Conditional independence test for longitudinal and clustered data: 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 whose GLMMressor 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. This test accepts a longitudinal target and longitudinal, categorical, continuous or mixed data as predictor variables.

Usage

testIndGLMM(target, reps = NULL, group, dataset, xIndex, csIndex, dataInfo=NULL, 
univariateModels=NULL, hash = FALSE, stat_hash=NULL, pvalue_hash=NULL, 
target_type=0, 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.

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.

group

A numeric vector containing the subjects or groups. It must be of the same legnth 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.

dataInfo

A 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 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 (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.

target_type

The type of the target variable. It is set to 0 by default. 1 for continuous variable (normal), 2 for binary variable (binomial) and 3 for discrete variable (Poisson).

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.

Value

A list including: A list including:

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.

The time effect 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.

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

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

Examples

Run this code

#data(sleepstudy)
#attach(sleepstudy)
#target <- Reaction
#x <- matrix(rnorm(180 * 10),ncol = 10) ## unrelated preidctor variables
#testIndGLMM(target, Days, Subject, x, 1,0,target_type = 1)

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