R: THE WEIGHTED SCORES EQUATIONS WITH INPUTS OF THE WEIGHT...

wtsc {weightedScores}

R Documentation

THE WEIGHTED SCORES EQUATIONS WITH INPUTS OF THE WEIGHT MATRICES AND THE DATA

Description

The weighted scores equations with inputs of the weight matrices and the data.

Usage

wtsc(param,WtScMat,xdat,ydat,id,tvec,margmodel,link)
wtsc.ord(param,WtScMat,xdat,ydat,id,tvec,link)

Arguments

`param`	The vector of regression and not regression parameters.
`WtScMat`	A list containing the following components. omega: The array with the `\Omega_i,\,i=1,\ldots,n` matrices; delta: The array with the `\Delta_i,\,i=1,\ldots,n` matrices; X: The array with the `X_i,\,i=1,\ldots,n` matrices.
`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).
`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 weighted scores estimating equations, with W_{i,\rm working} based on a working discretized MVN, have the form:

g_1= g_1( a)=\sum_{i=1}^n X_i^T\, W_{i,{\rm working}}^{-1}\, s_i( a)=0,

where W_{i,\rm working}^{-1}=\Delta_i\Omega_{i,\rm working}^{-1}= \Delta_i({\tilde a})\Omega_i({\tilde a},{\tilde R})^{-1} is based on the covariance matrix of s_i( a) computed from the fitted discretized MVN model with estimated parameters {\tilde a}, {\tilde R}.

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

Value

The weighted scores equations.

References

Nikoloulopoulos, A.K., Joe, H. and Chaganty, N.R. (2011) Weighted scores method for regression models with dependent data. Biostatistics, 12, 653–665. doi: 10.1093/biostatistics/kxr005.

Nikoloulopoulos, A.K. (2016) Correlation structure and variable selection in generalized estimating equations via composite likelihood information criteria. Statistics in Medicine, 35, 2377–2390. doi: 10.1002/sim.6871.

Nikoloulopoulos, A.K. (2017) Weighted scores method for longitudinal ordinal data. Arxiv e-prints, <arXiv:1510.07376>. https://arxiv.org/abs/1510.07376.