MXM (version 0.7)

testIndMVreg: Linear regression conditional independence test for continous class multivariate target variables.

Description

The main task of this test is to provide a p-value PVALUE for the null hypothesis: feature 'X' is independent from 'MULTIVARIATE 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

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

Arguments

target

A numeric matrix containing the values of the multivariate target variable.

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 robustified version of the multivariate linear regression. Currently it is not available for these cases.

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, testIndMVreg 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. 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.

References

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

SES, testIndRQ, testIndFisher, censIndLR, CondIndTests

Examples

#simulate a dataset with continuous data
dataset <- matrix(runif(2000 * 50, 1, 100), nrow = 1000 , ncol = 50)
#the target feature is the last column of the dataset as a vector
b <- matrix( rnorm(100, 3, 0.4), ncol = 2 ) 
id <- sample(1:50, 5)
b[-id,] <- 0
e <- matrix( rnorm(2 * 1000, 0, 5), ncol = 2 )
target <- crossprod( t(cbind(1, dataset)), rbind(c(10, 15), b) ) + e
results <- testIndMVreg(target, dataset, xIndex = 1, csIndex = 50)
results
aa <- SES(as.matrix(target), dataset, max_k = 3, threshold = 0.05)