mmpc.glmm2: mmpc.glmm2/mmpc.gee2: Fast Feature selection algorithm for...

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

mmpc.glmm2/mmpc.gee2: Fast Feature selection algorithm for identifying minimal feature subsets with correlated data

Description

SES.glmm algorithm follows a forward-backward filter approach for feature selection in order to provide minimal, highly-predictive, statistically-equivalent, multiple feature subsets of a high dimensional dataset. See also Details. MMPC.glmm algorithm follows the same approach without generating multiple feature subsets. They are both adapted to longitudinal target variables.

Usage

mmpc.glmm2(target, reps = NULL, group, dataset, prior = NULL, max_k = 3, 
threshold = 0.05, test = NULL, ini = NULL, wei = NULL, slopes = FALSE, ncores = 1)

mmpc.gee2(target, reps = NULL, group, dataset, prior = NULL, max_k = 3, 
threshold = 0.05, test = NULL, ini = NULL, wei = NULL, correl = "exchangeable", 
se = "jack", ncores = 1)

Arguments

target	The class variable. Provide a vector with continuous (normal), binary (binomial) or discrete (Poisson) data. For the GEE the data must be sorted so that observations on a cluster are contiguous rows for all entities in the formula.
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. For the GEE the data must be sorted so that observations on a cluster are contiguous rows for all entities in the formula.
group	A numeric vector containing the subjects or groups. It must be of the same length as target. For the GEE the data must be sorted so that observations on a cluster are contiguous rows for all entities in the formula.
dataset	The dataset; provide either a data frame or a matrix (columns = variables, rows = samples). Currently, only continuous datasets are supported. For the GEE the data must be sorted so that observations on a cluster are contiguous rows for all entities in the formula.
prior	If you have prior knowledge of some variables that must be in the variable selection phase add them here. This an be a vector (if you have one variable) or a matrix (if you more variables).
max_k	The maximum conditioning set to use in the conditional indepedence test (see Details). Integer, default value is 3.
threshold	Threshold (suitable values in (0, 1)) for assessing p-values significance. Default value is 0.05.
test	The conditional independence test to use. Default value is NULL. Currently, the only available conditional independence test are the testIndGLMMLogistic, testIndGLMMPois, testIndGLMMGamma, testIndGLMMNormLog and testIndGLMMReg which fit linear mixed models. For the GEE the options are testIndGEELogistic, testIndGEEPois, testIndGEEGamma, testIndGEENormLog and testIndGEENormLog.
ini	This is a supposed to be a list. After running SES or MMPC with some hyper-parameters you might want to run SES again with different hyper-parameters. To avoid calculating the univariate associations (first step of SES and of MPPC) again, you can extract them from the first run of SES and plug them here. This can speed up the second run (and subequent runs of course) by 50%. See the details and the argument "univ" in the output values.
wei	A vector of weights to be used for weighted regression. The default value is NULL.
slopes	Should random slopes for the ime effect be fitted as well? Default value is FALSE.
correl	The correlation structure of the GEE. 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). All observations must be ordered according to time within each subject. See the vignette of geepack to understand how.
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': approximate jackknife variance estimate. c) 'j1s': if 1-step jackknife variance estimate and d) 'fij': fully iterated jackknife variance estimate. If you have many clusters (sets of repeated measurements) "san.se" is fine as it is asympotically 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.
ncores	How many cores to use. This plays an important role if you have tens of thousands of variables or really large sample sizes and tens of thousands of variables and a regression based test which requires numerical optimisation. In other cases it will not make a difference in the overall time (in fact it can be slower). The parallel computation is used in the first step of the algorithm, where univariate associations are examined, those take place in parallel. We have seen a reduction in time of 50% with 4 cores in comparison to 1 core. Note also, that the amount of reduction is definetely not linear in the number of cores.

Details

These are faster versions of MMPC using GLMM or GEE methodologies. See also mmpc2 for more details on the algorithm.

If you want to use the GEE methodology, make sure you load the library geepack first.

Value

The output of the algorithm is an object of the class 'SES.glmm.output' for SES.glmm or 'MMPC.glmm.output' for MMPC.glmm including:

selectedVars	The selected variables, i.e., the signature of the target variable.
pvalues	For each feature included in the dataset, this vector reports the strength of its association with the target in the context of all other variables. Particularly, this vector reports the max p-values foudn when the association of each variable with the target is tested against different conditional sets. Lower values indicate higher association. Note that these are the logarithm of the p-values.
univ	A vector with the logged p-values of the univariate associations. This vector is very important for subsequent runs of MMPC with different hyper-parameters. After running SES with some hyper-parameters you might want to run MMPCagain with different hyper-parameters. To avoid calculating the univariate associations (first step) again, you can take this list from the first run of SES and plug it in the argument "ini" in the next run(s) of MMPC. This can speed up the second run (and subequent runs of course) by 50%. See the argument "univ" in the output values.
kapa_pval	A list with the same number of elements as the max$_k$. Every element in the list is a matrix. The first row is the logged p-values, the second row is the variable whose conditional association with the target variable was tests and the other rows are the conditioning variables.
max_k	The max_k option used in the current run.
threshold	The threshold option used in the current run.
n.tests	If you have set hash = TRUE, then the number of tests performed by SES or MMPC will be returned. If you have not set this to TRUE, the number of univariate associations will be returned. So be careful with this number.
runtime	The run time of the algorithm. A numeric vector. The first element is the user time, the second element is the system time and the third element is the elapsed time.
test	The character name of the statistic test used.
slope	Whether random slopes for the time effects were used or not, TRUE or FALSE.

Author(s)

Ioannis Tsamardinos, Vincenzo Lagani

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

References

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

I. Tsamardinos, M. Tsagris and V. Lagani (2015). Feature selection for longitudinal data. Proceedings of the 10th conference of the Hellenic Society for Computational Biology & Bioinformatics (HSCBB15).

I. Tsamardinos, V. Lagani and D. Pappas (2012). Discovering multiple, equivalent biomarker signatures. In proceedings of the 7th conference of the Hellenic Society for Computational Biology & Bioinformatics - HSCBB12.

Tsamardinos, Brown and Aliferis (2006). The max-min hill-climbing Bayesian network structure learning algorithm. Machine learning, 65(1), 31-78.

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

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

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.

See Also

CondIndTests, testIndGLMMReg

Examples

## Not run: 
require(lme4)
data(sleepstudy)
reaction <- sleepstudy$Reaction
days <- sleepstudy$Days
subject <- sleepstudy$Subject
x <- matrix(rnorm(180 * 100), ncol = 100) ## unrelated predictor variables
m1 <- mmpc.glmm2(target = reaction, reps = days, group = subject, dataset = x)
m2 <- MMPC.glmm(target = reaction, reps = days, group = subject, dataset = x)

## End(Not run)

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