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#' @title Examp3.3 from Duchateau, L. and Janssen, P. and Rowlands, G. J. (1998).\emph{Linear Mixed Models. An Introduction with applications in Veterinary Research}. International Livestock Research Institute.
#' @name Examp3.3
#' @docType data
#' @keywords datasets
#' @description Examp3.3 is used for inspecting probability distribution and to define a plausible process through
#' linear models and generalized linear models.
#' @author \enumerate{
#' \item Muhammad Yaseen (\email{myaseen208@@gmail.com})
#' }
#' @references \enumerate{
#' \item Duchateau, L. and Janssen, P. and Rowlands, G. J. (1998).\emph{Linear Mixed Models. An Introduction with applications in Veterinary Research}.
#' International Livestock Research Institute.
#' }
#' @seealso
#' \code{\link{ex124}}
#' @importFrom ggplot2 ggplot
#' @importFrom lme4 lmer
#' @importFrom lmerTest lsmeansLT
#' @examples
#' #-------------------------------------------------------------
#' ## Example 3.3 Model 1 p-88
#' #-------------------------------------------------------------
#' # PROC MIXED DATA=ex33;
#' # CLASS breed animal_id;
#' # MODEL pcv = breed breed*time/SOLUTION;
#' # RANDOM animal_id(breed)/SOLUTION;
#' # RUN;
#'
#' library(lme4)
#' options(contrasts = c(factor = "contr.SAS", ordered = "contr.poly"))
#' str(ex33)
#'
#' fm3.5 <-
#' lme4::lmer(
#' formula = PCV ~ breed + breed:time + (1|animal_id:breed)
#' , data = ex33
#' , REML = TRUE
#' , control = lmerControl()
#' , start = NULL
#' , verbose = 0L
#' # , subset
#' # , weights
#' # , na.action
#' # , offset
#' , contrasts = list(breed = "contr.SAS")
#' , devFunOnly = FALSE
#' # , ...
#' )
#' summary(fm3.5)
#' anova(fm3.5)
#'
#' library(lmerTest)
#' fm3.6 <-
#' lmerTest::lmer(
#' formula = PCV ~ breed + breed:time + (1|animal_id:breed)
#' , data = ex33
#' , REML = TRUE
#' , control = lmerControl()
#' , start = NULL
#' , verbose = 0L
#' # , subset
#' # , weights
#' # , na.action
#' # , offset
#' , contrasts = list(breed = "contr.SAS")
#' , devFunOnly = FALSE
#' # , ...
#' )
#' summary(fm3.6)
#' anova(object = fm3.6, ddf = "Satterthwaite")
#'
#'
#' # PROC MIXED DATA=ex33;
#' # CLASS breed animal_id;
#' # MODEL pcv = breed breed*time/SOLUTION;
#' # REPEATED/TYPE=CS SUB = animal_id(breed) R;
#' # RUN;
#'
#'
#' library(nlme)
#' fm3.7 <-
#' nlme::gls(
#' model = PCV ~ breed + breed:time
#' , data = ex33
#' , correlation = corCompSymm(, form = ~ 1|animal_id/breed)
#' , weights = NULL
#' # , subset =
#' , method = "REML" # c("REML", "ML")
#' , na.action = na.fail
#' , control = list()
#' )
#' summary(fm3.7)
#' anova(fm3.7)
#'
#'
#'
#' # PROC MIXED DATA=ex33;
#' # CLASS breed animal_id;
#' # MODEL pcv = time breed breed*time/SOLUTION;
#' # RANDOM animal_id(breed)/SOLUTION;
#' # RUN;
#'
#' fm3.8 <-
#' lme4::lmer(
#' formula = PCV ~ time + breed + breed:time + (1|animal_id:breed)
#' , data = ex33
#' , REML = TRUE
#' , control = lmerControl()
#' , start = NULL
#' , verbose = 0L
#' # , subset
#' # , weights
#' # , na.action
#' # , offset
#' , contrasts = list(breed = "contr.SAS")
#' , devFunOnly = FALSE
#' # , ...
#' )
#' summary(fm3.8)
#' anova(fm3.8)
#'
#'
#' fm3.9 <-
#' lmerTest::lmer(
#' formula = PCV ~ time + breed + breed:time + (1|animal_id:breed)
#' , data = ex33
#' , REML = TRUE
#' , control = lmerControl()
#' , start = NULL
#' , verbose = 0L
#' # , subset
#' # , weights
#' # , na.action
#' # , offset
#' , contrasts = list(breed = "contr.SAS")
#' , devFunOnly = FALSE
#' # , ...
#' )
#' summary(fm3.9)
#' anova(object = fm3.9, ddf = "Satterthwaite", type = 3)
#'
#'
#' # PROC MIXED DATA=ex33;
#' # CLASS breed animal_id;
#' # MODEL pcv = breed breed*time/SOLUTION;
#' # REPEATED/TYPE=AR(1) SUBJET = animal_id(breed) R;
#' # RUN;
#'
#'
#' library(nlme)
#' fm3.10 <-
#' nlme::gls(
#' model = PCV ~ breed + breed:time
#' , data = ex33
#' , correlation = corAR1(, form = ~ 1|animal_id/breed)
#' , weights = NULL
#' # , subset =
#' , method = "REML" # c("REML", "ML")
#' , na.action = na.fail
#' , control = list()
#' )
#' summary(fm3.10)
#' anova(fm3.10)
#'
#' # PROC MIXED DATA=ex33;
#' # CLASS breed animal_id;
#' # MODEL pcv = breed breed*time/SOLUTION;
#' # RANDOM INTERCEPT time/TYPE=UN SUBJET = animal_id(breed) SOLUTION;
#' # RUN;
#'
#'
#' library(nlme)
#' # fm3.11 <-
#' # nlme::gls(
#' # model = PCV ~ breed + breed:time
#' # , data = ex33
#' # , random = ~1|animal_id/breed
#' # , correlation = corAR1(, form = ~ 1|animal_id/breed)
#' # , weights = NULL
#' # # , subset =
#' # , method = "REML" # c("REML", "ML")
#' # , na.action = na.fail
#' # , control = list()
#' # )
#' # summary(fm3.11)
#' # anova(fm3.11)
#'
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