistic: the value of goodness-of-fit statistic.

• p-value: the approximate p-value for the goodness-of-fit test based on empirical distribution function. if method = 'cvm' or method = 'ad', it returns a numeric value for the statistic and p-value. If method = 'both', it returns a numeric vector with two elements and one for each statistic.

• converged: logical to indicate if the IWLS algorithm have converged or not.

Examples

set.seed(123)
n <- 50
p <- 5
x <- matrix( rnorm(n*p, mean = 10, sd = 0.1), nrow = n, ncol = p)
b <- runif(p)
e <- rgamma(n, shape = 3)
y <- exp(x %*% b) * e
testGLMGamma(x, y, l = 'log')
myfit <- glm(y ~ x, family = Gamma('log'), x = TRUE, y = TRUE)
testGLMGamma(fit = myfit)