# multinomial_data_aug: Data Augmentation algorithm for multinomial data In imputeMulti: Imputation Methods for Multivariate Multinomial Data

## Description

Implement the Data Augmentation algorithm for multvariate multinomial data given observed counts of complete and missing data (Y_obs and Y_mis). Allows for specification of a Dirichlet conjugate prior.

## Usage

 ```1 2 3``` ```multinomial_data_aug(x_y, z_Os_y, enum_comp, conj_prior = c("none", "data.dep", "flat.prior", "non.informative"), alpha = NULL, burnin = 100, post_draws = 1000, verbose = FALSE) ```

## Arguments

 `x_y` A `data.frame` of observed counts for complete observations. `z_Os_y` A `data.frame` of observed marginal-counts for incomplete observations. `enum_comp` A `data.frame` specifying a vector of all possible observed patterns. `conj_prior` A string specifying the conjugate prior. One of `c("none", "data.dep", "flat.prior", "non.informative")`. `alpha` The vector of counts α for a Dir(α) prior. Must be specified if `conj_prior` is either `c("data.dep", "flat.prior")`. If `flat.prior`, specify as a scalar. If `data.dep`, specify as a vector with key matching `enum_comp`. `burnin` A scalar specifying the number of iterations to use as a burnin. Defaults to `100`. `post_draws` An integer specifying the number of draws from the posterior distribution. Defaults to `1000`. `verbose` Logical. If `TRUE`, provide verbose output on each iteration.

## Value

An object of class `mod_imputeMulti-class`.

`multinomial_em`, `multinomial_impute`
 ``` 1 2 3 4 5 6 7 8 9 10``` ```## Not run: data(tract2221) x_y <- multinomial_stats(tract2221[,1:4], output= "x_y") z_Os_y <- multinomial_stats(tract2221[,1:4], output= "z_Os_y") x_possible <- multinomial_stats(tract2221[,1:4], output= "possible.obs") imputeDA_mle <- multinomial_data_aug(x_y, z_Os_y, x_possible, n_obs= nrow(tract2221), conj_prior= "none", verbose= TRUE) ## End(Not run) ```