GDINA: The Generalized DINA Model Framework

#' Examination for the Certificate of Proficiency in English (ECPE) data
#'
#' Examination for the Certificate of Proficiency in English (ECPE) data (the grammar section) has been used
#' in Henson and Templin (2007), Templin and Hoffman (2013), Feng, Habing, and Huebner (2014), and
#' Templin and Bradshaw (2014), among others.
#'
#' The data consists of responses of 2922 examinees to 28 items involving 3 attributes.
#' Attribute 1 is morphosyntactic rules, Attribute 2 is cohesive rules and
#' Attribute 3 is lexical rules.
#'
#'
#' @format A list of responses and Q-matrix with components:
#' \describe{
#' \item{\code{dat}}{Responses of 2922 examinees to 28 items.}
#' \item{\code{Q}}{The \eqn{28 \times 3} Q-matrix.}
#' }
#'
#' @author {Wenchao Ma, The University of Alabama, \email{wenchao.ma@@ua.edu}}
#' @references
#'
#' Ma, W., & de la Torre, J. (2020). GDINA: An R Package for Cognitive Diagnosis Modeling. \emph{Journal of Statistical Software, 93(14)}, 1-26.
#'
#' @examples
#' \dontrun{
#' mod1 <- GDINA(ecpe$dat,ecpe$Q)
#' mod1
#' summary(mod1)
#'
#' mod2 <- GDINA(ecpe$dat,ecpe$Q,model="RRUM")
#' mod2
#' anova(mod1,mod2)
#' # You may compare the following results with Feng, Habing, and Huebner (2014)
#' coef(mod2,"rrum")
#'
#' # G-DINA with hierarchical structure
#' # see Templin & Bradshaw, 2014
#' ast <- att.structure(list(c(3,2),c(2,1)),K=3)
#'
#' est.gdina2 <- GDINA(ecpe$dat,ecpe$Q,model = "GDINA",
#'                    control = list(conv.crit = 1e-6),
#'                    att.str = list(c(3,2),c(2,1)))
#' # see Table 7 in Templin & Bradshaw, 2014
#' summary(est.gdina2)
#'}
#'
#' @references
#'
#' Feng, Y., Habing, B. T., & Huebner, A. (2014). Parameter estimation of the reduced RUM using the EM algorithm. \emph{Applied Psychological Measurement, 38}, 137-150.
#'
#' Henson, R. A., & Templin, J. (2007, April). Large-scale language assessment using cognitive diagnosis models. Paper presented at the annual meeting of the National Council for Measurement in Education in Chicago, Illinois.
#'
#' Templin, J., & Bradshaw, L. (2014). Hierarchical diagnostic classification models: A family of models for estimating and testing attribute hierarchies. \emph{Psychometrika, 79}, 317-339.
#'
#' Templin, J., & Hoffman, L. (2013). Obtaining diagnostic classification model estimates using Mplus. \emph{Educational Measurement: Issues and Practice, 32}, 37-50.
"ecpe"