# Fit zero-inflated count data linear model with lasso (or elastic net), snet or mnet regularization Fit zero-inflated regression models for count data via penalized maximum likelihood. ```r ## S3 method for class 'formula' zipath(formula, data, weights, offset=NULL, contrasts=NULL, ... ) ## S3 method for class 'matrix' zipath(X, Z, Y, weights, offsetx=NULL, offsetz=NULL, ...) ## Default S3 method: zipath(X, ...) ``` ## Arguments - `formula`: symbolic description of the model, see details. - `data`: argument controlling formula processing via `model.frame`. - `weights`: optional numeric vector of weights. - `offset`: optional numeric vector with an a priori known component to be included in the linear predictor of the count model or zero model. See below for an example. - `contrasts`: a list with elements `"count"` and `"zero"` containing the contrasts corresponding to `levels` from the respective models - `X`: predictor matrix of the count model - `Z`: predictor matrix of the zero model - `Y`: response variable - `offsetx, offsetz`: optional numeric vector with an a priori known component to be included in the linear predictor of the count model (offsetx)or zero model (offsetz). - `...`: Other arguments which can be passed to `glmreg` or `glmregNB` ## Returns An object of class `"zipath"`, i.e., a list with components including - **coefficients**: a list with elements `"count"` and `"zero"` containing the coefficients from the respective models, - **residuals**: a vector of raw residuals (observed - fitted), - **fitted.values**: a vector of fitted means, - **weights**: the case weights used, - **terms**: a list with elements `"count"`, `"zero"` and `"full"` containing the terms objects for the respective models, - **theta**: estimate of the additional $theta$ parameter of the negative binomial model (if a negative binomial regression is used), - **loglik**: log-likelihood of the fitted model, - **family**: character string describing the count distribution used, - **link**: character string describing the link of the zero-inflation model, - **linkinv**: the inverse link function corresponding to `link`, - **converged**: logical value, TRUE indicating successful convergence of `zipath`, FALSE indicating otherwise - **call**: the original function call - **formula**: the original formula - **levels**: levels of the categorical regressors - **contrasts**: a list with elements `"count"` and `"zero"` containing the contrasts corresponding to `levels` from the respective models, - **model**: the full model frame (if `model = TRUE`), - **y**: the response count vector (if `y = TRUE`), - **x**: a list with elements `"count"` and `"zero"` containing the model matrices from the respective models (if `x = TRUE`), ## References Zhu Wang, Shuangge Ma, Michael Zappitelli, Chirag Parikh, Ching-Yun Wang and Prasad Devarajan (2014) **Penalized Count Data Regression with Application to Hospital Stay after Pediatric Cardiac Surgery**, **Statistical Methods in Medical Research**. 2014 Apr 17. [Epub ahead of print] Zhu Wang, Shuangge Ma, Ching-Yun Wang, Michael Zappitelli, Prasad Devarajan and Chirag R. Parikh (2014) **EM for Regularized Zero Inflated Regression Models with Applications to Postoperative Morbidity after Cardiac Surgery in Children**, **Statistics in Medicine**. 33(29):5192-208. Zhu Wang, Shuangge Ma and Ching-Yun Wang (2015) **Variable selection for zero-inflated and overdispersed data with application to health care demand in Germany**, **Biometrical Journal**. 57(5):867-84. ## Author(s) Zhu Wang ## See Also `zipath_fit`, `glmreg`, `glmregNB` ## Examples ```r ## data data("bioChemists", package = "pscl") ## with simple inflation (no regressors for zero component) fm_zip <- zipath(art ~ 1 | ., data = bioChemists, nlambda=10) summary(fm_zip) fm_zip <- zipath(art ~ . | 1, data = bioChemists, nlambda=10) summary(fm_zip) ## Not run: fm_zip <- zipath(art ~ . | 1, data = bioChemists, nlambda=10) summary(fm_zip) fm_zinb <- zipath(art ~ . | 1, data = bioChemists, family = "negbin", nlambda=10) summary(fm_zinb) ## inflation with regressors ## ("art ~ . | ." is "art ~ fem + mar + kid5 + phd + ment | fem + mar + kid5 + phd + ment") fm_zip2 <- zipath(art ~ . | ., data = bioChemists, nlambda=10) summary(fm_zip2) fm_zinb2 <- zipath(art ~ . | ., data = bioChemists, family = "negbin", nlambda=10) summary(fm_zinb2) ### non-penalized regression, compare with zeroinfl fm_zinb3 <- zipath(art ~ . | ., data = bioChemists, family = "negbin", lambda.count=0, lambda.zero=0, reltol=1e-12) summary(fm_zinb3) library("pscl") fm_zinb4 <- zeroinfl(art ~ . | ., data = bioChemists, dist = "negbin") summary(fm_zinb4) ### offset exposure <- rep(0.5, dim(bioChemists)[1]) fm_zinb <- zipath(art ~ . +offset(log(exposure))| ., data = bioChemists, family = "poisson", nlambda=10) coef <- coef(fm_zinb) ### offset can't be specified in predict function as it has been contained pred <- predict(fm_zinb) ## without inflation ## ("art ~ ." is "art ~ fem + mar + kid5 + phd + ment") fm_pois <- glmreg(art ~ ., data = bioChemists, family = "poisson") coef <- coef(fm_pois) fm_nb <- glmregNB(art ~ ., data = bioChemists) coef <- coef(fm_nb) ### high-dimensional #R CMD check --use-valgrind can be too time extensive for the following model #bioChemists <- cbind(matrix(rnorm(915*100), nrow=915), bioChemists) #fm_zinb <- zipath(art ~ . | ., data = bioChemists, family = "negbin", nlambda=10) ## End(Not run) ```

zipath function