#' @title Example 4.1 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup(p-138)
#' @name Exam4.1
#' @docType data
#' @keywords datasets
#' @description Exam4.1 REML vs ML criterion is used keeping block effects random
#' @author \enumerate{
#' \item Muhammad Yaseen (\email{myaseen208@@gmail.com})
#' \item Adeela Munawar (\email{adeela.uaf@@gmail.com})
#' }
#' @references \enumerate{
#' \item Stroup, W. W. (2012).
#' \emph{Generalized Linear Mixed Models: Modern Concepts, Methods and Applications}.
#' CRC Press.
#' }
#' @seealso
#' \code{\link{DataSet4.1}}
#'
#' @importFrom lme4 lmer
#'
#' @examples
#'
#' DataSet4.1$trt <- factor(x = DataSet4.1$trt)
#' DataSet4.1$block <- factor(x = DataSet4.1$block)
#'
#'##---REML estimates on page 138(article 4.4.3.3)
#'library(lme4)
#' Exam4.1REML <-
#' lmer(
#' formula = y~ trt +( 1|block )
#' , data = DataSet4.1
#' , REML = TRUE
#' # , control = lmerControl()
#' , start = NULL
#' # , verbose = 0L
#' # , subset
#' # , weights
#' # , na.action
#' # , offset
#' , contrasts = NULL
#' , devFunOnly = FALSE
#' # , ...
#' )
#'
#' VarCompREML4.1 <-
#' VarCorr(x = Exam4.1REML
#' # , sigma = 1
#' # , ...
#' )
#' print(VarCompREML4.1, comp=c("Variance"))
#'
#' ##---ML estimates on page 138(article 4.4.3.3)
#' Exam4.1ML <-
#' lmer(
#' formula = y ~ trt + (1|block)
#' , data = DataSet4.1
#' , REML = FALSE
#' # , control = lmerControl()
#' , start = NULL
#' # , verbose = 0L
#' # , subset
#' # , weights
#' # , na.action
#' # , offset
#' , contrasts = NULL
#' , devFunOnly = FALSE
#' # , ...
#' )
#' VarCompML4.1 <-
#' VarCorr(x = Exam4.1ML
#' # , sigma = 1
#' # , ...
#' )
#' print(VarCompML4.1,comp=c("Variance"))
#'
#' Exam4.1.lm <-
#' lm(
#' formula = y~ trt + block
#' , data = DataSet4.1
#' # , subset
#' # , weights
#' # , na.action
#' , method = "qr"
#' , model = TRUE
#' # , x = FALSE
#' # , y = FALSE
#' , qr = TRUE
#' , singular.ok = TRUE
#' , contrasts = NULL
#' # , offset
#' # , ...
#' )
#' summary(anova(object = Exam4.1.lm))
NULL
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