# Zelig-tobit-bayes-class: Bayesian Tobit Regression In Zelig: Everyone's Statistical Software

## Description

Bayesian Tobit Regression

## Arguments

 `formula` a symbolic representation of the model to be estimated, in the form `y ~ x1 + x2`, where `y` is the dependent variable and `x1` and `x2` are the explanatory variables, and `y`, `x1`, and `x2` are contained in the same dataset. (You may include more than two explanatory variables, of course.) The `+` symbol means “inclusion” not “addition.” You may also include interaction terms and main effects in the form `x1*x2` without computing them in prior steps; `I(x1*x2)` to include only the interaction term and exclude the main effects; and quadratic terms in the form `I(x1^2)`. `model` the name of a statistical model to estimate. For a list of other supported models and their documentation see: http://docs.zeligproject.org/articles/. `data` the name of a data frame containing the variables referenced in the formula or a list of multiply imputed data frames each having the same variable names and row numbers (created by `Amelia` or `to_zelig_mi`). `...` additional arguments passed to `zelig`, relevant for the model to be estimated. `by` a factor variable contained in `data`. If supplied, `zelig` will subset the data frame based on the levels in the `by` variable, and estimate a model for each subset. This can save a considerable amount of effort. You may also use `by` to run models using MatchIt subclasses. `cite` If is set to 'TRUE' (default), the model citation will be printed to the console. `below:` point at which the dependent variable is censored from below. If the dependent variable is only censored from above, set below = -Inf. The default value is 0. `above:` point at which the dependent variable is censored from above. If the dependent variable is only censored from below, set above = Inf. The default value is Inf.

## Details

Additional parameters avaialable to this model include:

• `weights`: vector of weight values or a name of a variable in the dataset by which to weight the model. For more information see: http://docs.zeligproject.org/articles/weights.html.

• `burnin`: number of the initial MCMC iterations to be discarded (defaults to 1,000).

• `mcmc`: number of the MCMC iterations after burnin (defaults to 10,000).

• `thin`: thinning interval for the Markov chain. Only every thin-th draw from the Markov chain is kept. The value of mcmc must be divisible by this value. The default value is 1.

• `verbose`: defaults to FALSE. If TRUE, the progress of the sampler (every 10%) is printed to the screen.

• `seed`: seed for the random number generator. The default is `NA` which corresponds to a random seed of 12345.

• `beta.start`: starting values for the Markov chain, either a scalar or vector with length equal to the number of estimated coefficients. The default is `NA`, such that the maximum likelihood estimates are used as the starting values.

Use the following parameters to specify the model's priors:

• `b0`: prior mean for the coefficients, either a numeric vector or a scalar. If a scalar value, that value will be the prior mean for all the coefficients. The default is 0.

• `B0`: prior precision parameter for the coefficients, either a square matrix (with the dimensions equal to the number of the coefficients) or a scalar. If a scalar value, that value times an identity matrix will be the prior precision parameter. The default is 0, which leads to an improper prior.

• `c0`: `c0`/2 is the shape parameter for the Inverse Gamma prior on the variance of the disturbance terms.

• `d0`: `d0`/2 is the scale parameter for the Inverse Gamma prior on the variance of the disturbance terms.

## Value

Depending on the class of model selected, `zelig` will return an object with elements including `coefficients`, `residuals`, and `formula` which may be summarized using `summary(z.out)` or individually extracted using, for example, `coef(z.out)`. See http://docs.zeligproject.org/articles/getters.html for a list of functions to extract model components. You can also extract whole fitted model objects using `from_zelig_model`.

 ```1 2``` ```data(turnout) z.out <- zelig(vote ~ race + educate, model = "tobit.bayes",data = turnout, verbose = FALSE) ```