fbed.gee.reg: Forward Backward Early Dropping selection regression with GEE
In MXM: Feature Selection (Including Multiple Solutions) and Bayesian Networks
Forward Backward Early Dropping selection regression with GEE R Documentation
Forward Backward Early Dropping selection regression with GEE
Description
Forward Backward Early Dropping selection regression with GEE.
Usage
fbed.gee.reg(target, dataset, id, prior = NULL, reps = NULL, ini = NULL,
threshold = 0.05, wei = NULL, K = 0, test = "testIndGEEReg",
correl = "exchangeable", se = "jack")
Arguments
target
The class variable. This can be a numerical vector with continuous data, binary, discrete or an ordered factor variable. It can also be a factor variable with two levels only. Pay attention to this. If you have ordinal data, then supply an ordered factor variable. The data must be sorted so that observations on a cluster are contiguous rows for all entities in the formula.
dataset
The set of candidate predictor variables provide a numerical matrix or a data.frame in case of categorical variables (columns = variables, rows = samples). In the case of ordinal regression, this can only be a numerical matrix, i.e. only continuous predictor variables. The data must be sorted so that observations on a cluster are contiguous rows for all entities in the formula.
id
This is a numerical vector of the same size as target denoting the groups or the subjects. 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).
reps
This is a numerical vector of the same size as target denoting the groups or the subjects. If you have longitudinal data and you know the time points, then supply them here. The data must be sorted so that observations on a cluster are contiguous rows for all entities in the formula.
ini
If you already have the test statistics and the logged p-values of the univariate associations (the first step of FBED) supply them as a list with the names "stat" and "pvalue" respectively.
threshold
Threshold (suitable values in (0, 1)) for asmmmbsing p-values significance. Default value is 0.05.
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.
K
How many times should the process be repated? The default value is 0.
test
This is for the type of regression to be used, "testIndGEEReg", for Gaussian regression,
"testIndGEEGamma" for Gamma regression, "testIndGEELogistic for logistic regression, "testIndGEENormLog" for linear regression witha log link, "testIndGEEPois" for Poisson regression or "testIndGEEOrdinal" for ordinal regression.
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). If you want to use the AR(1) correlation structure you must be careful with the input dat you give. All data (target and dataset) must be sorted according to the id and time points. All observations must be ordered according to time within each subject. See the vignette of geepack to understand how. 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
The algorithm is a variation of the usual forward selection. At every step, the most significant variable enters the selected variables set. In addition, only the significant variables stay and are further examined. The non signifcant ones are dropped. This goes until no variable can enter the set. The user has the option to redo this step 1 or more times (the argument K). In the end, a backward selection is performed to remove falsely selected variables.
Since GEE are likelihood free, all significance tests take place using the Wald test, hence we decided not to have a backward phase. This algorithm is suitable for both clustered and longitudinal (glmm) data.
If you specify a range of values of K it returns the results of fbed.reg for this range of values of K. For example, instead of runnning fbed.reg with K=0, K=1, K=2 and so on, you can run fbed.reg with K=0:2 and the selected variables found at K=2, K=1 and K=0 are returned. Note also, that you may specify maximum value of K to be 10, but the maximum value FBED used was 4 (for example).
For GEE make sure you load the library geepack first.
Value
If K is a single number a list including:
res
A matrix with the selected variables, their test statistic and the associated logged p-value.
info
A matrix with the number of variables and the number of tests performed (or models fitted) at each round (value of K).
runtime
The runtime required.
If K is a sequence of numbers a list tincluding:
univ
If you have used the log-likelihood ratio test this list contains the test statistics and the associated logged p-values of the univariate associations tests. If you have used the EBIc this list contains the eBIC of the univariate associations.
res
The results of fbed.gee.reg with the maximum value of K.
mod
A list where each element refers to a K value. If you run FBEd with method = "LR" the selected variables, their test statistic and their p-value is returned. If you run it with method = "eBIC", the selected variables and the eBIC of the model with those variables are returned.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr
References
Borboudakis G. and Tsamardinos I. (2019). Forward-backward selection with early dropping. Journal of Machine Learning Research, 20(8): 1-39.
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.
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.
The R package geepack vignette.
See Also
fbed.glmm.reg, glmm.bsreg, MMPC.glmm, fbed.reg
Examples
## Not run:
require(lme4)
data(sleepstudy)
reaction <- sleepstudy$Reaction
days <- sleepstudy$Days
subject <- sleepstudy$Subject
x <- matrix(rnorm(180 * 200),ncol = 200) ## unrelated predictor variables
m1 <- fbed.gee.reg(reaction, x, subject)
m2 <- fbed.glmm.reg(reaction, x, subject, backward = FALSE)
## End(Not run)
MXM documentation built on Aug. 25, 2022, 9:05 a.m.
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| Forward Backward Early Dropping selection regression with GEE | R Documentation |
Forward Backward Early Dropping selection regression with GEE
Description
Forward Backward Early Dropping selection regression with GEE.
Usage
fbed.gee.reg(target, dataset, id, prior = NULL, reps = NULL, ini = NULL, threshold = 0.05, wei = NULL, K = 0, test = "testIndGEEReg", correl = "exchangeable", se = "jack")
Arguments
target |
The class variable. This can be a numerical vector with continuous data, binary, discrete or an ordered factor variable. It can also be a factor variable with two levels only. Pay attention to this. If you have ordinal data, then supply an ordered factor variable. The data must be sorted so that observations on a cluster are contiguous rows for all entities in the formula. |
dataset |
The set of candidate predictor variables provide a numerical matrix or a data.frame in case of categorical variables (columns = variables, rows = samples). In the case of ordinal regression, this can only be a numerical matrix, i.e. only continuous predictor variables. The data must be sorted so that observations on a cluster are contiguous rows for all entities in the formula. |
id |
This is a numerical vector of the same size as target denoting the groups or the subjects. 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). |
reps |
This is a numerical vector of the same size as target denoting the groups or the subjects. If you have longitudinal data and you know the time points, then supply them here. The data must be sorted so that observations on a cluster are contiguous rows for all entities in the formula. |
ini |
If you already have the test statistics and the logged p-values of the univariate associations (the first step of FBED) supply them as a list with the names "stat" and "pvalue" respectively. |
threshold |
Threshold (suitable values in (0, 1)) for asmmmbsing p-values significance. Default value is 0.05. |
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. |
K |
How many times should the process be repated? The default value is 0. |
test |
This is for the type of regression to be used, "testIndGEEReg", for Gaussian regression, "testIndGEEGamma" for Gamma regression, "testIndGEELogistic for logistic regression, "testIndGEENormLog" for linear regression witha log link, "testIndGEEPois" for Poisson regression or "testIndGEEOrdinal" for ordinal regression. |
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). If you want to use the AR(1) correlation structure you must be careful with the input dat you give. All data (target and dataset) must be sorted according to the id and time points. All observations must be ordered according to time within each subject. See the vignette of geepack to understand how. 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
The algorithm is a variation of the usual forward selection. At every step, the most significant variable enters the selected variables set. In addition, only the significant variables stay and are further examined. The non signifcant ones are dropped. This goes until no variable can enter the set. The user has the option to redo this step 1 or more times (the argument K). In the end, a backward selection is performed to remove falsely selected variables.
Since GEE are likelihood free, all significance tests take place using the Wald test, hence we decided not to have a backward phase. This algorithm is suitable for both clustered and longitudinal (glmm) data.
If you specify a range of values of K it returns the results of fbed.reg for this range of values of K. For example, instead of runnning fbed.reg with K=0, K=1, K=2 and so on, you can run fbed.reg with K=0:2 and the selected variables found at K=2, K=1 and K=0 are returned. Note also, that you may specify maximum value of K to be 10, but the maximum value FBED used was 4 (for example).
For GEE make sure you load the library geepack first.
Value
If K is a single number a list including:
res |
A matrix with the selected variables, their test statistic and the associated logged p-value. |
info |
A matrix with the number of variables and the number of tests performed (or models fitted) at each round (value of K). |
runtime |
The runtime required. |
If K is a sequence of numbers a list tincluding:
univ |
If you have used the log-likelihood ratio test this list contains the test statistics and the associated logged p-values of the univariate associations tests. If you have used the EBIc this list contains the eBIC of the univariate associations. |
res |
The results of fbed.gee.reg with the maximum value of K. |
mod |
A list where each element refers to a K value. If you run FBEd with method = "LR" the selected variables, their test statistic and their p-value is returned. If you run it with method = "eBIC", the selected variables and the eBIC of the model with those variables are returned. |
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr
References
Borboudakis G. and Tsamardinos I. (2019). Forward-backward selection with early dropping. Journal of Machine Learning Research, 20(8): 1-39.
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.
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.
The R package geepack vignette.
See Also
fbed.glmm.reg, glmm.bsreg, MMPC.glmm, fbed.reg
Examples
## Not run: require(lme4) data(sleepstudy) reaction <- sleepstudy$Reaction days <- sleepstudy$Days subject <- sleepstudy$Subject x <- matrix(rnorm(180 * 200),ncol = 200) ## unrelated predictor variables m1 <- fbed.gee.reg(reaction, x, subject) m2 <- fbed.glmm.reg(reaction, x, subject, backward = FALSE) ## End(Not run)
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