# multinomT: Multinomial Multivariate-T Estimation In multinomRob: Robust Estimation of Overdispersed Multinomial Regression Models

## Description

`multinomT` fits the multinomial multivariate-t regression for grouped count data. This function is not meant to be called directly by the user. It is called by `multinomRob`, which constructs the various arguments.

## Usage

 `1` ```multinomT(Yp, Xarray, xvec, jacstack, start = NA, nobsvec, fixed.df = NA) ```

## Arguments

 `Yp` Matrix (observations by alternatives) of outcome proportions. Values must be between 0 and 1. Missing data (`NA` values) are not allowed. `Xarray` Array of regressors. dim(Xarray) = c(observations, parameters, alternatives). `xvec` Matrix (parameters by alternatives) that represents the model structure. It has a 1 for an estimated parameter, an integer greater than 1 for an estimated parameter constrained equal to another estimated parameter (all parameters constrained to be equal to one another have the same integer value in xvec) and a 0 otherwize. `jacstack` Array of regressors used to facilitate computing the gradient and the hessian matrix. dim(jacstack) = c(observations, unique parameters, alternatives). `start` A list of starting values of three kinds of parameters: `start\$beta`, the values for the regression coefficients; `start\$Omega`, the values for the variance-covariance matrix; `start\$df`, the value for the multivariate-t degrees of freedom parameter. `nobsvec` Vector of the total number of counts for each observation. `fixed.df` The degrees of freedom to be used for the multivariate-t distribution. When this is specified, the DF will not be estimated.

## Details

The function often provides good starting values for multinomRob's LQD estimator, but the standard errors it reports are not correct, in part because they ignore heteroscedasticity.

## Value

 `call` Names and values of all of the arguments which were passed to the function. See `match.call` for further details. `logL` Log likelihood. `deviance` Deviance. `par` A list of three kinds of parameter estimates: `par\$beta`, the estimates for the regression coefficients; `par\$Omega`, the estimates for the variance-covariance matrix; `par\$df`, the estimate of the multivariate-t degrees of freedom parameter. `se` Vector of standard errors for the regression coefficients. WARNING: these are not correct in part because the model ignores heteroscedasticity. `optim` Returned by `optim`. `pred` A matrix of predicted probabilities with the same dimentions as `Yp`.

## Author(s)

Walter R. Mebane, Jr., University of Michigan, wmebane@umich.edu, http://www-personal.umich.edu/~wmebane

Jasjeet S. Sekhon, UC Berkeley, sekhon@berkeley.edu, http://sekhon.berkeley.edu/

## References

Walter R. Mebane, Jr. and Jasjeet Singh Sekhon. 2004. “Robust Estimation and Outlier Detection for Overdispersed Multinomial Models of Count Data.” American Journal of Political Science 48 (April): 391–410. http://sekhon.berkeley.edu/multinom.pdf

`match.call`. `optim`.