# Hurdle Model Count Data Regression `hurdle` is used to fit single or double-hurdle regression models to count data via Bayesian inference. ```r hurdle(y, x = NULL, hurd = Inf, dist = c("poisson", "nb", "lognormal"), dist.2 = c("gpd", "poisson", "lognormal", "nb"), control = hurdle_control(), iters = 1000, burn = 500, nthin = 1, plots = FALSE, progress.bar = TRUE) ``` ## Arguments - `y`: numeric response vector. - `x`: numeric predictor matrix. - `hurd`: numeric threshold for 'extreme' observations of two-hurdle models. `Inf` for one-hurdle models. - `dist`: character specification of response distribution. - `dist.2`: character specification of response distribution for 'extreme' observations of two-hurdle models. - `control`: list of parameters for controlling the fitting process, specified by `hurdle_control`. - `iters`: number of iterations for the Markov chain to run. - `burn`: numeric burn-in length. - `nthin`: numeric thinning rate. - `plots`: logical operator. `TRUE` to output plots. - `progress.bar`: logical operator. `TRUE` to print progress bar. ## Returns `hurdle` returns a list which includes the items - **pD**: measure of model dimensionality $p_D$ where $p_D = \bar{D} - D(\bar{\theta}$) is the c("$\"mean posterior deviance - \n$", "$ deviance of posterior means\"$") - **DIC**: Deviance Information Criterion where $DIC = \bar{D} - p_D$ - **PPO**: Posterior Predictive Ordinate (PPO) measure of fit - **CPO**: Conditional Predictive Ordinate (CPO) measure of fit - **pars.means**: posterior mean(s) of third-component parameter(s) if `hurd != Inf` - **ll.means**: posterior means of the log-likelihood distributions of all model components - **beta.means**: posterior means regression coefficients - **dev**: posterior deviation where $D = -2LogL$ - **beta**: posterior distributions of regression coefficients - **pars**: posterior distribution(s) of third-component parameter(s) if `hurd != Inf` ## Details Setting `dist` and `dist.2` to be the same distribution creates a single `dist`-hurdle model, not a double-hurdle model. However, this is being considered in future package updates. ## Examples ```r #Generate some data: p=0.5; q=0.25; lam=3; mu=10; sigma=7; xi=0.75; n=200 set.seed(2016) y <- rbinom(n,1,p) nz <- sum(1-y) extremes <- rbinom(sum(y),1,q) ne <- sum(extremes) nt <- n-nz-ne yt <- sample(mu-1,nt,replace=TRUE,prob=dpois(1:(mu-1),3)/(ppois(mu-1,lam)-ppois(0,lam))) yz <- round(rgpd(nz,mu,sigma,xi)) y[y==1] <- c(yt,yz) g <- hurdle(y) ``` ## Author(s) Taylor Trippe Earvin Balderama

hurdle function