Integrated Regression Goodness of Fit to test if a given model is suitable to represent the regression function for a given data.
1 2  intRegGOF(obj, covars = NULL, B = 499, LINMOD = FALSE)
print.intRegGOF(x,...)

obj 
An object of class 
covars 
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. 
B 
Bootstrap resampling size. 
LINMOD 
When 
x 
An object of class 
... 
Further parameters for print command. 
The Integrated Regression Goodness of Fit technique is introduce in Stute(1997). The main idea is to study the process that results from the cumulation of the residuals up to a given value of the covariates. Once this process is built, different functional over it can be considered to measure the discrepany between the true regression function and its estimation.
The tests that implements this function is
H_0:m\in M \ \textrm{vs} \ H_1:m\notin M
being m the regression function, and M a given class of functions. The statistics considered are
K_n=\sup_{x\in R^d}R^w_n(x)
W^2_n=\int_{R^d}R^w_n(z)^2 \,dF(z).
where R^w_n(z) is the cumulated residual process:
R^w_n(x)=n^{1/2}∑^n_{i=1}(y_i\hat y_i)I(x_i≤ x).
As the stochastic behaviour of this cumulated residual process is quite complex, the implementation of the technique is based on resampling techniques. In particular the chosen implementation is based on Wild Bootstrap methods.
The method also handles selection biased data by means of compensation, by means of the weights used to fit the resgression function when computing the cumulated residual process.
At the moment only 'response'
type of residuals are considered,
jointly with wild bootstrap resampling technique and the result for
discrete responses might no be proper.
This function returns an object of class intRegGOF
, a
list
which cointains following objects:
call 
The call to the function 
regObj 
String with the 
regModel 

p.value 
p–values for K_n and W^2_n statistics. 
datStat 
value of K_n and W^2_n statistics. 
covars 
continuous (numerical) variates used to compute Integrated Regression. 
intErr 
cumulated residual process at the values of

xLT 
structure with the order of 
bootSamp 
Bootstrap samples for K_n and W^2_n. 
This method requires more testing, and careful study of the effect of factors (discrete random variables) when fitting the model.
Jorge Luis Ojeda Cabrera (jojeda@unizar.es).
Stute, W. (1997). Nonparametric model checks for regression. Ann. Statist., 25(2), pp. 613–641.
Ojeda, J. L., W. GonzálezManteiga W. and Cristóbal, J. A A bootstrap based Model Checking for Selection–Biased data Reports in Statistics and Operations Research, U. de Santiago de Compostela. Report 0705 http://eio.usc.es/eipc1/BASE/BASEMASTER/FORMULARIOSPHPDPTO/REPORTS/447report07_05.pdf
Ojeda, J. L., Cristóbal, J. A., and Alcalá, J. T. (2008). A bootstrap approach to model checking for linear models under lengthbiased data. Ann. Inst. Statist. Math., 60(3), pp. 519–543.
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