testIndGLMMReg: Linear mixed models conditional independence test for...

In MXM: Feature Selection (Including Multiple Solutions) and Bayesian Networks

Linear mixed models conditional independence test for longitudinal 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 with 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. This test accepts a longitudinal target and longitudinal, categorical, continuous or mixed data as predictor variables.

Usage

testIndGLMMReg(target, reps = NULL, group, dataset, xIndex, csIndex, wei = NULL,
univariateModels = NULL, hash = FALSE, stat_hash = NULL, 
pvalue_hash = NULL, slopes = FALSE)

testIndGLMMLogistic(target, reps = NULL, group, dataset, xIndex, csIndex, wei = NULL,
univariateModels = NULL, hash = FALSE, stat_hash = NULL, 
pvalue_hash = NULL, slopes = FALSE)

testIndGLMMPois(target, reps = NULL, group, dataset, xIndex, csIndex, wei = NULL,
univariateModels = NULL, hash = FALSE, stat_hash = NULL, 
pvalue_hash = NULL, slopes = FALSE)

testIndGLMMNB(target, reps = NULL, group, dataset, xIndex, csIndex, wei = NULL,
univariateModels = NULL, hash = FALSE, stat_hash = NULL, 
pvalue_hash = NULL, slopes = FALSE)

testIndGLMMGamma(target, reps = NULL, group, dataset, xIndex, csIndex, wei = NULL,
univariateModels = NULL, hash = FALSE, stat_hash = NULL, 
pvalue_hash = NULL, slopes = FALSE)

testIndGLMMNormLog(target, reps = NULL, group, dataset, xIndex, csIndex, wei = NULL,
univariateModels = NULL, hash = FALSE, stat_hash = NULL, 
pvalue_hash = NULL, slopes = FALSE)

testIndGLMMOrdinal(target, reps = NULL, group, dataset, xIndex, csIndex, wei = NULL,
univariateModels = NULL, hash = FALSE, stat_hash = NULL, 
pvalue_hash = NULL, slopes = FALSE)

testIndGLMMCR(target, reps = NULL, group, dataset, xIndex, csIndex, wei = NULL,
univariateModels = NULL, hash = FALSE, stat_hash = NULL, 
pvalue_hash = NULL, slopes = FALSE)

testIndLMM(target, reps = NULL, group, dataset, xIndex, csIndex, wei = NULL,
univariateModels = NULL, hash = FALSE, stat_hash = NULL, 
pvalue_hash = NULL, slopes = 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 both cases a linear mixed model is applied. It can also be a binary variable (binary logistic regression) or a discrete, counts (Poisson regression), thus fitting generalised linear mixed models. In the case of "testIndGLMMOrdinal" this must be an ordered factor.
reps	A numeric vector containing the time points of the subjects. It's length is equal to the length of the target variable. If you have clustered data, leave this NULL. This is not applied in ordinal and Cox regression.
group	A numeric vector containing the subjects or groups. It must be of the same length as 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. If you have no variables set this equal to 0.
wei	A vector of weights to be used for weighted regression. The default value is NULL. An example where weights are used is surveys when stratified sampling has occured.
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 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.
slopes	A boolean variable which indicates whether (TRUE) to or not (FALSE) random slopes in the time effect as well. By deault random intercepts are considered. This is not applied in ordinal and Cox regression.

Details

If hash = TRUE, testIndGLMM 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.temp 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".

This test is for longitudinal and clustered data. Bear in mind that the time effect, for the longitudinal data case, is linear. It could be of higer order as well, but this would be a hyper-parameter, increasing the complexity of the models to be tested.

The testIndLMM is used for linear mixed models with no weights, no slopes and no reps. This is a random intercepts model only. The advantage of this function is that it is tens of times faster than testIndGLMM.

Value

A list including:

pvalue	A numeric value that represents the logarithm of the generated p-value due to the (generalised) linear mixed model (see reference below).
stat	A numeric value that represents the generated statistic due to the (generalised) linear mixed model (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)

Vincenzo Lagani, Ioannis Tsamardinos, Michail Tsagris and Giorgos Athineou

R implementation and documentation: Giorgos Athineou <[e-mail]>, Vincenzo Lagani <[e-mail]> and Michail Tsagris [e-mail]

References

Eugene Demidenko (2013). Mixed Models: Theory and Applications with R, 2nd Edition. New Jersey: Wiley & Sons.

Jose Pinheiro Jose and Douglas Bates. Mixed-effects models in S and S-PLUS. Springer Science & Business Media, 2006.

See Also

SES.glmm, MMPC.glmm, CondIndTests

Examples

y <- rnorm(150)
x <- matrix(rnorm(150 * 5), ncol = 5)
id <- sample(1:20, 150, replace = TRUE)
testIndGLMMReg(y, group = id, dataset = x, xIndex = 1, csIndex = 3)
testIndLMM(y, group = id, dataset = x, xIndex = 1, csIndex = 3)

MXM documentation built on Aug. 25, 2022, 9:05 a.m.