mle.FactorTree | R Documentation |
We use a two-stage estimation approach toward the estimation of factor tree copula models for item response data.
mle1FactorTree(y, A, cop, gl, hessian, print.level) mle2FactorTree(y, A, cop, gl, hessian, print.level)
y |
n \times d matrix with the ordinal reponse data, where n and d is the number of observations and ordinal variables, respectively. |
A |
d \times d vine array with 1,...,d on diagonal, note only the first row and diagnoal values are used for the 1-truncated vine model |
cop |
(2d-1)-vector with the names of bivariate copulas that link each of the oberved variabels with the 1st factor (1-factor part of the model), and conditional dependence of variables given the latent factor (1-truncated vine tree part of the model) . Choices are “bvn” for BVN, “bvtν” with ν = \{1, …, 9\} degrees of freedom for t-copula, “frk” for Frank, “gum” for Gumbel, “rgum” for reflected Gumbel, “1rgum” for 1-reflected Gumbel, “2rgum” for 2-reflected Gumbel. |
gl |
Gauss legendre quardrature nodes and weights. |
hessian |
If TRUE, the hessian of the negative log-likelihood is calculated during the minimization process. |
print.level |
Determines the level of printing which is done during the minimization process; same as in |
Estimation is achieved by maximizing the joint log-likelihood over the copula parameters with the univariate cutpoints fixed as estimated at the first step of the proposed two-step estimation approach.
A list containing the following components:
cutpoints |
The estimated univariate cutpoints. |
loglik |
The maximized joint log-likelihood. |
taus |
The estimated copula parameters in Kendall's tau scale. |
SEs |
The SEs of the Kendall's tau estimates. |
Sayed H. Kadhem
Aristidis K. Nikoloulopoulos a.nikoloulopoulos@uea.ac.uk
Joe, H. (2014). Dependence Modelling with Copulas. Chapman & Hall, London.
Kadhem, S.H. and Nikoloulopoulos, A.K. (2022b) Factor tree copula models for item response data. Arxiv e-prints, <arXiv: 2201.00339>. https://arxiv.org/abs/2201.00339.
#------------------------------------------------ # Setting quadreture points nq <- 5 gl <- gauss.quad.prob(nq) #------------------------------------------------ # PTSD Data #------------------ ----------------- data(PTSD) ydat=PTSD n=nrow(ydat) d=ncol(ydat) #------------------------------------------------ # Estimation #------------------ ----------------- #selecting vine tree based on polychoric rmat=polychoric0(ydat)$p A.polychoric=selectFactorTrVine(y=ydat,rmat,alg=3) #---------------- 1-factor tree ---------------- # 1-factor tree copula model copf1 <- rep("frk",d) coptree <- rep("frk",d-1) cop <- c(copf1,coptree) est1factortree <- mle1FactorTree(y=ydat, A=A.polychoric$VineTreeA, cop, gl, hessian=FALSE, print.level=2) #---------------- 2-factor tree ---------------- # 2-factor tree copula model copf1 <- rep("frk",d) copf2 <- rep("frk",d) coptree <- rep("frk",d-1) cop <- c(copf1,copf2,coptree) est2factortree <- mle2FactorTree(y=ydat, A=A.polychoric$VineTreeA, cop, gl, hessian=FALSE, print.level=2)
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.