multinomRob (version 1.8-6.1)

# Multinomial Multivariate-T Regression: Multinomial Multivariate-T Estimation

## 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

`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.

## 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`.

## 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.

## 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 For additional documentation please visit http://sekhon.berkeley.edu/robust/.

`match.call`. `optim`.