an n x p matrix of covariates for the zero part data, where each row is an observation and each column is a predictor. MUST be ordered such that the first n_s rows align with the observations in x_s and s

a length n vector of responses taking positive values

a length n vector of treatment variables with 1 indicating treatment and -1 indicating control

a length n vector of sample weights

number of folds for cross fitting

tweedie mixing parameter. See HDtweedie for details

boolean variable of whether or not to fit model with interactions. For predictions, interactions will be integrated out

an n x p matrix of covariates for the zero part data, where each row is an observation and each column is a predictor. MUST be ordered such that the first n_s rows align with the observations in x_s and s

a length n vector of responses taking values 1 and 0, where 1 indicates the response is positive and zero indicates the response has value 0. MUST be ordered such that the first n_s values align with the observations in x_s and s

an n_s x p matrix of covariates (which is a submatrix of x) for the positive part data, where each row is an observation and each column is a predictor

a length n_s vector of responses taking strictly positive values

a length n vector of observation weights for the zero part data

a length n_s vector of observation weights for the positive part data

a length n vector of offset terms for the zero part data

a length n_s vector of offset terms for the positive part data

A user supplied lambda sequence. By default, the program computes its own lambda sequence based on nlambda and lambda.min.ratio. Supplying a value of lambda overrides this.

measure to evaluate for cross-validation. Will add more description later

number of folds for cross-validation. default is 10. 3 is smallest value allowed.

an optional vector of values between 1 and nfold specifying which fold each observation belongs to.

Like in glmnet, this is an experimental argument, with default TRUE, and can be ignored by most users. For all models, this refers to computing nfolds separate statistics, and then using their mean and estimated standard error to describe the CV curve. If grouped = FALSE, an error matrix is built up at the observation level from the predictions from the nfold fits, and then summarized (does not apply to type.measure = "auc").

If keep = TRUE, a prevalidated list of arrasy is returned containing fitted values for each observation and each value of lambda for each model. This means these fits are computed with this observation and the rest of its fold omitted. The folid vector is also returned. Default is keep = FALSE

If TRUE, use parallel foreach to fit each fold. Must register parallel before hand, such as doMC.

other parameters to be passed to hd2part function

The design matrix (not including intercept term)

The nonnegative response vector

treatment vector with each element equal to a 0 or a 1, with 1 indicating treatment status is active.

function that inputs the design matrix x and the treatment vector trt and outputs the propensity score, ie Pr(trt = 1 | X = x). Function should take two arguments 1) x and 2) trt. See example below. For a randomized controlled trial this can simply be a function that returns a constant equal to the proportion of patients assigned to the treatment group, i.e.: propensity.func = function(x, trt) 0.5.

function that inputs the design matrix x and the treatment vector trt and outputs the propensity score for units with positive outcome values, ie Pr(trt = 1 | X = x, Z = 1). Function should take two arguments 1) x and 2) trt. See example below. For a randomized controlled trial this can simply be a function that returns a constant equal to the proportion of patients assigned to the treatment group, i.e.: propensity.func = function(x, trt) 0.5.

a (character, factor, or integer) vector with length equal to the number of observations in x indicating using integers or levels of a factor vector which patients are in which matched groups. Defaults to NULL and assumes the samples are not from a matched cohort. Matched case-control groups can be created using any method (propensity score matching, optimal matching, etc). If each case is matched with a control or multiple controls, this would indicate which case-control pairs or groups go together. If match.id is supplied, then it is unecessary to specify a function via the propensity.func argument. A quick usage example: if the first patient is a case and the second and third are controls matched to it, and the fouth patient is a case and the fifth through seventh patients are matched with it, then the user should specify match.id = c(1,1,1,2,2,2,2) or match.id = c(rep("Grp1", 3),rep("Grp2", 4)) the covariates x, and trt and outputs predicted values (on the probability scale) for the response using a model constructed with x. augment.func.zero() can also be simply a function of x and y. This function is used for efficiency augmentation. When the form of the augmentation function is correct, it can provide efficient estimation of the subgroups. Some examples of possible augmentation functions are:

Example 1: augment.func <- function(x, y) {lmod <- glm(y ~ x, family = binomial()); return(fitted(lmod))}

Example 2:

augment.func <- function(x, y, trt) {
    data <- data.frame(x, y, trt)
    lmod <- glm(y ~ x * trt, family = binomial())
    ## get predictions when trt = 1
    data$trt <- 1
    preds_1  <- predict(lmod, data, type = "response")

    ## get predictions when trt = -1
    data$trt <- -1
    preds_n1 <- predict(lmod, data, type = "response")

    ## return predictions averaged over trt
    return(0.5 * (preds_1 + preds_n1))
}

(similar to augment.func.positive) function which inputs the indicators of whether each response is positive (1*(y > 0)), the covariates x, and trt for all samples and outputs predicted values (on the link scale) for the response using a model constructed with x. augment.func.positive() can also be simply a function of x and y. This function is used for efficiency augmentation.

(similar to augment.func.zero) function which inputs the positive part response (ie all observations in y which are strictly positive), the covariates x, and trt and outputs predicted values (on the link scale) for the response using a model constructed with x. augment.func.positive() can also be simply a function of x and y. This function is used for efficiency augmentation.

numeric value for patients with benefit scores above which (or below which if larger.outcome.better = FALSE) will be recommended to be in the treatment group. Defaults to 1, since the benefit score is a risk ratio

boolean value of whether a larger outcome is better/preferable. Set to TRUE if a larger outcome is better/preferable and set to FALSE if a smaller outcome is better/preferable. Defaults to TRUE.

should the treatment main effect (ATE) be penalized too?

positive value above which observations in y will be considered positive

options to be passed to cv.hd2part

an n x p matrix of covariates for the zero part data, where each row is an observation and each column is a predictor

a length n vector of responses taking values 1 and 0, where 1 indicates the response is positive and zero indicates the response has value 0.

an n_s x p matrix of covariates (which is a submatrix of x) for the positive part data, where each row is an observation and each column is a predictor

a length n_s vector of responses taking strictly positive values

a length n vector of observation weights for the zero part data

a length n_s vector of observation weights for the positive part data

a length n vector of offset terms for the zero part data

a length n_s vector of offset terms for the positive part data

either "grp.lasso" for the group lasso penalty or "coop.lasso" for the cooperative lasso penalty

a length p vector of penalty adjustment factors corresponding to each covariate. A value of 0 in the jth location indicates no penalization on the jth variable, and any positive value will indicate a multiplicative factor on top of the common penalization amount. The default value is 1 for all variables

the number of lambda values. The default is 100.

Smallest value for lambda, as a fraction of lambda.max, the data-derived largest lambda value The default depends on the sample size relative to the number of variables.

a user supplied sequence of penalization tuning parameters. By default, the program automatically chooses a sequence of lambda values based on nlambda and lambda_min_ratio

value between 0 and 1 for sparse group mixing penalty. 0 implies either group lasso or coop lasso and 1 implies lasso

a boolean variable indicating whether the signs of coefficients across models should be encouraged to have opposite signs instead of the same signs. Default is FALSE. This variable has no effect for group lasso.

should we flip the signs of the parameters for the zero part model? Defaults to FALSE. Should only be used for good reason

whether or not to include an intercept in the zero part model. Default is TRUE.

whether or not to include an intercept in the positive part model. Default is TRUE.

should a strong rule be used? Defaults to TRUE

maximum number of IRLS iterations

convergence tolerance for IRLS iterations

maximum number of MM iterations. Note that for algorithm = "irls", MM is used within each IRLS iteration, so maxit_mm applies to the convergence of the inner iterations in this case.

convergence tolerance for MM iterations. Note that for algorithm = "irls", MM is used within each IRLS iteration, so tol_mm applies to the convergence of the inner iterations in this case.

should the likelihoods be balanced so variables would enter both models at the same value of lambda if the penalty were a lasso penalty? Recommended to keep at the default, TRUE

an n x p matrix of covariates for the zero part data, where each row is an observation and each column is a predictor

a length n vector of responses taking strictly positive values.

a length n vector of observation weights

a length n vector of offset terms

a length p vector of penalty adjustment factors corresponding to each covariate. A value of 0 in the jth location indicates no penalization on the jth variable, and any positive value will indicate a multiplicative factor on top of the common penalization amount. The default value is 1 for all variables

the number of lambda values. The default is 100.

Smallest value for lambda, as a fraction of lambda.max, the data-derived largest lambda value The default depends on the sample size relative to the number of variables.

a user supplied sequence of penalization tuning parameters. By default, the program automatically chooses a sequence of lambda values based on nlambda and lambda_min_ratio

a scalar numeric value between 0 and 1 (included) which is a mixing parameter for sparse group lasso penalty. 0 indicates group lasso and 1 indicates lasso, values in between reflect different emphasis on group and lasso penalties

whether or not to include an intercept. Default is TRUE.

should a strong rule be used?

maximum number of IRLS iterations

convergence tolerance for IRLS iterations

maximum number of MM iterations. Note that for algorithm = "irls", MM is used within each IRLS iteration, so maxit_mm applies to the convergence of the inner iterations in this case.

convergence tolerance for MM iterations. Note that for algorithm = "irls", MM is used within each IRLS iteration, so tol_mm applies to the convergence of the inner iterations in this case.

fitted "hd2part" model object

either "zero" for the zero part model or "positive" for the positive part model

What is on the X-axis. "norm" plots against the L1-norm of the coefficients, "lambda" against the log-lambda sequence, and "dev" against the percent deviance explained.

size of labels for variable names. If labsize = 0, then no variable names will be plotted

label for x-axis

label for y-axis

main title for plot

other graphical parameters for the plot

Either plot against log(lambda) (default) or its negative if sign.lambda = -1.

fitted "cv.hd2part" model object

Matrix of new values for x at which predictions are to be made. Must be a matrix; can be sparse as in the CsparseMatrix objects of the Matrix package This argument is not used for type = c("coefficients","nonzero")

either "zero" for the zero part model or "positive" for the positive part model

Value(s) of the penalty parameter lambda at which predictions are required. Default is the entire sequence used to create the model. For predict.cv.hd2part(), can also specify "lambda.1se" or "lambda.min" for best lambdas estimated by cross validation.

Type of prediction required. type = "link" gives the linear predictors; type = "model_response" gives the fitted probabilities for the zero part and fitted expected values for the positive part. type = "response" gives the combined response prediction across the two models using the full unconditional expected value of the response. When type = "response", argument "model" is unused. type = "coefficients" computes the coefficients at the requested values for s.

arguments to be passed to predict.hd2part

fitted "hd2part" model object

Matrix of new values for x at which predictions are to be made. Must be a matrix This argument is not used for type=c("coefficients","nonzero")

Value(s) of the penalty parameter lambda for the zero part at which predictions are required. Default is the entire sequence used to create the model.

either "zero" for the zero part model or "positive" for the positive part model

Type of prediction required. type = "link" gives the linear predictors; type = "model_response" gives the fitted probabilities for the zero part and fitted expected values for the positive part. type = "response" gives the combined response prediction across the two models using the full unconditional expected value of the response. When type = "response", argument "model" is unused. type = "coefficients" computes the coefficients at the requested values for s.

f an offset is used in the fit, then one must be supplied for making predictions

not used

number of observations

number of variables. Must be at least 10