Extract Coefficients From a "cv.galasso" Object

Description

Extract Coefficients From a "cv.galasso" Object

Usage

## S3 method for class 'cv.galasso'
coef(object, lambda = object$lambda.min, ...)

Arguments

Value

A list of numeric vectors containing the coefficients from running galasso on lambda for each imputation.

Extract Coefficients From a "cv.saenet" Object

Description

Extract Coefficients From a "cv.saenet" Object

Usage

## S3 method for class 'cv.saenet'
coef(object, lambda = object$lambda.min, alpha = object$alpha.min, ...)

Arguments

Value

A numeric vector containing the coefficients from running saenet on lambda and alpha.

Extract Coefficients From a "galasso" Object

Description

Extract Coefficients From a "galasso" Object

Usage

## S3 method for class 'galasso'
coef(object, lambda, ...)

Arguments

Value

A list of length D containing the coefficient estimates from running galasso on lambda.

Extract Coefficients From a "saenet" Object

Description

coef.galasso averages the estimates across imputations to return a single vector instead of a matrix.

Usage

## S3 method for class 'saenet'
coef(object, lambda, alpha, ...)

Arguments

Value

A numeric vector containing the coefficients from running saenet on lambda and alpha.

Cross Validated Multiple Imputation Grouped Adaptive LASSO

Description

Does k-fold cross-validation for galasso, and returns an optimal value for lambda.

Usage

cv.galasso(
  x,
  y,
  pf,
  adWeight,
  family = c("gaussian", "binomial"),
  nlambda = 100,
  lambda.min.ratio = ifelse(isTRUE(all.equal(adWeight, rep(1, p))), 0.001, 1e-06),
  lambda = NULL,
  nfolds = 5,
  foldid = NULL,
  maxit = 1000,
  eps = 1e-05
)

Arguments

Details

cv.galasso works by adding a group penalty to the aggregated objective function to ensure selection consistency across imputations. Simulations suggest that the "stacked" objective function approaches (i.e., saenet) tend to be more computationally efficient and have better estimation and selection properties.

Value

An object of type "cv.galasso" with 7 elements:

call

The call that generated the output.

lambda

The sequence of lambdas fit.

cvm

Average cross validation error for each "lambda". For family = "gaussian", "cvm" corresponds to mean squared error, and for binomial "cvm" corresponds to deviance.

cvse

Standard error of "cvm".

galasso.fit

A "galasso" object fit to the full data.

lambda.min

The lambda value for the model with the minimum cross validation error.

lambda.1se

The lambda value for the sparsest model within one standard error of the minimum cross validation error.

df

The number of nonzero coefficients for each value of lambda.

References

Du, J., Boss, J., Han, P., Beesley, L. J., Kleinsasser, M., Goutman, S. A., ... & Mukherjee, B. (2022). Variable selection with multiply-imputed datasets: choosing between stacked and grouped methods. Journal of Computational and Graphical Statistics, 31(4), 1063-1075. <doi:10.1080/10618600.2022.2035739>

Examples

library(miselect)
library(mice)

set.seed(48109)

# Using the mice defaults for sake of example only.
mids <- mice(miselect.df, m = 5, printFlag = FALSE)
dfs <- lapply(1:5, function(i) complete(mids, action = i))

# Generate list of imputed design matrices and imputed responses
x <- list()
y <- list()
for (i in 1:5) {
    x[[i]] <- as.matrix(dfs[[i]][, paste0("X", 1:20)])
    y[[i]] <- dfs[[i]]$Y
}

pf       <- rep(1, 20)
adWeight <- rep(1, 20)

fit <- cv.galasso(x, y, pf, adWeight)

# By default 'coef' returns the betas for lambda.min.
coef(fit)

Cross Validated Multiple Imputation Stacked Adaptive Elastic Net

Description

Does k-fold cross-validation for saenet, and returns optimal values for lambda and alpha.

Usage

cv.saenet(
  x,
  y,
  pf,
  adWeight,
  weights,
  family = c("gaussian", "binomial"),
  alpha = 1,
  nlambda = 100,
  lambda.min.ratio = ifelse(isTRUE(all.equal(adWeight, rep(1, p))), 0.001, 1e-06),
  lambda = NULL,
  nfolds = 5,
  foldid = NULL,
  maxit = 1000,
  eps = 1e-05
)

Arguments

Details

cv.saenet works by stacking the multiply imputed data into a single matrix and running a weighted adaptive elastic net on it. Simulations suggest that the "stacked" objective function approaches tend to be more computationally efficient and have better estimation and selection properties.

Due to stacking, the automatically generated lambda sequence cv.saenet generates may end up underestimating lambda.max, and thus the degrees of freedom may be nonzero at the first lambda value.

Value

An object of type "cv.saenet" with 9 elements:

call

The call that generated the output.

lambda

Sequence of lambdas fit.

cvm

Average cross validation error for each lambda and alpha. For family = "gaussian", "cvm" corresponds to mean squared error, and for binomial "cvm" corresponds to deviance.

cvse

Standard error of "cvm".

saenet.fit

A "saenet" object fit to the full data.

lambda.min

The lambda value for the model with the minimum cross validation error.

lambda.1se

The lambda value for the sparsest model within one standard error of the minimum cross validation error.

alpha.min

The alpha value for the model with the minimum cross validation error.

alpha.1se

The alpha value for the sparsest model within one standard error of the minimum cross validation error.

df

The number of nonzero coefficients for each value of lambda and alpha.

References

Du, J., Boss, J., Han, P., Beesley, L. J., Kleinsasser, M., Goutman, S. A., ... & Mukherjee, B. (2022). Variable selection with multiply-imputed datasets: choosing between stacked and grouped methods. Journal of Computational and Graphical Statistics, 31(4), 1063-1075. <doi:10.1080/10618600.2022.2035739>

Examples

library(miselect)
library(mice)

set.seed(48109)

# Using the mice defaults for sake of example only.
mids <- mice(miselect.df, m = 5, printFlag = FALSE)
dfs <- lapply(1:5, function(i) complete(mids, action = i))

# Generate list of imputed design matrices and imputed responses
x <- list()
y <- list()
for (i in 1:5) {
    x[[i]] <- as.matrix(dfs[[i]][, paste0("X", 1:20)])
    y[[i]] <- dfs[[i]]$Y
}

# Calculate observational weights
weights  <- 1 - rowMeans(is.na(miselect.df))
pf       <- rep(1, 20)
adWeight <- rep(1, 20)

# Since 'Y' is a binary variable, we use 'family = "binomial"'
fit <- cv.saenet(x, y, pf, adWeight, weights, family = "binomial")

# By default 'coef' returns the betas for (lambda.min , alpha.min)
coef(fit)


# You can also cross validate over alpha

fit <- cv.saenet(x, y, pf, adWeight, weights, family = "binomial",
                 alpha = c(.5, 1))
# Get selected variables from the 1 standard error rule
coef(fit, lambda = fit$lambda.1se, alpha = fit$alpha.1se)

Multiple Imputation Grouped Adaptive LASSO

Description

galasso fits an adaptive LASSO for multiply imputed data. "galasso" supports both continuous and binary responses.

Usage

galasso(
  x,
  y,
  pf,
  adWeight,
  family = c("gaussian", "binomial"),
  nlambda = 100,
  lambda.min.ratio = ifelse(isTRUE(all.equal(adWeight, rep(1, p))), 0.001, 1e-06),
  lambda = NULL,
  maxit = 10000,
  eps = 1e-05
)

Arguments

Details

galasso works by adding a group penalty to the aggregated objective function to ensure selection consistency across imputations. The objective function is:

argmin_{\beta_{jk}} - L(\beta_{jk}| X_{ijk}, Y_{ik})

+ \lambda * \Sigma_{j=1}^{p} \hat{a}_j * pf_j * \sqrt{\Sigma_{k=1}^{m} \beta_{jk}^2}

Where L is the log likelihood,a is the adaptive weights, and pf is the penalty factor. Simulations suggest that the "stacked" objective function approach (i.e., saenet) tends to be more computationally efficient and have better estimation and selection properties. However, the advantage of galasso is that it allows one to look at the differences between coefficient estimates across imputations.

Value

An object with type galasso and subtype galasso.gaussian or galasso.binomial, depending on which family was used. Both subtypes have 4 elements:

lambda

Sequence of lambda fit.

coef

a list of length D containing the coefficient estimates from running galasso at each value of lambda. Each element in the list is a nlambda x (p+1) matrix.

df

Number of nonzero betas at each value of lambda.

References

Du, J., Boss, J., Han, P., Beesley, L. J., Kleinsasser, M., Goutman, S. A., ... & Mukherjee, B. (2022). Variable selection with multiply-imputed datasets: choosing between stacked and grouped methods. Journal of Computational and Graphical Statistics, 31(4), 1063-1075. <doi:10.1080/10618600.2022.2035739>

Examples

library(miselect)
library(mice)

mids <- mice(miselect.df, m = 5, printFlag = FALSE)
dfs <- lapply(1:5, function(i) complete(mids, action = i))

# Generate list of imputed design matrices and imputed responses
x <- list()
y <- list()
for (i in 1:5) {
    x[[i]] <- as.matrix(dfs[[i]][, paste0("X", 1:20)])
    y[[i]] <- dfs[[i]]$Y
}

pf       <- rep(1, 20)
adWeight <- rep(1, 20)

fit <- galasso(x, y, pf, adWeight)

Synthetic Example Data For "miselect"

Description

This synthetic data is taken from the first simulation case from the miselect paper

Usage

miselect.df

Format

A data.frame with 500 observations on 21 variables:

Y

Binary response.

X1-X20

Covariates with missing data.

Print cv.galasso Objects

Description

print.cv.galasso print the fit and returns it invisibly.

Usage

## S3 method for class 'cv.galasso'
print(x, ...)

Arguments

Print cv.saenet Objects

Description

print.cv.saenet print the fit and returns it invisibly.

Usage

## S3 method for class 'cv.saenet'
print(x, ...)

Arguments

Multiple Imputation Stacked Adaptive Elastic Net

Description

Fits an adaptive elastic net for multiply imputed data. The data is stacked and is penalized that each imputation selects the same betas at each value of lambda. "saenet" supports both continuous and binary responses.

Usage

saenet(
  x,
  y,
  pf,
  adWeight,
  weights,
  family = c("gaussian", "binomial"),
  alpha = 1,
  nlambda = 100,
  lambda.min.ratio = ifelse(isTRUE(all.equal(adWeight, rep(1, p))), 0.001, 1e-06),
  lambda = NULL,
  maxit = 1000,
  eps = 1e-05
)

Arguments

Details

saenet works by stacking the multiply imputed data into a single matrix and running a weighted adaptive elastic net on it. The objective function is:

argmin_{\beta_j} -\frac{1}{n} \sum_{k=1}^{m} \sum_{i=1}^{n} o_i * L(\beta_j|Y_{ik},X_{ijk})

+ \lambda (\alpha \sum_{j=1}^{p} \hat{a}_j * pf_j |\beta_{j}|

+ (1 - \alpha)\sum_{j=1}^{p} pf_j * \beta_{j}^2)

Where L is the log likelihood, o = w / m, a is the adaptive weights, and pf is the penalty factor. Simulations suggest that the "stacked" objective function approach (i.e., saenet) tends to be more computationally efficient and have better estimation and selection properties. However, the advantage of galasso is that it allows one to look at the differences between coefficient estimates across imputations.

Value

An object with type saenet and subtype saenet.gaussian or saenet.binomial, depending on which family was used. Both subtypes have 4 elements:

lambda

Sequence of lambda fit.

coef

nlambda x nalpha x p + 1 tensor representing the estimated betas at each value of lambda and alpha.

df

Number of nonzero betas at each value of lambda and alpha.

References

Du, J., Boss, J., Han, P., Beesley, L. J., Kleinsasser, M., Goutman, S. A., ... & Mukherjee, B. (2022). Variable selection with multiply-imputed datasets: choosing between stacked and grouped methods. Journal of Computational and Graphical Statistics, 31(4), 1063-1075. <doi:10.1080/10618600.2022.2035739>

Examples

library(miselect)
library(mice)

mids <- mice(miselect.df, m = 5, printFlag = FALSE)
dfs <- lapply(1:5, function(i) complete(mids, action = i))

# Generate list of imputed design matrices and imputed responses
x <- list()
y <- list()
for (i in 1:5) {
    x[[i]] <- as.matrix(dfs[[i]][, paste0("X", 1:20)])
    y[[i]] <- dfs[[i]]$Y
}

# Calculate observational weights
weights  <- 1 - rowMeans(is.na(miselect.df))
pf       <- rep(1, 20)
adWeight <- rep(1, 20)

# Since 'Y' is a binary variable, we use 'family = "binomial"'
fit <- saenet(x, y, pf, adWeight, weights, family = "binomial")