matrix with n rows and q columns containing the categorical responses. Each line is a vector of size q representing the responses for a single statistical unit.
x
additional n times p matrix of subject specific covariates.
K
Number of levels of the categorical responses.
start.par
list containing parameters for the maximization algorithm:
type is character string. If "default" the initialization is as default. Otherwise each value should be passed, cor is a vector with the initial values for the polycoric correlations, beta is a vector with the initial values for the regression coefficients, xi is a vector with the initial values for the column specific means, and thres is a vector with the initial values for the thresholds.
same.means
logical. If codeTRUE all the q variable are assumed to have the same mean.
eval.max
see help(nlminb)
iter.max
see help(nlminb)
...
additional arguments to be passed.
Details
The code is implemented in R software with call to C functions for the most demanding operations. To evaluate the Gaussian integrals, the package uses the Fortran 77 subroutine SADMVN. The default choice of initialization is the first threshold equal to zero and the remaining thresholds equally spaced with distance one. As for the covariance components, we consider as starting values the sample covariances of the observed categorical variables treated as continuous. Optimization of the pairwise log-likelihood function is performed via quasi-Newton box-constrained optimization algorithm, as implemented in nlminb.
Value
A list with components:
par
The best set of parameters found.
objective
The value of the negative pairwise likelihood corresponding to par
convergence
An integer code. 0 indicates successful convergence.
message
A character string giving any additional information returned by the optimizer, or NULL. For details, see nlminb documentation.
iterations
Number of iterations performed.
evaluations
Number of objective function and gradient function evaluations.
thresh
The set of thresholds partitioning the latent sample space.
xi
Vector of the item means.
cor
Estimated polychoric correlation matrix.
References
Cox D. R. , Reid N. (2004) A note on pseudolikelihood constructed from marginal densities. Biometrika, 91, 729–737.
Genz A. (1992) Numerical computation of multivariate normal probabilities. Journal of computational and graphical statistics, 2, 141–149.
Kenne Pagui, E. C. and Canale, A. (2014) Pairwise likelihood inference for multivariate categorical responses, Technical Report, Department of Statistics, University of Padua.
Lindsay B. (1988) Composite likelihood methods. Comtemporary Mathematics, 80, 221–240.