# CL1 INFORMATION CRITERIA Composite likelihood (CL1) information criteria. ```r clic1dePar(nbcl,r,b,gam,xdat,id,tvec,corstr,WtScMat,link,mvncmp) clic(nbcl,r,b,gam,xdat,id,tvec,corstr,WtScMat,link,mvncmp) ``` ## Arguments - `nbcl`: The negative value of the sum of bivariate marginal log-likelihoods at CL1 estimates. - `r`: The CL1 estimates of the latent correlations. - `b`: The CL1 estimates of the regression coefficients. - `gam`: The CL1 estimates of the cutpoints. - `xdat`: c("$(\\mathbf{x}_1 , \\mathbf{x}_2 , \\ldots ,\n$", "$ \\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. 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. - `id`: An index for individuals or clusters. - `tvec`: A vector with the time indicator of individuals or clusters. - `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. - `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 logit for the logit link function, and probit for the probit link function. - `mvncmp`: The method of computation of the MVN rectangle probabilities. Choices are 1 for `mvnapp` (faster), and 2 for `pmvnorm` (more accurate). ## Details First, consider the sum of univariate log-likelihoods $$ L_1= \sum_{i=1}^n\sum_{j=1}^d\, \log f_1(y_{ij};\nu_{ij},\boldsymbol{\gamma})=\sum_{i=1}^n\sum_{j=1}^d\,\ell_1(\nu_{ij},\boldsymbol{\gamma},\, y_{ij}), $$ and then the sum of bivariate log-likelihoods $$ L_2=\sum_{i=1}^{n}\sum_{j. [https://arxiv.org/abs/1510.07376](https://arxiv.org/abs/1510.07376). Varin, C. and Vidoni, P. (2005). A note on composite likelihood inference and model selection. **Biometrika** 92 , 519--528. Zhao, Y. and Joe, H. (2005) Composite likelihood estimation in multivariate data analysis. **The Canadian Journal of Statistics**, 33 , 335--356. ## Author(s) Aristidis K. Nikoloulopoulos A.Nikoloulopoulos@uea.ac.uk ## See Also `solvewtsc`, `wtsc.wrapper` ## Examples ```r ################################################################################ # Binary regression ################################################################################ ################################################################################ # read and set up the data set ################################################################################ data(childvisit) # covariates season1<-childvisit$q season1[season1>1]<-0 xdat<-cbind(childvisit$sex,childvisit$age,childvisit$m,season1) # response ydat<-childvisit$hosp ydat[ydat>0]=1 ydat=2-ydat #id id<-childvisit$id #time tvec<-childvisit$q ################################################################################ # select the link ################################################################################ link="logit" ################################################################################ # select the correlation structure ################################################################################ corstr="exch" ################################################################################ # perform CL1 estimation ################################################################################ i.est<-iee.ord(xdat,ydat,link) cat("\niest: IEE estimates\n") print(c(i.est$reg,i.est$gam)) est.rho<-cl1.ord(b=i.est$reg,gam=i.est$gam,xdat,ydat,id,tvec,corstr,link) cat("\nest.rho: CL1 estimates\n") print(est.rho$e) cat("\nest.rho: negative CL1 log-likelhood\n") print(est.rho$m) ################################################################################ # obtain the fixed weight matrices ################################################################################ WtScMat<-weightMat.ord(b=i.est$reg,gam=i.est$gam,rh=0.1961,xdat,ydat,id, tvec,corstr,link) ################################################################################ # obtain the CL1 information criteria ################################################################################ out<-clic1dePar(nbcl=est.rho$m,r=est.rho$e,i.est$r,i.est$g,xdat,id,tvec,corstr,WtScMat,link,1) ```

CLIC function