cumres.glm: Calculates GoF statistics based on cumulative residual...

In gof: Model-diagnostics based on cumulative residuals

Description

Given the generalized linear models model

g(E(Y_i|X_{i1},...,X_{ik})) = ∑_{i=1}^k β_jX_{ij}

the cumres-function calculates the the observed cumulative sum of residual process, cumulating the residuals, e_i, by the jth covariate:

W_j(t) = n^{-1/2}∑_{i=1}^n 1_{\{X_{ij}<t\}}e_i

and Kolmogorov-Smirnov and Cramer-von-Mises test statistics are calculated via simulation from the asymptotic distribution of the cumulative residual process under the null (Lin et al., 2002).

Usage

  ## S3 method for class 'glm'
 cumres(model,
    variable = c("predicted", colnames(model.matrix(model))),
    data = data.frame(model.matrix(model)), R = 1000,
    b = 0, plots = min(R, 50), breakties = 1e-12,
    seed = round(runif(1, 1, 1e+09)), ...)

Arguments

model	Model object (lm or glm)
variable	List of variable to order the residuals after
data	data.frame used to fit model (complete cases)
R	Number of samples used in simulation
b	Moving average bandwidth (0 corresponds to infinity = standard cumulated residuals)
plots	Number of realizations to save for use in the plot-routine
breakties	Add unif[0,breakties] to observations
seed	Random seed
...	additional arguments

Value

Returns an object of class 'cumres'.

Note

Currently linear (normal), logistic and poisson regression models with canonical links are supported.

Author(s)

Klaus K. Holst

References

D.Y. Lin and L.J. Wei and Z. Ying (2002) Model-Checking Techniques Based on Cumulative Residuals. Biometrics, Volume 58, pp 1-12.

John Q. Su and L.J. Wei (1991) A lack-of-fit test for the mean function in a generalized linear model. Journal. Amer. Statist. Assoc., Volume 86, Number 414, pp 420-426.

See Also

cox.aalen in the timereg-package for similar GoF-methods for survival-data.

Examples

sim1 <- function(n=100, f=function(x1,x2) {10+x1+x2^2}, sd=1, seed=1) {
  if (!is.null(seed))
    set.seed(seed)
  x1 <- rnorm(n);
  x2 <- rnorm(n)
  X <- cbind(1,x1,x2)
  y <- f(x1,x2) + rnorm(n,sd=sd)
  d <- data.frame(y,x1,x2)
  return(d)
}
d <- sim1(100); l <- lm(y ~ x1 + x2,d)
system.time(g <- cumres(l, R=100, plots=50))
g
plot(g)
g1 <- cumres(l, c("y"), R=100, plots=50)
g1
g2 <- cumres(l, c("y"), R=100, plots=50, b=0.5)
g2

Example output

Loading 'gof' version 0.9.1
   user  system elapsed 
  0.046   0.000   0.046 

Kolmogorov-Smirnov-test: p-value=0.32
Cramer von Mises-test: p-value=0.36
Based on 100 realizations. Cumulated residuals ordered by predicted-variable.
---
Kolmogorov-Smirnov-test: p-value=0.51
Cramer von Mises-test: p-value=0.26
Based on 100 realizations. Cumulated residuals ordered by x1-variable.
---
Kolmogorov-Smirnov-test: p-value=0
Cramer von Mises-test: p-value=0
Based on 100 realizations. Cumulated residuals ordered by x2-variable.
---

Kolmogorov-Smirnov-test: p-value=0.26
Cramer von Mises-test: p-value=0.32
Based on 100 realizations. Cumulated residuals ordered by predicted-variable.
---

Kolmogorov-Smirnov-test: p-value=0.39
Cramer von Mises-test: p-value=0.21
Based on 100 realizations. Cumulated residuals ordered by predicted-variable.
---

gof documentation built on May 2, 2019, 5:52 p.m.