MXM (version 0.7)

testIndReg: Linear regression conditional independence test for continous class 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 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, 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) ).

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.

dataInfo

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 val

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 M-estimation available from the "rlm" in MASS. It takes more time than non robust version but it is suggested in case of outliers. Default value is FALSE.

Value

• A list including:
• pvalue
  A numeric value that represents the generated p-value due to linear regression (see reference below).
• stat
  A numeric value that represents the generated statistic due to linear regression (see reference below).
• flag
  A numeric value (control flag) which indicates whether the test was succesful (0) or not (1).
• stat_hash
  The current hash object used for the statistics. See argument stat_hash and details. If argument hash = FALSE this is NULL.
• pvalue_hash
  The current hash object used for the p-values. See argument stat_hash and details. If argument hash = FALSE this is NULL.

Details

If hash = TRUE, testIndReg requires 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. 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.

See Also

SES, testIndRQ, testIndFisher, testIndSpearman, CondIndTests

Examples

#simulate a dataset with continuous data
dataset <- matrix(runif(500 * 100, 1, 100), ncol = 500 )
#the target feature is the last column of the dataset as a vector
target <- dataset[, 100]
dataset <- dataset[, -100]
results <- testIndReg(target, dataset, xIndex = 44, csIndex = 50)
results

#require(gRbase)  #for faster computations in the internal functions
#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");
#print summary of the SES output
summary(sesObject);
#plot the SES output
plot(sesObject, mode = "all");