# Collaborative Targeted Maximum Likelihood Estimation for hyper-parameter tuning of LASSO This function computes the Collaborative Maximum Likelihood Estimation for hyper-parameter tuning of LASSO. ```r ctmleGlmnet(Y, A, W, Wg = W, Q, lambdas = NULL, ctmletype, V = 5, folds = NULL, alpha = 0.995, family = "gaussian", gbound = 0.025, like_type = "RSS", fluctuation = "logistic", verbose = FALSE, detailed = FALSE, PEN = FALSE, g1W = NULL, g1WPrev = NULL, stopFactor = 10^6) ``` ## Arguments - `Y`: continuous or binary outcome variable - `A`: binary treatment indicator, 1 for treatment, 0 for control - `W`: vector, matrix, or dataframe containing baseline covariates for Q bar - `Wg`: vector, matrix, or dataframe containing baseline covariates for propensity score model (defaults to W if not supplied by user) - `Q`: n by 2 matrix of initial values for Q0W, Q1W in columns 1 and 2, respectively. Current version does not support SL for automatic initial estimation of Q bar - `lambdas`: numeric vector of lambdas (regularization parameter) for glmnet estimation of propensity score, with decreasing order. We recommend the first lambda is selected by external cross-validation. - `ctmletype`: 1, 2 or 3. Type of general C-TMLE. Type 1 uses cross-validation to select best gn, Type 3 directly solves extra clever covariates, and Type 2 uses both cross-validation and extra covariate. See more details in !!! - `V`: Number of folds. Only used if folds is not specified - `folds`: The list of indices for cross-validation step. We recommend the cv-splits in C-TMLE matchs that in gn_candidate_cv - `alpha`: used to keep predicted initial values bounded away from (0,1) for logistic fluctuation, 0.995 (default) - `family`: family specification for working regression models, generally 'gaussian' for continuous outcomes (default), 'binomial' for binary outcomes - `gbound`: bound on P(A=1|W), defaults to 0.025 - `like_type`: 'RSS' or 'loglike'. The metric to use for forward selection and cross-validation - `fluctuation`: 'logistic' (default) or 'linear', for targeting step - `verbose`: print status messages if TRUE - `detailed`: boolean number. If it is TRUE, return more detailed results - `PEN`: boolean. If true, penalized loss is used in cross-validation step - `g1W`: Only used when type is 3. a user-supplied propensity score estimate. - `g1WPrev`: Only used when type is 3. a user-supplied propensity score estimate, with small fluctuation compared to g1W. - `stopFactor`: Numerical value with default 1e6. If the current empirical likelihood is stopFactor times larger than the best previous one, the construction would stop ## Returns best_k the index of estimate that selected by cross-validation est estimate of psi_0 CI IC-based 95 pvalue pvalue for the null hypothesis that Psi = 0 likelihood sum of squared residuals, based on selected estimator evaluated on all obs or, logistic loglikelihood if like_type != 'RSS' varIC empirical variance of the influence curve adjusted for estimation of g varDstar empirical variance of the influence curve var.psi variance of the estimate varIC.cv cross-validated variance of the influence curve penlikelihood.cv penalized cross-validatedlikelihood cv.res all cross-validation results for each fold ## Examples ```r ## Not run: set.seed(123) N <- 1000 p = 10 Wmat <- matrix(rnorm(N * p), ncol = p) beta1 <- 4+2*Wmat[,1]+2*Wmat[,2]+2*Wmat[,5]+2*Wmat[,6]+2*Wmat[,8] beta0 <- 2+2*Wmat[,1]+2*Wmat[,2]+2*Wmat[,5]+2*Wmat[,6]+2*Wmat[,8] tau <- 2 gcoef <- matrix(c(-1,-1,rep(0,(p)-2)),ncol=1) Wm <- as.matrix(Wmat) g <- 1/(1+exp(Wm%*%gcoef / 3)) A <- rbinom(N, 1, prob = g) sigma <- 1 epsilon <-rnorm(N,0,sigma) Y <- beta0 + tau * A + epsilon # ctmleGlmnet must provide user-specified Q W_tmp <- data.frame(Wm[,1:3]) treated<- W_tmp[which(A==1),] untreated<-W_tmp[which(A==0),] Y1<-Y[which(A==1)] Y0<-Y[which(A==0)] # Initial Q-estimate beta1hat <- predict(lm(Y1~.,data=treated),newdata=W_tmp) beta0hat <- predict(lm(Y0~., data=untreated),newdata=W_tmp) Q <- matrix(c(beta0hat,beta1hat),ncol=2) W = Wm glmnet_fit <- cv.glmnet(y = A, x = Wm, family = 'binomial', nlambda = 40) start = which(glmnet_fit$lambda==glmnet_fit$lambda.min)) end = length(glmnet_fit$lambda) lambdas <-glmnet_fit$lambda[start:end] ctmle_fit1 <- ctmleGlmnet(Y=Y, A=A, W=data.frame(W=W), Q = Q, lambdas = lambdas, ctmletype=1, alpha=.995, family="gaussian", gbound=0.025,like_type="loglik" , fluctuation="logistic", verbose=FALSE, detailed=FALSE, PEN=FALSE, V=5, stopFactor=10^6) ## End(Not run) ```

ctmleGlmnet function