# The function to perform variable selection for marginalized multivariate zero-inflated Poisson models The function can be used to perform variable selection for marginalized multivariate zero-inflated Poisson models. ```r mmzipBvs(Y, lin.pred, data, offset = NULL, zero_cutoff = 0.05, hyperParams, startValues, mcmcParams) ``` ## Arguments - `Y`: a data.frame containing $q$ count outcomes from `n` subjects. It is of dimension $n\times q$. - `lin.pred`: a list containing three formula objects: the first formula specifies the $p_z$ covariates for which variable selection is to be performed in the binary component of the model; the second formula specifies the $p_x$ covariates for which variable selection is to be performed in the count part of the model; the third formula specifies the $p_0$ confounders to be adjusted for (but on which variable selection is not to be performed) in the regression analysis. - `data`: a data.frame containing the variables named in the formulas in `lin.pred`. - `offset`: an optional numeric vector with an a priori known component to be included as the linear predictor in the count part of model. - `zero_cutoff`: Response variable with proportions of zeros less than `zero.cutoff` will be removed from the binary model. - `hyperParams`: (update this) a list containing lists or vectors for hyperparameter values in hierarchical models. Components include, `rho0` (degrees of freedom for inverse-Wishart prior for $\Sigma_V$), `Psi0` (a scale matrix for inverse-Wishart prior for $\Sigma_V$), `mu_alpha0` (hyperparameter $\mu_{\alpha_0}$ in the prior of $\alpha_0$), `mu_alpha` (a numeric vector of length $q$ for hyperparameter $\mu_{\alpha}$ in the prior of $\alpha$), `mu_beta0` (hyperparameter $\mu_{\beta_0}$ in the prior of $\beta_0$), `mu_beta` (a numeric vector of length $q$ for hyperparameter $\mu_{\beta}$ in the prior of $\beta$), `a_alpha0` (hyperparameter $a_{\alpha_0}$ in the prior of $\sigma^2_{\alpha_0}$), `b_alpha0` (hyperparameter $b_{\alpha_0}$ in the prior of $\sigma^2_{\alpha_0}$), `a_alpha` (hyperparameter $a_{\alpha}$ in the prior of $\sigma^2_{\alpha}$), `b_alpha` (hyperparameter $b_{\alpha}$ in the prior of $\sigma^2_{\alpha}$), `a_beta0` (hyperparameter $a_{\beta_0}$ in the prior of $\sigma^2_{\beta_0}$), `b_beta0` (hyperparameter $b_{\beta_0}$ in the prior of $\sigma^2_{\beta_0}$), `a_beta` (hyperparameter $a_{\beta}$ in the prior of $\sigma^2_{\beta}$), `b_beta` (hyperparameter $b_{\beta}$ in the prior of $\sigma^2_{\beta}$), `v_beta` (a numeric vector of length $q$ for the standard deviation hyperparameter $v_{\beta}$ of the regression parameter $\beta$ prior), `omega_beta` (a numeric vector of length $p_x-p_0$ for the hyperparameter $\omega_{\beta}$ in the prior of the variable selection indicator), `v_alpha` (a numeric vector of length $q$ for the standard deviation hyperparameter $v_{\alpha}$ of the regression parameter $\alpha$ prior), `omega_alpha` (a numeric vector of length $p_z-p_0$ for the hyperparameter $\omega_{\alpha}$ in the prior of the variable selection indicator), See Examples below. - `startValues`: a numeric vector containing starting values for model parameters. See Examples below. - `mcmcParams`: (update this) a list containing variables required for MCMC sampling. Components include, `run` (a list containing numeric values for setting the overall run: `numReps`, total number of scans; `thin`, extent of thinning; `burninPerc`, the proportion of burn-in). `tuning` (a list containing numeric values relevant to tuning parameters for specific updates in Metropolis-Hastings algorithm: `beta0.prop.var`, variance of the proposal density for $\beta_0$;`beta.prop.var`, variance of the proposal density for $B$;`alpha.prop.var`, variance of the proposal density for $A$;`V.prop.var`, variance of the proposal density for $V$.) See Examples below. ## Returns `mmzipBvs` returns an object of class `mmzipBvs`. ## References update this ## Author(s) Kyu Ha Lee, Brent A. Coull, Jacqueline R. Starr Maintainer: Kyu Ha Lee ## Examples ```r ## Not run: # loading a data set data(simData_mzip) Y <- simData_mzip$Y data <- simData_mzip$X n = dim(Y)[1] q = dim(Y)[2] form.bin <- as.formula(~cov.1) form.count <- as.formula(~cov.1) form.adj <- as.formula(~1) form <- list(form.bin, form.count, form.adj) p_adj = dim(model.frame(form[[3]], data=data))[2] p0 <- dim(model.frame(form[[1]], data=data))[2] + p_adj p1 <- dim(model.frame(form[[2]], data=data))[2] + p_adj ##################### ## Hyperparameters ## Sigma_me <- 0.5 Sigma_var <- 1 rho0 <- 2*Sigma_me^2/Sigma_var+q+3 psi0 <- Sigma_me*(rho0-q-1) hyperParams_mmzip <- list(v_beta=rep(3, q), omega_beta=rep(0.5, p1-p_adj), a_beta=rep(0.5, p1), b_beta=rep(0.5, p1), mu_beta0=rep(0, q), a_beta0=0.5, b_beta0=0.5, v_alpha=rep(3, q), omega_alpha=rep(0.5, p0-p_adj), a_alpha=rep(0.5, p0), b_alpha=rep(0.5, p0), mu_alpha0=rep(0, q), a_alpha0=0.5, b_alpha0=0.5, rho0=rho0, Psi0=diag(psi0, q), mu_m=rep(0, q), v_m=0.5) ################### ## MCMC SETTINGS ## run <- list(numReps=100, thin=1, burninPerc=0.5) storage <- list(storeV=FALSE, storeW=FALSE) vs <- list(count=TRUE, binary=TRUE) tuning <- list(L_group=100, L_m=20, eps_group=0.00001, eps_m=0.00001, Mvar_group=1, Mvar_m=1, beta_prop_var=0.0001, alpha_prop_var=0.0001) mcmc_mmzip <- list(run=run, storage=storage, vs=vs, tuning=tuning) ##################### ## Starting Values startValues_mmzip <- initiate_startValues(form, Y, data, "MMZIP") ##################### ## Other settings offset <- data$total zero_cutoff=0.05 ####################### ## Fitting the MMZIP ## ####################### fit.mmzip <- mmzipBvs(Y, form, data, offset, zero_cutoff, hyperParams_mmzip, startValues_mmzip, mcmc_mmzip) print(fit.mmzip) summ.fit.mmzip <- summary(fit.mmzip); names(fit.mmzip) summ.fit.mmzip ## End(Not run) ```

mmzipBvs function