Multinomial Regression {multinomRob}R Documentation

Multinomial Regression Maximum Likelihood Estimator with Overdispersion

Description

multinomMLE estimates the coefficients of the multinomial regression model for grouped count data by maximum likelihood, then computes a moment estimator for overdispersion and reports standard errors for the coefficients that take overdispersion into account. This function is not meant to be called directly by the user. It is called by multinomRob, which constructs the various arguments.

Usage

multinomMLE(Y, Ypos, Xarray, xvec, jacstack, itmax=100, xvar.labels,
                   choice.labels, print.level)

Arguments

Y Matrix (observations by alternatives) of outcome counts. Values must be nonnegative. Missing data (NA values) are not allowed.
Ypos Matrix indicating which elements of Y are counts to be analyzed (TRUE) and which are values to be skipped (FALSE). This allows the set of outcome alternatives to vary over observations.
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).
itmax The maximum number of iterations to be done in the Gauss-Newton optimization.
xvar.labels Vector of labels for observations.
choice.labels Vector of labels for outcome alternatives.
print.level Specify 0 for minimal printing (error messages only) or 3 to print details about the MLE computations.

Details

Following the generalized linear models approach, the coefficient parameters in an overdispersed multinomial regression model may be estimated using the likelihood for a standard multinomial regression model. A moment estimator may be used for the dispersion parameter, given the coefficient estimates, with little efficiency loss.

Value

multinomMLE returns a list of 20 objects. The returned objects are:

coefficients The maximum likelihood coefficient estimates in matrix format. The value 0 is used in the matrix to fill in for values that do not correspond to a regressor.
coeffvec A vector containing the maximum likelihood coefficient estimates.
dispersion Moment estimate of the dispersion: mean sum of squared orthogonalized residuals (adjusted for degrees of freedom lost to estimated coefficients).
se The tanh coefficient estimate standard errors in matrix format. The format and labelling used for the matrix is the same as is used for the coefficients. The standard errors are derived from the estimated asymptotic sandwich covariance estimate.
se.opg The tanh coefficient estimate standard errors derived from the asymptotic covariance estimated using the outer product of the gradient (expected information) divided by the moment estimate of the dispersion.
se.hes The tanh coefficient estimate standard errors derived from the asymptotic covariance estimated using the hessian matrix (observed information).
se.vec A vector containing the tanh coefficient sandwich estimate standard errors.
se.opg.vec A vector containing the tanh coefficient OPG estimate standard errors.
A The outer product of the gradient (expected information) divided by the moment estimate of the dispersion.
B The inverse of the hessian matrix (observed formation).
covmat Sandwich estimate of the asymptotic covariance of the maximum likelihood coefficient estimates.
iters Number of Gauss-Newton iterations.
error Exit error code.
GNlist List reporting final results of the Gauss-Newton optimization. Elements: coefficients, vector of coefficient parameters (same as coeffvec value in list returned by multinomMLE); tvec, matrix of coefficient parameters (same as coefficients value in list returned by multinomMLE); formation, inverse Hessian matrix; score, score (or gradient element) matrix; LLvals, list containing log-likelihood value; convflag, TRUE/FALSE convergence flag; iters, number of iterations done in final Gauss-Newton stage; posdef, TRUE if Hessian is positive definite.
sigma2 Moment estimate of the dispersion: mean sum of squared orthogonalized residuals (adjusted for degrees of freedom lost to estimated coefficients).
Y The same Y matrix that was supplied as input, except modified by having done Y[!Ypos] <- 0.
Ypos The same Ypos matrix that was supplied as input.
fitted.prob The matrix of predicted probabilities for each category for each observation based on the coefficient estimates.
jacstack The same jacstack that was supplied as an input argument.

Author(s)

Walter R. Mebane, Jr., Cornell University, wrm1@cornell.edu, http://macht.arts.cornell.edu/wrm1/

Jasjeet S. Sekhon, Harvard University, jasjeet_sekhon@harvard.edu, http://jsekhon.fas.harvard.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://macht.arts.cornell.edu/wrm1/multinom.pdf

For the most current code and related material see http://jsekhon.fas.harvard.edu/robust/


[Package multinomRob version 1.2 Index]