MXM (version 0.7)

testIndSpearman: Spearman's conditional independence test for continuous 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.

Usage

testIndSpearman(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 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 the 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

This is not used in this test as Spearman's correlation is robut by creation. It's influence fnction, unlike Pearson's correlation coefficient, is bounded ().

Value

• A list including:
• pvalue
  A numeric value that represents the generated p-value due to Spearman's method (see reference below).
• stat
  A numeric value that represents the generated statistic due to Spearman's method (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, testIndSpearman 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". BE CAREFUL with this test. The Pearson's correlation coefficient is actually calculated. So, you must have transformed the data into their ranks before plugging them here. The reason for this is to speed up the computation time, as this test can be uses in SES, MMPC and mmhc.skel. The variance of the Fisher transformed Spearman's correlation is $frac{1.06}{n-3}$ and the variance of the Fisher transformed Pearson's correlation coefficient is $frac{1}{n-3}$.

References

Peter Spirtes, Clark Glymour, and Richard Scheines. Causation, Prediction, and Search. The MIT Press, Cambridge, MA, USA, second edition, January 2001. Croux C. and Dehon C. (2010). Influence functions of the Spearman and Kendall correlation measures. Statistical methods & applications, 19(4): 497-515. Fieller E.C. Herman O.H. and Pearson E.S. (1957). Tests for rank correlation coefficients. I. Biometrika, 44(3/4): 470-481. Fieller E.C. and Pearson E.S. (1961). Tests for rank correlation coefficients: II. Biometrika, 48(1/2): 29-40.

See Also

SES, testIndFisher, gSquare, censIndLR, CondIndTests

Examples

#simulate a dataset with continuous data
dataset <- matrix(runif(1000 * 100, 1, 1000), nrow = 1000 ) 
#the target feature is the last column of the dataset as a vector
target <- dataset[, 100]
dataset <- dataset[, -100]
results <- testIndSpearman(target, dataset, xIndex = 44, csIndex = 67)
results

#require(gRbase)  #for faster computations in the internal functions
#define class variable (here the last column of the dataset)
target <- 99;
#run the SES algorithm using the testIndSpearman conditional independence test
sesObject <- SES(target, dataset, max_k = 3, threshold = 0.05, test = "testIndSpearman");
sesObject <- SES(target, dataset, max_k = 3, threshold = 0.05, test = "testIndFisher");
#print summary of the SES output
summary(sesObject);
#plot the SES output
plot(sesObject, mode = "all");