Integrated Regression Goodness of Fit to test the adequacy of different model to represent the regression function for a given data.
anovarIntReg(objH0, ..., covars = NULL, B = 499,
LINMOD = FALSE, INCREMENTAL = FALSE)
# S3 method for anovarIntReg
print(x,...)Names of continuous (numerical) variates used to
compute Integrated Regression. They should be variables contained
in the data frame used to compute the regression fit. When NULL it
is obtained as the max. number of different covariates in all tested
models. It also can be a formula like ~x1+x2+....
Bootstrap resampling size.
When TRUE and if obj is an object of class
print.intRegGOFprint.intRegGOFlm Linear Model matrix fitting equations are used.
When is FALSE all models in … are
tested against objH0, while when TRUE each of the
models are checked against the next one startin in objH0.
An object of class anovarIntReg.
This function returns an object of class anovarIntReg, a
matrix like structure whose rows refers to models and
columns to statistics and its \(p\)-values. It also has
an attribute heading to support printing the object.
This function implements the test
$$
H_0:m\in M_0 \ \textrm{vs} \ H_1:m\in M_1
$$
for two different models \(M_0\), \(M_1\) using the
Integrated Regression Goodness of Fit as os done in intRegGOF,
but instead of the accumulation of the residual of a givem model, in
this case, the accumuation of the difference in the fits is considered:
$$
R^w_n(x)=n^{-1/2}\sum^n_{i=1}(\hat y_{0i}-\hat y_{1i})I(x_i\le x).
$$
The test statistics considered are $K_n$ and $W^2_n$.
If objH0 and objH1 are lm, glm
or nls fits for the models in classes \(M_0\) and
\(M_1\) respectively, then anovarIntReg(objH0,objH1) computes
test \(H_0:m\in M_0\) vs \(H_1:m\notin M_1\). When
anovarIntReg(objH0,objH1,…,objHk) is executed (notice
that by default INCREMENTAL=FALSE) we obtain a table with
the statistics \(K_n\) and \(W^2_n\) and its associated
\(p\)-values for each of the tests \(H_0:m\in M_0\) vs
\(H_i:m\notin M_i\) being \(i=1,\dots,k\). On the other hand,
if the parameter INCREMENTAL is set to TRUE, the
command returns the results for the tests \(H_i:m\in M_i\) vs
\(H_{i+1}:m\notin M_{i+1}\) being \(i=1,\dots,k-1\).
# NOT RUN {
n <- 50
d <- data.frame( X1=runif(n),X2=runif(n))
d$Y <- 1 - 2*d$X1 - 5*d$X2 + rnorm(n,sd=.125)
a0 <- lm(Y~1,d)
a1 <- lm(Y~X1,d)
a2 <- lm(Y~X1+X2,d)
anovarIntReg(a0,a1,a2,B=50)
anovarIntReg(a0,a1,a2,B=50,INCREMENTAL=TRUE)
# }
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