bcl {weightedScores}

BIVARIATE COMPOSITE LIKELIHOOD FOR MULTIVARIATE NORMAL COPULA WITH CATEGORICAL AND COUNT REGRESSION

Description

Bivariate composite likelihood for multivariate normal copula with categorical and count regression.

Usage

bcl(r,b,gam,xdat,ydat,id,tvec,margmodel,corstr,link)
bcl.ord(r,b,gam,xdat,ydat,id,tvec,corstr,link)

Arguments

r

The vector of normal copula parameters.

b

The regression coefficients.

gam

The uinivariate parameters that are not regression coefficients. That is the parameter \gamma of negative binomial distribution or the q-dimensional vector of the univariate cutpoints of ordinal model. \gamma is NULL for Poisson and binary regression.

xdat

(\mathbf{x}_1 , \mathbf{x}_2 , \ldots , \mathbf{x}_n )^\top, where the matrix \mathbf{x}_i,\,i=1,\ldots,n for a given unit will depend on the times of observation for that unit (j_i) and will have number of rows j_i, each row corresponding to one of the j_i elements of y_i and p columns where p is the number of covariates including the unit first column to account for the intercept (except for ordinal regression where there is no intercept). This xdat matrix is of dimension (N\times p), where N =\sum_{i=1}^n j_i is the total number of observations from all units.

ydat

(y_1 , y_2 , \ldots , y_n )^\top, where the response data vectors y_i,\,i=1,\ldots,n are of possibly different lengths for different units. In particular, we now have that y_i is (j_i \times 1), where j_i is the number of observations on unit i. The total number of observations from all units is N =\sum_{i=1}^n j_i. The ydat are the collection of data vectors y_i, i = 1,\ldots,n one from each unit which summarize all the data together in a single, long vector of length N.

id

An index for individuals or clusters.

tvec

A vector with the time indicator of individuals or clusters.

margmodel

Indicates the marginal model. Choices are “poisson” for Poisson, “bernoulli” for Bernoulli, and “nb1” , “nb2” for the NB1 and NB2 parametrization of negative binomial in Cameron and Trivedi (1998).

corstr

Indicates the latent correlation structure of normal copula. Choices are “exch”, “ar”, and “unstr” for exchangeable, ar(1) and unstructured correlation structure, respectively.

link

The link function. Choices are “log” for the log link function, “logit” for the logit link function, and “probit” for the probit link function.

Details

The CL1 composite likelihood in Zhao and Joe (2005). That is the sum of bivariate marginal log-likelihoods.

bcl.ord is a variant of the code for ordinal (probit and logistic) regression.

Value

The negative bivariate composite likelihood for multivariate normal copula with Poisson or binary or negative binomial or ordinal regression.

Author(s)

Aristidis K. Nikoloulopoulos [e-mail]
Harry Joe [e-mail]

References

Zhao, Y. and Joe, H. (2005) Composite likelihood estimation in multivariate data analysis. The Canadian Journal of Statistics, 33, 335–356.

Cameron, A. C. and Trivedi, P. K. (1998) Regression Analysis of Count Data. Cambridge: Cambridge University Press.

See Also

cl1, iee