MXM (version 0.9.5)

Conditional independence tests for continous univariate and multivariate data : Linear (and non-linear) regression conditional independence test for continous univariate and multivariate response variables

Description

The main task of this test is to provide a p-value PVALUE for the null hypothesis: feature 'X' is independent from 'TARGET' given a conditioning set CS. The pvalue is calculated by comparing a linear regression model based on the conditioning set CS against a model whose regressor are both X and CS. The comparison is performed through an F test the appropriate degrees of freedom on the difference between the deviances of the two models.

Usage

testIndReg(target, dataset, xIndex, csIndex, wei = NULL, dataInfo = NULL, 
univariateModels = NULL, hash = FALSE, stat_hash = NULL, pvalue_hash = NULL, 
robust = FALSE)
testIndRQ(target, dataset, xIndex, csIndex, wei = NULL, dataInfo = NULL, 
univariateModels = NULL, hash = FALSE, stat_hash = NULL, pvalue_hash = NULL, 
robust = FALSE)
testIndMVreg(target, dataset, xIndex, csIndex, wei = NULL, dataInfo = NULL, 
univariateModels = NULL, hash = FALSE, stat_hash = NULL, pvalue_hash = NULL, 
robust = FALSE)
testIndIGreg(target, dataset, xIndex, csIndex, wei = NULL, dataInfo = NULL, 
univariateModels = NULL, hash = FALSE, stat_hash = NULL, pvalue_hash = NULL, 
robust = FALSE)

Arguments

target

A numeric vector containing the values of the target variable. If the values are proportions or percentages, i.e. strictly within 0 and 1 they are mapped into R using log( target/(1 - target) ). In the case of testIndMVreg, the same takes place true. See details for more information.

dataset

A numeric matrix or data frame, in case of categorical predictors (factors), containing the variables for performing the test. Rows as samples and columns as features.

xIndex

The index of the variable whose association with the target we want to test.

csIndex

The indices of the variables to condition on.

wei

A vector of weights to be used for weighted regression. The default value is NULL. We suggest not to use weights if you choose testIndReg and robust = TRUE (robust regression via M estimation)

dataInfo

A list object with information on the structure of the data. Default value is NULL.

univariateModels

Fast alternative to the hash object for univariate test. List with vectors "pvalues" (p-values), "stats" (statistics) and "flags" (flag = TRUE if the test was succesful) representing the univariate association of each variable with the target. Default value is NULL.

hash

A boolean variable which indicates whether (TRUE) or not (FALSE) to use tha hash-based implementation of the statistics of SES. Default value is FALSE. If TRUE you have to specify the stat_hash argument and the pvalue_hash argument.

stat_hash

A hash object (hash package required) which contains the cached generated statistics of a SES run in the current dataset, using the current test.

pvalue_hash

A hash object (hash package required) which contains the cached generated p-values of a SES run in the current dataset, using the current test.

robust

A boolean variable which indicates whether (TRUE) or not (FALSE) to use a robust regression via MM-estimation available from rlm in the package "MASS". A robust F test is also performed.It takes more time than non robust version but it is suggested in case of outliers. Default value is FALSE. This is only used in testIndReg. Quantile regression is robust by default and for multivariate regression this has not been incorporated yet.

Value

A list including: A list including:

Details

If hash = TRUE, all three tests require the arguments 'stat_hash' and 'pvalue_hash' for the hash-based implementation of the statistic test. These hash Objects are produced or updated by each run of SES (if hash == TRUE) and they can be reused in order to speed up next runs of the current statistic test. If "SESoutput" is the output of a SES run, then these objects can be retrieved by SESoutput@hashObject$stat_hash and the SESoutput@hashObject$pvalue_hash.

Important: Use these arguments only with the same dataset that was used at initialization.

TestIndReg offers linear and robust linear (via M estimation) regression.

TestIndRQ offers quantile (median) regression as a robust alternative to linear regression.

In both cases, if the dependent variable consists of proportions (values between 0 and 1) the logit transformation is applied and the tests are applied then.

testIndMVreg is for multivariate continuous response variables. Compositional data are positive multivariate data and each vector (observation) sums to the same constant, usually taken 1 for convenience. A check is performed and if such data are found, the additive log-ratio (multivariate logit) transformation (Aitchison, 1986) is applied beforehand. Zeros are not allowed. TestIndIGreg is for non negative data. It fits an inverse gaussian distribution with a log link. Or you cound see it as a non linear Gaussian model where the conditional mean is related with the covariate(s) via an exponential function.

For all the available conditional independence tests that are currently included on the package, please see "?CondIndTests".

References

Draper, N.R. and Smith H. (1988). Applied regression analysis. New York, Wiley, 3rd edition.

Hampel F. R., Ronchetti E. M., Rousseeuw P. J., and Stahel W. A. (1986). Robust statistics: the approach based on influence functions. John Wiley & Sons.

Koenker R.W. (2005). Quantile regression. New York, Cambridge University Press.

Mardia, Kanti, John T. Kent and John M. Bibby. Multivariate analysis. Academic press, 1979.

John Aitchison. The Statistical Analysis of Compositional Data, Chapman & Hall; reprinted in 2003, with additional material, by The Blackburn Press.

See Also

testIndSpeedglm, testIndRQ, testIndFisher, testIndSpearman, CondIndTests

Examples

#simulate a dataset with continuous data
dataset <- matrix(runif(100 * 100, 1, 100), ncol = 100 )
#the target feature is the last column of the dataset as a vector
target <- dataset[, 100]
dataset <- dataset[, -100]

testIndReg(target, dataset, xIndex = 44, csIndex = 50)
testIndReg(target, dataset, xIndex = 44, csIndex = 50, robust = TRUE)
testIndRQ(target, dataset, xIndex = 44, csIndex = 50)
testIndIGreg(target, dataset, xIndex = 44, csIndex = 50)

#define class variable (here tha last column of the dataset)
#run the SES algorithm using the testIndReg conditional independence test
sesObject <- SES(target, dataset, max_k = 3, threshold = 0.05, test = "testIndReg");
sesObject2 <- SES(target, dataset, max_k = 3, threshold = 0.05, test = "testIndRQ");
#print summary of the SES output

summary(sesObject);
summary(sesObject2);
# plot the SES output
# plot(sesObject, mode = "all");