# joint.2z1: Jointly modelling of multiple variables taking values from... In zoib: Bayesian Inference for Beta Regression and Zero-or-One Inflated Beta Regression

## Description

Internal function to be called by function zoib. Jointly models multiple (0,1]-bounded variables with inflation at 1 when there are multiple random variables in the linear predictors of the link functions

## Usage

 ```1 2 3``` ```joint.2z1(y, n, q, xmu.1, p.xmu, xsum.1, p.xsum, x1.1, p.x1, inflate1, zdummy, qz, nz0, m, rid, EUID, nEU, prior1, prior2, prior.beta, prior.Sigma, prec.int, prec.DN, lambda.L1, lambda.L2, lambda.ARD, scale.unif, scale.halft, link, n.chain,inits, seed) ```

## Arguments

 `y` >=2 response variables taking value from (0, 1]. `n` Number of rows in the data set. `q` Number of response variables. `xmu.1` Design matrix associated with the fixed effects in the linear predictor of g(mean of the beta piece), where g() is a link function. `p.xmu` Number of columns in xmu.1. `xsum.1` Design matrix associated with the fixed effects in linear predictor of the log(dispersion parameter of the beta piece). `p.xsum` Number of columns in xsum.1. `x1.1` Design matrix associated with the fixed effects in the linear predictor of g(Pr(y=1)), where g() is a link function. `p.x1` Number of columns in x1.1. `inflate1` A vector containing information on which response variables have inflation at 1. `zdummy` Design matrix associated with the random effects. `qz` Number of columns in zdummy. `nz0` Number of original random variables (before dummy coding). `m` A vector with nz0 element that contains the number of levels of each random varaibles. `rid` A vector containing information on which linear predictors have a random component. `EUID` Listing of the experimental unit ID for each row of the data set. `nEU` Number of experimental units. `prior1` A vector containing information on the prior choice for the regression coefficients in each of the 4 linear predictors of the 4 link functions. `prior2` A matrix containing information on the prior choice for the covariance structure of the random variables. `prior.beta` Prior choice for the regression coefficients in each of the 4 link functions). `prior.Sigma` Prior choice for the Covariance structure of the random variables. `prec.int` The precision parameter of the prior distributions (diffuse normal) of the intercepts in the linear predictors. `prec.DN` The precision parameter of the prior distributions of the regression coefficients in the linear predictors if diffuse normal prior is chosen. `lambda.ARD` The scale parameter in the prior distributions of the regression coefficients in the linear predictors if the ARD prior is chosen. `lambda.L1` The scale parameter in the prior distributions of the regression coefficients in the linear predictors if the L1-like prior is chosen. `lambda.L2` The scale parameter in the prior distributions of the regression coefficients in the linear predictors if the L2-like prior is chosen. `scale.unif` The upper bound of the uniform distribution for the standard deviation of each random variable. `scale.halft` The scale parameter of the half-Cauchy distribution for the standard deviation of each random variable. `link` A vector containing information onthe choice of link function for the mean of the beta piece. `n.chain` Number of chains for the MCMC sampling. `inits` initial parameter for model parameters. `seed` seeds for results reproducibility

## Value

Internal function. Returned values are used internally

## Author(s)

Fang Liu ([email protected])

See Also as `zoib`