testIndGEEReg: 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

testIndGEEReg(target, reps = NULL, group, dataset, xIndex, csIndex,  wei =  NULL, 
univariateModels = NULL, hash = FALSE, stat_hash = NULL, pvalue_hash = NULL, 
correl = "exchangeable", se = "jack")

testIndGEELogistic(target, reps = NULL, group, dataset, xIndex, csIndex,  wei =  NULL, 
univariateModels = NULL, hash = FALSE, stat_hash = NULL, pvalue_hash = NULL, 
correl = "exchangeable", se = "jack")

testIndGEEPois(target, reps = NULL, group, dataset, xIndex, csIndex,  wei =  NULL, 
univariateModels = NULL, hash = FALSE, stat_hash = NULL, pvalue_hash = NULL, 
correl = "exchangeable", se = "jack")

testIndGEEGamma(target, reps = NULL, group, dataset, xIndex, csIndex,  wei =  NULL, 
univariateModels = NULL, hash = FALSE, stat_hash = NULL, pvalue_hash = NULL, 
correl = "exchangeable", se = "jack")

testIndGEENormLog(target, reps = NULL, group, dataset, xIndex, csIndex,  wei =  NULL, 
univariateModels = NULL, hash = FALSE, stat_hash = NULL, pvalue_hash = NULL, 
correl = "exchangeable", se = "jack")

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 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. It is mentioned in the "geepack" that weights is not (yet) the weight as in sas proc genmod, and hence is not recommended to use.
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.
correl	The correlation structure. For the Gaussian, Logistic, Poisson and Gamma regression this can be either "exchangeable" (compound symmetry, suitable for clustered data) or "ar1" (AR(1) model, suitable for longitudinal data). For the ordinal logistic regression its only the "exchangeable" correlation sturcture.
se	The method for estimating standard errors. This is very important and crucial. The available options for Gaussian, Logistic, Poisson and Gamma regression are: a) 'san.se', the usual robust estimate. b) 'jack': if approximate jackknife variance estimate should be computed. c) 'j1s': if 1-step jackknife variance estimate should be computed and d) 'fij': logical indicating if fully iterated jackknife variance estimate should be computed. If you have many clusters (sets of repeated measurements) "san.se" is fine as it is astmpotically correct, plus jacknife estimates will take longer. If you have a few clusters, then maybe it's better to use jacknife estimates. The jackknife variance estimator was suggested by Paik (1988), which is quite suitable for cases when the number of subjects is small (K < 30), as in many biological studies. The simulation studies conducted by Ziegler et al. (2000) and Yan and Fine (2004) showed that the approximate jackknife estimates are in many cases in good agreement with the fully iterated ones.

Details

If hash = TRUE, testIndGEE 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.

Make sure you load the library geepack first.

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)

Michail Tsagris

R implementation and documentation: Michail Tsagris [e-mail]

References

Liang K.Y. and Zeger S.L. (1986). Longitudinal data analysis using generalized linear models. Biometrika, 73(1): 13-22.

Prentice R.L. and Zhao L.P. (1991). Estimating equations for parameters in means and covariances of multivariate discrete and continuous responses. Biometrics, 47(3): 825-839.

Heagerty P.J. and Zeger S.L. (1996) Marginal regression models for clustered ordinal measurements. Journal of the American Statistical Association, 91(435): 1024-1036.

Paik M.C. (1988). Repeated measurement analysis for nonnormal data in small samples. Communications in Statistics-Simulation and Computation, 17(4): 1155-1171.

Ziegler A., Kastner C., Brunner D. and Blettner M. (2000). Familial associations of lipid profiles: A generalised estimating equations approach. Statistics in medicine, 19(24): 3345-3357

Yan J. and Fine J. (2004). Estimating equations for association structures. Statistics in medicine, 23(6): 859-874.

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

Tsagris, M., Lagani, V., & Tsamardinos, I. (2018). Feature selection for high-dimensional glmm data. BMC bioinformatics, 19(1), 17.

See Also

SES.glmm, MMPC.glmm, CondIndTests

Examples

library("geepack", quietly = TRUE)
y <- rnorm(150)
x <- matrix(rnorm(150 * 5), ncol = 5)
id <- sample(1:20, 150, replace = TRUE)
testIndGEEReg(y, group = id, dataset = x, xIndex = 1, csIndex = 3)

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