welnet: Weighted (linear or logistic) elastic-nets for complex survey...

In svyVarSel: Variable Selection for Complex Survey Data

Weighted (linear or logistic) elastic-nets for complex survey data

Description

This function allows as to fit elastic nets (linear or logistic) to complex survey data, considering sampling weights in the estimation process and selects the lambda that minimizes the error based on different replicate weights methods.

Usage

welnet(
  data = NULL,
  col.y = NULL,
  col.x = NULL,
  cluster = NULL,
  strata = NULL,
  weights = NULL,
  design = NULL,
  family = c("gaussian", "binomial"),
  alpha = 1,
  lambda.grid = NULL,
  method = c("dCV", "JKn", "bootstrap", "subbootstrap", "BRR", "split", "extrapolation"),
  k = 10,
  R = 1,
  B = 200,
  dCV.sw.test = FALSE,
  train.prob = 0.7,
  method.split = c("dCV", "bootstrap", "subbootstrap"),
  print.rw = FALSE
)

Arguments

data	A data frame with information about the response variable and covariates, as well as sampling weights and strata and cluster indicators. It could be NULL if the sampling design is indicated in the design argument.
col.y	A numeric value indicating the number of the column in which information on the response variable can be found or a character string indicating the name of that column.
col.x	A numeric vector indicating the numbers of the columns in which information on the covariates can be found or a vector of character strings indicating the names of these columns.
cluster	A character string indicating the name of the column with cluster identifiers. It could be NULL if the sampling design is indicated in the design argument.
strata	A character string indicating the name of the column with strata identifiers. It could be NULL if the sampling design is indicated in the design argument.
weights	A character string indicating the name of the column with sampling weights. It could be NULL if the sampling design is indicated in the design argument.
design	An object of class survey.design generated by survey::svydesign(). It could be NULL if information about cluster, strata, weights and data are given.
family	A character string indicating the family to fit LASSO models. Choose between gaussian (to fit linear models) or binomial (for logistic models).
alpha	A numeric value between 0 and 1, indicating the elastic-net parameter. alpha=1 is the LASSO penalty (equivalent to using wlasso()) and alpha=0 the ridge penalty. Default alpha=1.
lambda.grid	A numeric vector indicating a grid for penalization parameters. The default option is lambda.grid = NULL, which considers the default grid selected by the function glmnet::glmnet().
method	A character string indicating the method to be applied to define replicate weights. Choose between one of these: JKn, dCV, bootstrap, subbootstrap, BRR, split, extrapolation.
k	A numeric value indicating the number of folds to be defined. Default is k=10. Only applies for the dCV method.
R	A numeric value indicating the number of times the sample is partitioned. Default is R=1. Only applies for dCV, split or extrapolation methods.
B	A numeric value indicating the number of bootstrap resamples. Default is B=200. Only applies for bootstrap and subbootstrap methods.
dCV.sw.test	A logical value indicating the method for estimating the error for dCV method. FALSE, (the default option) estimates the error for each test set and defines the cross-validated error based on the average strategy. Option TRUE estimates the cross-validated error based on the pooling strategy
train.prob	A numeric value between 0 and 1, indicating the proportion of clusters (for the method split) or strata (for the method extrapolation) to be set in the training sets. Default is train.prob = 0.7. Only applies for split and extrapolation methods.
method.split	A character string indicating the way in which replicate weights should be defined in the split method. Choose one of the following: dCV, bootstrap or subbootstrap. Only applies for split method.
print.rw	A logical value. If TRUE, the data set with the replicate weights is saved in the output object. Default print.rw=FALSE.

Details

The parameter alpha indicates the penalty to be used to fit the elastic net as in glmnet:

(1-\alpha)/2||\beta||_2^2+\alpha||\beta||_1.

Value

The output object of the function welnet() is an object of class welnet. This object is a list containing 4 or 5 elements, depending on the value set to the argument print.rw. Below we describe the contents of these elements:

• lambda: A list containing information of two elements:

  • grid: A numeric vector indicating all the values considered for the tuning parameter.

  • min: A numeric value indicating the value of the tuning parameter that minimizes the average error (i.e., selected optimal tuning parameter).

• error: A list containing information of two elements:

  • average: A numeric vector indicating the average error corresponding to each tuning parameter.

  • all: A numeric matrix indicating the error of each test set for each tuning parameter.

• model: A list containing information of two elements in relation to the fitted models. Note that all these models are fitted considering the whole data set (and not uniquely the training sets).

  • grid: A list with the information about the models fitted for each of the tuning parameters considered (i.e., all the values in the lambda$grid object):

    • a0: a numeric vector of model intercepts across the whole grid of tuning parameters (hence, of the same length as lambda$grid).

    • beta: a matrix of regression coefficients corresponding to all the considered covariates across the whole grid of tuning parameters (the number of rows is equal to the number of covariates considered and the number of columns to the length of lambda$grid).

    • df: a numeric vector of the degrees of freedom (i.e., the number of coefficients different from zero) across the whole grid of tuning parameters (hence, of the same length as lambda$grid).

  • min: A list with the information about the model fitted considering uniquely the tuning parameter that minimizes the error in the training models (i.e., the optimal tuning parameter selected between the elements in lambda$grid):

    • a0: a numeric value indicating the intercept value of the selected model.

    • beta: a matrix of regression coefficients corresponding to all the considered covariates for the selected tuning parameters (the number of rows is equal to the number of covariates considered and the number of columns is one).

    • df: a numeric value indicating the degrees of freedom (i.e., the number of coefficients different from zero) of the selected model.

• data.rw: A data frame containing the original data set and the replicate weights added to define training and test sets. Only included in the output object if print.rw=TRUE.

• call: an object containing the information about the way in which the function has been run.

Examples

data(simdata_lasso_binomial)
mcv <- welnet(data = simdata_lasso_binomial,
              col.y = "y", col.x = 1:50,
              family = "binomial",
              alpha = 0.5,
              cluster = "cluster", strata = "strata", weights = "weights",
              method = "dCV", k=10, R=1)

# Or equivalently:

mydesign <- survey::svydesign(ids=~cluster, strata = ~strata, weights = ~weights,
                              nest = TRUE, data = simdata_lasso_binomial)
mcv <- welnet(col.y = "y", col.x = 1:50, design = mydesign,
              family = "binomial", alpha = 0.5,
              method = "dCV", k=10, R=1)

svyVarSel documentation built on Oct. 15, 2024, 5:06 p.m.