#' @title Example 7.1 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup (p-213)
#' @name Exam7.1
#' @docType data
#' @keywords datasets
#' @description Exam7.1 explains multifactor models with all factors qualitative
#' @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{DataSet7.1}}
#'
#' @importFrom lsmeans lsmeans contrast lsmip
#' @importFrom phia testInteractions
#' @importFrom car linearHypothesis
#'
#' @examples
#'
#' library(lsmeans)
#' library(car)
#' data(DataSet7.1)
#'
#' DataSet7.1$a <- factor(x = DataSet7.1$a)
#' DataSet7.1$b <- factor(x = DataSet7.1$b)
#'
#' Exam7.1.lm1 <-
#' lm(
#' formula = y ~ a + b + a*b
#' , data = DataSet7.1
#' # , subset
#' # , weights
#' # , na.action
#' , method = "qr"
#' , model = TRUE
#' # , x = FALSE
#' # , y = FALSE
#' , qr = TRUE
#' , singular.ok = TRUE
#' , contrasts = NULL
#' # , offset
#' # , ...
#' )
#'
#' summary( Exam7.1.lm1 )
#' anova(Exam7.1.lm1)
#' ##---Result obtained as in SLICE statement in SAS for a0 & a1
#' library(phia)
#' a0 <- list(a=c("0"=1))
#' phia::testInteractions(Exam7.1.lm1, custom=a0, across="b")
#' a1 <- list(a=c("1"=1))
#' phia::testInteractions(Exam7.1.lm1, custom=a1, across="b")
#'
#'
#' ##---Interaction plot
#' lsmip(
#' object = Exam7.1.lm1
#' , formula = a~b
#' , ylab = "y Lsmeans"
#' , main = "Lsmeans for a*b"
#' )
#' #-------------------------------------------------------------
#' ## Individula least squares treatment means
#' #-------------------------------------------------------------
#' Lsm7.1 <-
#' lsmeans::lsmeans(
#' object = Exam7.1.lm1
#' , specs = ~a*b
#' # , ...
#' )
#'
#' Lsm7.1
#' ##---Simpe effects comparison of interaction by a
#' ## (but it doesn't give the same p-value as in article 7.4.2 page#215)
#' SimpleEff7.1 <-
#' lsmeans::lsmeans(
#' object = Exam7.1.lm1
#' , specs = pairwise~b|a
#' # , ...
#' )$contrasts
#'
#' SimpleEff7.1
#'
#' ##---Alternative method of pairwise comparisons by applying contrast
#' ## coefficient (gives the same p-value as in 7.4.2)
#' ContrastLsm7.1 <-
#' lsmeans::contrast(
#' Lsm7.1
#' , list (
#' c1 = c(1,0,-1,0,0,0)
#' , c2 = c(1,0,0,0,-1,0)
#' , c3 = c(0,0,1,0,-1,0)
#' , c4 = c(0,1,0,-1,0,0)
#' , c5 = c(0,1,0,0,0,-1)
#' , c6 = c(0,1,0,0,-1,0)
#' )
#' )
#'
#' ContrastLsm7.1
#'
#' ##---Nested Model (page 216)----
#' Exam7.1.lm2 <-
#' lm(
#' formula = y ~ a + a %in% b
#' , data = DataSet7.1
#' # , subset
#' # , weights
#' # , na.action
#' , method = "qr"
#' , model = TRUE
#' # , x = FALSE
#' # , y = FALSE
#' , qr = TRUE
#' , singular.ok = TRUE
#' , contrasts = NULL
#' # , offset
#' # , ...
#' )
#'
#' summary( Exam7.1.lm2 )
#' anova(Exam7.1.lm2)
#'
#' ContrastA0lm2 <- car::linearHypothesis(Exam7.1.lm2, c("a0:b1=a0:b2"))
#' ContrastA0lm2
#' ContrastA1lm2 <- car::linearHypothesis(Exam7.1.lm2,c("a1:b1=a1:b2"))
#' ContrastA1lm2
#'
#' ##---Bonferroni's adjusted p-values
#' SimpleEff7.1B <-
#' lsmeans::lsmeans(
#' object = Exam7.1.lm2
#' , specs = pairwise~b|a
#' , adjust = "bonferroni"
#' )$contrasts
#'
#' SimpleEff7.1B
#'
#' ##---Alternative method of pairwise comparisons by applying contrast coefficient with Bonferroni adjustment
#' Bonferroni7.1 <-
#' lsmeans::contrast(
#' Lsm7.1
#' , list(
#' c1 = c(1,0,-1,0,0,0)
#' , c2 = c(1,0,0,0,-1,0)
#' , c3 = c(0,0,1,0,-1,0)
#' , c4 = c(0,1,0,-1,0,0)
#' , c5 = c(0,1,0,0,0,-1)
#' , c6 = c(0,1,0,0,-1,0)
#' )
#' , adjust="bonferroni"
#' )
#' Bonferroni7.1
NULL
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