Description Usage Arguments Value Note Author(s) References See Also Examples
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).
1 2 3 4 5 6 | ## 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)), ...)
|
model |
Model object ( |
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 |
Returns an object of class 'cumres'.
Currently linear (normal), logistic and poisson regression models with canonical links are supported.
Klaus K. Holst
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.
cox.aalen
in the
timereg
-package for similar GoF-methods for
survival-data.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | 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
|
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.
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