Package 'intRegGOF' reference manual

Title:	Integrated Regression Goodness of Fit
Description:	Performs Goodness of Fit for regression models using Integrated Regression method. Works for several different fitting techniques.
Authors:	Jorge Luis Ojeda Cabrera <[email protected]>
Maintainer:	Jorge Luis Ojeda Cabrera <[email protected]>
License:	GPL (>= 2)
Version:	0.85-5
Built:	2025-02-17 06:42:02 UTC
Source:	CRAN

Integrated Regression Goodness of Fit

Description

Integrated Regression Goodness of Fit to test the adequacy of different model to represent the regression function for a given data.

Usage

  anovarIntReg(objH0, ..., covars = NULL, B = 499, 
    LINMOD = FALSE, INCREMENTAL = FALSE)
  ## S3 method for class 'anovarIntReg'
print(x,...)
anovarIntReg(objH0, ..., covars = NULL, B = 499, 
    LINMOD = FALSE, INCREMENTAL = FALSE)
  ## S3 method for class 'anovarIntReg'
print(x,...)

Arguments

objH0

An object of class lm, glm or nls which will be considered as hull hypotheses model or the base reference mode when INCREMENTAL is set to TRUE

`...`	One or more objects of class `lm`, `glm` or `nls`
`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. 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+...`.
`B`	Bootstrap resampling size.
`LINMOD`	When `TRUE` and if `obj` is an object of class print.intRegGOFprint.intRegGOFlm Linear Model matrix fitting equations are used.
`INCREMENTAL`	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`.
`x`	An object of class `anovarIntReg`.

Details

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 $i=1,\dots,k-1$ .

Value

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.

Note

This method requires more testing, and careful study of the effect of factors (discrete random variables) when fitting the model.

Author(s)

Jorge Luis Ojeda Cabrera ([email protected]).

Examples

  n <- 50
  d <- data.frame( X1=runif(n),X2=runif(n))
  d$Y <- 1 - 2*d$X1 - 5*d$X2 + rnorm(n,sd=.125)
  a0 <- lm(Y~1,d) 
  a1 <- lm(Y~X1,d) 
  a2 <- lm(Y~X1+X2,d) 
  anovarIntReg(a0,a1,a2,B=50) 
  anovarIntReg(a0,a1,a2,B=50,INCREMENTAL=TRUE) 
n <- 50
  d <- data.frame( X1=runif(n),X2=runif(n))
  d$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)

Utility functions for Integrated Regression Goodness of Fit

Description

Core functions for the computation of the Integrated Regression Goodness of Fit

Usage

compIntRegProc(y, xord, weig = rep(1, length(y)))
compBootSamp(obj, datLT, B = 999, LINMOD = FALSE)
plotIntRegProc(y, x, weig = rep(1, length(y)), ADD = FALSE, ...)
getModelFrame(obj)
getResiduals(obj,type)
compIntRegProc(y, xord, weig = rep(1, length(y)))
compBootSamp(obj, datLT, B = 999, LINMOD = FALSE)
plotIntRegProc(y, x, weig = rep(1, length(y)), ADD = FALSE, ...)
getModelFrame(obj)
getResiduals(obj,type)

Arguments

`y`	vector, values to add to compute the Integrated Regression.
`xord`	list of list with the index of covariate points that are less than covariate data. This tells how to cumulate according to covariates,
`weig`	vector of weights, specifically used to fit and compute test statistics when data is selection biased.
`obj`	An object of class `lm`, `glm` or `nls`.
`datLT`	structure as `xord` telling how to cumulate according to covariates.
`B`	Bootstrap resampling size.
`LINMOD`	When `TRUE` and if `obj` is an object of class `lm` Linear Model matrix fitting equations are used.
`x`	vector with covarates to plot
`ADD`	If `TRUE` the plot is added to existing plot.
`type`	Type of residual.
`...`	Further parameters to plot.

Details

...TODO: Each of them computes what in which way

Note

Surely they can better implemented.

Author(s)

Jorge Luis Ojeda Cabrera ([email protected]).

Integrated Regression Goodness of Fit

Description

Integrated Regression Goodness of Fit to test if a given model is suitable to represent the regression function for a given data.

Usage

  intRegGOF(obj, covars = NULL, B = 499, LINMOD = FALSE)
  ## S3 method for class 'intRegGOF'
print(x,...)
intRegGOF(obj, covars = NULL, B = 499, LINMOD = FALSE)
  ## S3 method for class 'intRegGOF'
print(x,...)

Arguments

`obj`	An object of class `lm`, `glm` or `nls`.
`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 `TRUE` and if `obj` is an object of class `lm` Linear Model matrix fitting equations are used.
`x`	An object of class `intRegGOF`.
`...`	Further parameters for print command.

Details

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:

$R^w_n(x)=n^{-1/2}\sum^n_{i=1}(y_i-\hat y_i)I(x_i\le x).$

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.

Value

This function returns an object of class intRegGOF, a list which cointains following objects:

`call`	The call to the function
`regObj`	String with the `lm`, `glm` or `nls` object whose fit is cheked
`regModel`	`lm`, `glm` or `nls` object call.
`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 `covars` in data.
`xLT`	structure with the order of `covars` summation.
`bootSamp`	Bootstrap samples for $K_n$ and $W^2_n$ .

Note

This method requires more testing, and careful study of the effect of factors (discrete random variables) when fitting the model.

Author(s)

Jorge Luis Ojeda Cabrera ([email protected]).

References

Stute, W. (1997). Nonparametric model checks for regression. Ann. Statist., 25(2), pp. 613–641.

Ojeda, J. L., W. González-Manteiga 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 07-05 http://eio.usc.es/eipc1/BASE/BASEMASTER/FORMULARIOS-PHP-DPTO/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 length-biased data. Ann. Inst. Statist. Math., 60(3), pp. 519–543.

Examples

n <- 50
d <- data.frame( X1=runif(n),X2=runif(n))
d$Y <- 1 + 2*d$X1 + rnorm(n,sd=.125)
plot( d ) 
intRegGOF(lm(Y~X1+X2,d),B=99)
intRegGOF(a <- lm(Y~X1-1,d),B=99) 
intRegGOF(a,c("X1","X2"),B=99) 
intRegGOF(a,~X2+X1,B=99) 
n <- 50
d <- data.frame( X1=runif(n),X2=runif(n))
d$Y <- 1 + 2*d$X1 + rnorm(n,sd=.125)
plot( d ) 
intRegGOF(lm(Y~X1+X2,d),B=99)
intRegGOF(a <- lm(Y~X1-1,d),B=99) 
intRegGOF(a,c("X1","X2"),B=99) 
intRegGOF(a,~X2+X1,B=99)

Integrated Regression Goodness of Fit graphical output

Description

Methods to develop model validation and visualization of Integrated Regression Goodness of Fit technique.

Usage

  plotAsIntRegGOF(obj, covar = 1, ADD = FALSE, ...)
  pointsAsIntRegGOF(obj,covar=1,...)
  linesAsIntRegGOF(obj,covar=1,...)
plotAsIntRegGOF(obj, covar = 1, ADD = FALSE, ...)
  pointsAsIntRegGOF(obj,covar=1,...)
  linesAsIntRegGOF(obj,covar=1,...)

Arguments

`obj`	An object of class `lm`, `glm` or `nls`.
`covar`	Variable name, number or vector for which Int. Reg. is computed. If it is a number, it reference a covariate in the model frame, while if it is a name refer to data in data frame using in the fitting process.
`ADD`	If `TRUE` the plot is added to existing plot.
`...`	Further parameters to for plotobj command.

Details

Currently, the implementation computes the accumulated residual process against a single covariate (covar). When the value of covar is set to 0, the response is used as the variable whose residual are accumulated against.

Notice that if covar is a vector its lenght should be equal to the number of residuals.

Note

lm objects that does not have a data parameter set when the call is executed does not work presently when the covar parameter is different than 0.

Author(s)

Jorge Luis Ojeda Cabrera ([email protected]).

Examples

  n <- 50
  d <- data.frame( X1=runif(n),X2=runif(n))
  d$Y <- 1 + 2*d$X1 + rnorm(n,sd=.125)
  par(ask=TRUE)
  plot( d ) 
  plotAsIntRegGOF(lm(Y~X1+X2,d),covar="X1") 
  plotAsIntRegGOF(a <- lm(Y~X1-1,d)) 
  plotAsIntRegGOF(a,c("X1")) 
  plotAsIntRegGOF(a,0) 
  plotAsIntRegGOF(a,fitted(a)) 
  par(ask=FALSE)
n <- 50
  d <- data.frame( X1=runif(n),X2=runif(n))
  d$Y <- 1 + 2*d$X1 + rnorm(n,sd=.125)
  par(ask=TRUE)
  plot( d ) 
  plotAsIntRegGOF(lm(Y~X1+X2,d),covar="X1") 
  plotAsIntRegGOF(a <- lm(Y~X1-1,d)) 
  plotAsIntRegGOF(a,c("X1")) 
  plotAsIntRegGOF(a,0) 
  plotAsIntRegGOF(a,fitted(a)) 
  par(ask=FALSE)

Utility functions for Integrated Regression Goodness of Fit

Description

Functions that are basic or/and useful for the computation of the Integrated Regression Goodness of Fit

Usage

  getLessThan(x, d)
  mvCumSum(x, ord)
  mvPartOrd(x1, x2)
  getContVar(df, vars = NULL)
  getModelCovars(obj)
  getModelWeights(obj)
  rWildBoot(n)
getLessThan(x, d)
  mvCumSum(x, ord)
  mvPartOrd(x1, x2)
  getContVar(df, vars = NULL)
  getModelCovars(obj)
  getModelWeights(obj)
  rWildBoot(n)

Arguments

`x`, `d`	matrix like structure.
`x1`, `x2`	vectors with the same length.
`df`	a data frame.
`ord`	list of list structure with the ordering to add data points according to a given covariates.
`obj`	An object of class `lm`, `glm` or `nls`.
`vars`	vector with variable names in observations data frame .
`n`	integer, sample size.

Details

...TODO: Each of them computes what in which way

Note

getLessThan can be ceitainly better implemented.

Author(s)

Jorge Luis Ojeda Cabrera ([email protected]).

Package 'intRegGOF'

Help Index

Integrated Regression Goodness of Fit

Description

Usage

Arguments

Details

Value

Note

Author(s)

See Also

Examples

Utility functions for Integrated Regression Goodness of Fit

Description

Usage

Arguments

Details

Note

Author(s)

Integrated Regression Goodness of Fit

Description

Usage

Arguments

Details

Value

Note

Author(s)

References

See Also

Examples

Integrated Regression Goodness of Fit graphical output

Description

Usage

Arguments

Details

Note

Author(s)

See Also

Examples

Utility functions for Integrated Regression Goodness of Fit

Description

Usage

Arguments

Details

Note

Author(s)