G-square conditional independence test for discrete data {MXM}

G-square conditional independence test for discrete data

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. This test is based on the log likelihood ratio test.

Usage

gSquare(target, dataset, xIndex, csIndex, wei = NULL,  
univariateModels = NULL, hash = FALSE, stat_hash = NULL, 
pvalue_hash = NULL)

permgSquare(target, dataset, xIndex, csIndex, wei = NULL,
univariateModels = NULL, hash = FALSE, stat_hash = NULL, 
pvalue_hash = NULL, threshold = 0.05, R = 999)

Arguments

target

A numeric vector containing the values of the target variable. The minimum value must be 0.

dataset

A numeric matrix containing the variables for performing the test. Rows as samples and columns as features. The minimum value must be 0.

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

This argument is not used in this test.

univariateModels

Fast alternative to the hash object for univariate tests. 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 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 which contains the cached generated statistics of a SES run in the current dataset, using the current test.

pvalue_hash

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

threshold

Threshold (suitable values in (0, 1)) for assessing p-values significance. Default value is 0.05. This is actually obsolete here, but has to be in order to have a concise list of input arguments across the same family of functions.

R

The number of permutations to use. The default value is 999.

Details

If the number of samples is at least 5 times the number of the parameters to be estimated, the test is performed, otherwise, independence is not rejected (see Tsmardinos et al., 2006, pg. 43)

If hash = TRUE, testIndLogistic requires the arguments 'stat_hash' and 'pvalue_hash' for the hash-based implementation of the statistical 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".

Value

A list including:

pvalue

A numeric value that represents the logarithm of the generated p-value of the G^2 test (see reference below).

stat

A numeric value that represents the generated statistic of the G^2 test (see reference below).

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.

Author(s)

R implementation and documentation: Giorgos Athineou <[e-mail]>

References

Tsamardinos, Ioannis, Laura E. Brown, and Constantin F. Aliferis. The max-min hill-climbing Bayesian network structure learning algorithm. Machine learning, 2006 65(1): 31–78.

See Also

SES, testIndFisher, testIndLogistic, censIndCR, CondIndTests

Examples

#simulate a dataset with binary data
dataset <- matrix(rbinom(500 * 51, 1, 0.6), ncol = 51)
#initialize binary target
target <- dataset[, 51]
#remove target from the dataset
dataset <- dataset[, -51]

#run the gSquare conditional independence test for the binary class variable
results <- gSquare(target, dataset, xIndex = 44, csIndex = c(10,20) )
results

#run SES algorithm using the gSquare conditional independence test for the binary class variable
sesObject <- SES(target, dataset, max_k = 3, threshold = 0.05, test = "gSquare");
target <- as.factor(target)
sesObject2 <- SES(target, dataset, max_k = 3, threshold = 0.05, test = "testIndLogistic");