Description Usage Arguments Details Value Author(s) References
mGNtanh
uses GaussNewton optimization to compute the
hyperbolic tangent (tanh) estimator for the overdispersed multinomial
regression model 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.
1 2  mGNtanh(bstart, sigma2, resstart, Y, Ypos, Xarray, xvec, tvec,
jacstack, itmax = 100, print.level = 0)

bstart 
Vector of starting values for the coefficient parameters. 
sigma2 
Value of the dispersion parameter (variance). The estimator does not update this value. 
resstart 
Array of initial orthogonalized (but not standardized) residuals. 
Y 
Matrix (observations by alternatives) of outcome counts.
Values must be nonnegative. Missing data ( 
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 otherwise. 
tvec 
Starting values for the regression coefficient parameters, as a matrix (parameters by alternatives). Parameters that are involved in equality constraints are repeated in tvec. 
jacstack 
Array of regressors used to facilitate computing the gradient and the Hessian matrix. dim(jacstack) = c(observations, unique parameters, alternatives). 
itmax 
Maximum number of GaussNewton stages. Each stage does at most 100 GaussNewton steps. 
print.level 
Specify 0 for minimal printing (error messages only) or 2 to print details about the tanh computations. 
The tanh estimator is a redescending Mestimator. Given an estimate of the scale of the overdispersion, the tanh estimator estimates the coefficient parameters of the linear predictors of the multinomial regression model.
mGNtanh returns a list of 16 objects. The returned objects are:
coefficients 
The tanh coefficient estimates in matrix format. The matrix has one
column for each outcome alternative. The label for each row of the matrix
gives the names of the regressors to which the coefficient values in the row
apply. The regressor names in each label are separated by a forward
slash (/), and 
coeffvec 
A vector containing the tanh coefficient estimates. 
dispersion 
Value of the dispersion parameter (variance). This is the value specified
in the argument 
w 
Vector of weights based on the tanh estimator's 
psi 
Vector of values of the tanh estimator's 
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 tanh coefficient estimates. 
iters 
Number of GaussNewton iterations. 
error 
Error code:
0, no errors;
2, 
GNlist 
List reporting final results of the GaussNewton optimization. Elements:

tanhsigma2 
The tanh overdispersion parameter estimate, which is a weighted moment estimate of the dispersion: weighted mean sum of squared orthogonalized residuals (adjusted for effective sample size after weighting and degrees of freedom lost to estimated coefficients). 
Y 
The same 
Ypos 
The same 
probmat 
The matrix of predicted probabilities for each category for each observation based on the coefficient estimates. 
jacstack 
The same 
Xarray 
The same 
Walter R. Mebane, Jr., University of Michigan,
wmebane@umich.edu, http://wwwpersonal.umich.edu/~wmebane
Jasjeet S. Sekhon, UC Berkeley, sekhon@berkeley.edu, http://sekhon.berkeley.edu/
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/.
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