# rigorous Lasso for Logistic Models: Inference The function estimates (low-dimensional) target coefficients in a high-dimensional logistic model. ```r rlassologitEffects(x, ...) ## Default S3 method: rlassologitEffects(x, y, index = c(1:ncol(x)), I3 = NULL, post = TRUE, ...) ## S3 method for class 'formula' rlassologitEffects(formula, data, I, included = NULL, post = TRUE, ...) rlassologitEffect(x, y, d, I3 = NULL, post = TRUE) ``` ## Arguments - `x`: matrix of regressor variables serving as controls and potential treatments. For `rlassologitEffect` it contains only controls, for `rlassologitEffects` both controls and potential treatments. For `rlassologitEffects` it must have at least two columns. - ``...``: additional parameters - `y`: outcome variable - `index`: vector of integers, logical or names indicating the position (column) or name of variables of x which should be used as treatment variables. - `I3`: logical vector with same length as the number of controls; indicates if variables (TRUE) should be included in any case. - `post`: logical. If `TRUE`, post-Lasso estimation is conducted. - `formula`: An element of class `formula` specifying the linear model. - `data`: an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which the function is called. - `I`: An one-sided formula specifying the variables for which inference is conducted. - `included`: One-sided formula of variables which should be included in any case. - `d`: variable for which inference is conducted (treatment variable) ## Returns The function returns an object of class `rlassologitEffects` with the following entries: - **coefficients**: estimated value of the coefficients - **se**: standard errors - **t**: t-statistics - **pval**: p-values - **samplesize**: sample size of the data set - **I**: index of variables of the union of the lasso regressions ## Details The functions estimates (low-dimensional) target coefficients in a high-dimensional logistic model. An application is e.g. estimation of a treatment effect $\alpha_0$ in a setting of high-dimensional controls. The function is a wrap function for `rlassologitEffect` which does inference for only one variable (d). ## Examples ```r ## Not run: library(hdm) ## DGP set.seed(2) n <- 250 p <- 100 px <- 10 X <- matrix(rnorm(n*p), ncol=p) colnames(X) = paste("V", 1:p, sep="") beta <- c(rep(2,px), rep(0,p-px)) intercept <- 1 P <- exp(intercept + X %*% beta)/(1+exp(intercept + X %*% beta)) y <- rbinom(n, size=1, prob=P) xd <- X[,2:50] d <- X[,1] logit.effect <- rlassologitEffect(x=xd, d=d, y=y) logit.effects <- rlassologitEffects(X,y, index=c(1,2,40)) logit.effects.f <- rlassologitEffects(y ~ X, I = ~ V1 + V2) ## End(Not run) ``` ## References A. Belloni, V. Chernozhukov, Y. Wei (2013). Honest confidence regions for a regression parameter in logistic regression with a loarge number of controls. cemmap working paper CWP67/13.

rlassologitEffects function