#' Growth curves of pigs in a 3x3 factorial experiment
#' 
#' The \code{dietox} data frame has 861 rows and 7 columns.
#'
#' @details Data contains weight of slaughter pigs measured weekly for 12
#'     weeks. Data also contains the startweight (i.e. the weight at week
#'     1). The treatments are 3 different levels of Evit = vitamin E (dose: 0,
#'     100, 200 mg dl-alpha-tocopheryl acetat /kg feed) in combination with 3
#'     different levels of Cu=copper (dose: 0, 35, 175 mg/kg feed) in the feed.
#'     The cumulated feed intake is also recorded. The pigs are littermates.
#' 
#' 
#' @format This data frame contains the following columns:
#' 
#' \describe{
#' \item{Weight}{Weight in Kg}
#' \item{Feed}{Cumulated feed intake in Kg}
#' \item{Time}{Time (in weeks) in the experiment}
#' \item{Pig}{Factor; id of each pig}
#' \item{Evit}{Factor; vitamin E dose; see 'details'.}
#' \item{Cu}{Factor, copper dose; see 'details'}
#' \item{Start}{Start weight in experiment, i.e. weight at week 1.}
#' \item{Litter}{Factor, id of litter of each pig}
#' }
#' 
#' @source Lauridsen, C., Højsgaard, S.,Sørensen, M.T. C. (1999) Influence of
#'     Dietary Rapeseed Oli, Vitamin E, and Copper on Performance and
#'     Antioxidant and Oxidative Status of Pigs. J. Anim. Sci.77:906-916
#' @keywords datasets
#' @examples
#' 
#' data(dietox)
#' head(dietox)
#' \dontrun{
#' if (require(ggplot2)){
#'   qplot(Time, Weight, data=dietox, col=Pig) + geom_line() +
#'         theme(legend.position = "none") + facet_grid(Evit~Cu)
#' } else {
#'   coplot(Weight ~ Time | Evit * Cu, data=dietox)
#' }
#' }
"dietox"



#' Ordinal Data from Koch
#' 
#' The \code{koch} data frame has 288 rows and 4 columns.
#' 
#' @format This data frame contains the following columns:
#' \describe{
#'     \item{trt}{a numeric vector}
#'     \item{day}{a numeric vector}
#'     \item{y}{an ordered factor with levels: \code{1} < \code{2} < \code{3}}
#'     \item{id}{a numeric vector}
#' }
#'
#' @keywords datasets
#' @examples
#' 
#' data(koch)
#' fit <- ordgee(ordered(y) ~ trt + as.factor(day), id=id, data=koch, corstr="exch")
#' summary(fit)
#' 
"koch"



#' Data on Obesity from the Muscatine Coronary Risk Factor Study.
#'
#' The data are from the Muscatine Coronary Risk Factor (MCRF) study,
#' a longitudinal survey of school-age children in Muscatine, Iowa.
#' The MCRF study had the goal of examining the development and
#' persistence of risk factors for coronary disease in children.  In
#' the MCRF study, weight and height measurements of five cohorts of
#' children, initially aged 5-7, 7-9, 9-11, 11-13, and 13-15 years,
#' were obtained biennially from 1977 to 1981. Data were collected on
#' 4856 boys and girls. On the basis of a comparison of their weight
#' to age-gender specific norms, children were classified as obese or
#' not obese.
#'                                                                                     
#' @format A dataframe with 14568 rows and 7 variables:
#' \describe{
#'   \item{id}{identifier of child.}
#'
#'   \item{gender}{gender of child}
#'
#'   \item{base_age}{baseline age}
#' 
#'   \item{age}{current age}
#'
#'   \item{occasion}{identifier of occasion of recording}
#' 
#'   \item{obese}{'yes' or 'no'}
#' 
#'   \item{numobese}{obese in numerical form: 1 corresponds to 'yes'
#' and 0 corresponds to 'no'.}
#'
#' }
#' @source
#'
#' \url{https://content.sph.harvard.edu/fitzmaur/ala2e/muscatine.txt}
#'
#' Woolson, R.F. and Clarke, W.R. (1984). Analysis of categorical
#' incompletel longitudinal data. Journal of the Royal Statistical Society,
#' Series A, 147, 87-99.
#'
#' @examples
#' muscatine$cage <- muscatine$age - 12                                         
#' muscatine$cage2 <- muscatine$cage^2                                          
#'                                                                         
#' f1 <- numobese ~ gender                                                 
#' f2 <- numobese ~ gender + cage + cage2 +                                
#'     gender:cage + gender:cage2                                          
#'                                                                         
#' gee1 <- geeglm(formula = f1, id = id,                                   
#'                waves = occasion, data = muscatine, family = binomial(),      
#'                corstr = "independence")                                 
#'                                                                         
#' gee2 <- geeglm(formula = f2, id = id,                                   
#'                waves = occasion, data = muscatine, family = binomial(),      
#'                corstr = "independence")                                 
#'                                                                         
#' tidy(gee1)                                                              
#' tidy(gee2)                                                              
#' QIC(gee1)
#' QIC(gee2)
#'
#' 
"muscatine"

#' Ohio Children Wheeze Status
#' 
#' The \code{ohio} data frame has 2148 rows and 4 columns. The dataset is a
#' subset of the six-city study, a longitudinal study of the health effects of
#' air pollution.
#' 
#' @format This data frame contains the following columns:
#'
#' \describe{
#'
#' \item{resp}{an indicator of wheeze status (1=yes, 0=no)}
#'
#' \item{id}{a numeric vector for subject id}
#'
#' \item{age}{a numeric vector of age, 0 is 9 years old}
#'
#' \item{smoke}{an indicator of maternal smoking at the first
#'     year of the study}
#' }
#'
#' @references Fitzmaurice, G.M. and Laird, N.M. (1993) A likelihood-based
#'     method for analyzing longitudinal binary responses, \emph{Biometrika}
#'     \bold{80}: 141--151.
#'
#' @keywords datasets
#' @examples
#' 
#' data(ohio)
#' 
#' fit.ex <- geeglm(resp ~ age + smoke + age:smoke, id=id, data=ohio,
#'    family=binomial, corstr="exch", scale.fix=TRUE)
#' QIC(fit.ex)
#'
#' fit.ar <- geeglm(resp ~ age + smoke + age:smoke, id=id, data=ohio,
#'    family=binomial, corstr="ar1", scale.fix=TRUE)
#' QIC(fit.ex)
"ohio"


#' Clustered Ordinal Respiratory Disorder
#' 
#' The \code{respdis} data frame has 111 rows and 3 columns. The study described
#' in Miller et. al. (1993) is a randomized clinical trial of a new treatment of
#' respiratory disorder. The study was conducted in 111 patients who were
#' randomly assigned to one of two treatments (active, placebo). At each of four
#' visits during the follow-up period, the response status of each patients was
#' classified on an ordinal scale.
#' 
#' 
#' @format This data frame contains the following columns:
#' \describe{
#' 
#'    \item{y1, y2, y3, y4}{ordered factor measured at 4 visits for the response with
#'     levels, \code{1} < \code{2} < \code{3}, 1 = poor, 2 = good, and 3 =
#'     excellent}
#'
#' \item{trt}{a factor for treatment with levels, 1 = active, 0 =
#'     placebo.}
#'
#' }
#'
#' @references Miller, M.E., David, C.S., and Landis, R.J. (1993) The analysis
#'     of longitudinal polytomous data: Generalized estimating equation and
#'     connections with weighted least squares, \emph{Biometrics} \bold{49}:
#'     1033-1048.
#' @keywords datasets
#' @examples
#' 
#' data(respdis)
#' resp.l <- reshape(respdis, varying = list(c("y1", "y2", "y3", "y4")),
#'                   v.names = "resp", direction = "long")
#' resp.l <- resp.l[order(resp.l$id, resp.l$time),]
#' fit <- ordgee(ordered(resp) ~ trt, id = id, data = resp.l, int.const = FALSE)
#' summary(fit)
#' 
#' z <- model.matrix( ~ trt - 1, data = respdis)
#' ind <- rep(1:111, 4*3/2 * 2^2)
#' zmat <- z[ind,,drop=FALSE]
#' fit <- ordgee(ordered(resp) ~ trt, id = id, data = resp.l, int.const = FALSE,
#'               z = zmat, corstr = "exchangeable")
#' summary(fit)
#' 
"respdis"


#' Data from a clinical trial comparing two treatments for a respiratory
#' illness
#' 
#' The data are from a clinical trial of patients with respiratory illness,
#' where 111 patients from two different clinics were randomized to receive
#' either placebo or an active treatment. Patients were examined at baseline
#' and at four visits during treatment. The respiratory
#' status (categorized as 1 = good, 0 = poor) was determined at each
#' visit.
#' 
#' @name respiratory
#' @aliases respiratory respiratoryWide
#' @docType data
#' 
#' @format A data frame with 444 observations on the following 8 variables.
#'
#' \describe{
#'
#' \item{center}{a numeric vector}
#' \item{id}{a numeric vector}
#' \item{treat}{treatment or placebo}
#' \item{sex}{M or F}
#' \item{age}{in years at baseline}
#' \item{baseline}{resporatory status at baseline}
#' \item{visit}{id of each of four visits}
#' \item{outcome}{respiratory status at each visit}
#' 
#' }
#'
#' @keywords datasets
#' @examples
#' 
#' data(respiratory)
#' data(respiratory, package="geepack")
#' respiratory$center <- factor(respiratory$center)
#' head(respiratory)
#'
#' m1 <- glm(outcome ~ center + treat + age + baseline, data=respiratory,                
#'           family=binomial())                                                          
#' gee.ind <- geeglm(outcome ~ center + treat + age + baseline, data=respiratory, id=id, 
#'           family=binomial(), corstr="independence")                                   
#' gee.exc <- geeglm(outcome ~ center + treat + age + baseline, data=respiratory, id=id, 
#'              family=binomial(), corstr="exchangeable")                                
#' gee.uns <- geeglm(outcome ~ center + treat + age + baseline, data=respiratory, id=id, 
#'              family=binomial(), corstr="unstructured")                                
#' gee.ar1 <- geeglm(outcome ~ center + treat + age + baseline, data=respiratory, id=id, 
#'              family=binomial(), corstr="ar1")                                         
#'
#' mlist <- list(gee.ind, gee.exc, gee.uns, gee.ar1)
#' do.call(rbind, lapply(mlist, QIC))
#' lapply(mlist, tidy)
#'
"respiratory"





#' Epiliptic Seizures
#' 
#' The \code{seizure} data frame has 59 rows and 7 columns. The dataset has the
#' number of epiliptic seizures in each of four two-week intervals, and in a
#' baseline eight-week inverval, for treatment and control groups with a total
#' of 59 individuals.
#' 
#' @format This data frame contains the following columns: \describe{
#'     \item{y1}{the number of epiliptic seizures in the 1st 2-week interval}
#'     \item{y2}{the number of epiliptic seizures in the 2nd 2-week interval}
#'     \item{y3}{the number of epiliptic seizures in the 3rd 2-week interval}
#'     \item{y4}{the number of epiliptic seizures in the 4th 2-week interval}
#'     \item{trt}{an indicator of treatment} \item{base}{the number of epilitic
#'     seizures in a baseline 8-week interval} \item{age}{a numeric vector of
#'     subject age} }
#' @references Diggle, P.J., Liang, K.Y., and Zeger, S.L. (1994) Analysis of
#'     Longitudinal Data. Clarendon Press.
#' @source Thall, P.F. and Vail S.C. (1990) Some covariance models for
#'     longitudinal count data with overdispersion. \emph{Biometrics} \bold{46}:
#'     657--671.
#' @keywords datasets
#' @examples
#' 
#' data(seizure)
#' ## Diggle, Liang, and Zeger (1994) pp166-168, compare Table 8.10
#' seiz.l <- reshape(seizure,
#'                   varying=list(c("base","y1", "y2", "y3", "y4")),
#'                   v.names="y", times=0:4, direction="long")
#' seiz.l <- seiz.l[order(seiz.l$id, seiz.l$time),]
#' seiz.l$t <- ifelse(seiz.l$time == 0, 8, 2)
#' seiz.l$x <- ifelse(seiz.l$time == 0, 0, 1)
#' m1 <- geese(y ~ offset(log(t)) + x + trt + x:trt, id = id,
#'             data=seiz.l, corstr="exch", family=poisson)
#' summary(m1)
#' m2 <- geese(y ~ offset(log(t)) + x + trt + x:trt, id = id,
#'             data = seiz.l, subset = id!=49,
#'             corstr = "exch", family=poisson)
#' summary(m2)
#' 
#' ## Thall and Vail (1990)
#' seiz.l <- reshape(seizure, varying=list(c("y1","y2","y3","y4")),
#'                   v.names="y", direction="long")
#' seiz.l <- seiz.l[order(seiz.l$id, seiz.l$time),]
#' seiz.l$lbase <- log(seiz.l$base / 4)
#' seiz.l$lage <- log(seiz.l$age)
#' seiz.l$v4 <- ifelse(seiz.l$time == 4, 1, 0)
#' m3 <- geese(y ~ lbase + trt + lbase:trt + lage + v4, 
#'             sformula = ~ as.factor(time) - 1, id = id,
#'             data = seiz.l, corstr = "exchangeable", family=poisson)
#' ## compare to Model 13 in Table 4, noticeable difference
#' summary(m3)
#' 
#' ## set up a design matrix for the correlation
#' z <- model.matrix(~ age, data = seizure)  # data is not seiz.l
#' ## just to illustrate the scale link and correlation link
#' m4 <- geese(y ~ lbase + trt + lbase:trt + lage + v4,
#'             sformula = ~ as.factor(time)-1, id = id,
#'             data = seiz.l, corstr = "ar1", family = poisson,
#'             zcor = z, cor.link = "fisherz", sca.link = "log")
#' summary(m4)
#' 
"seizure"





#' Growth of Sitka Spruce Trees
#' 
#' Impact of ozone on the growth of sitka spruce trees.
#' 
#' @format A dataframe
#'
#' \describe{
#' \item{size:}{size of the tree measured in \eqn{log(height*diamter^2)}}
#'
#' \item{time:}{days after the 1st january, 1988}
#'
#' \item{tree:}{id number of a tree}
#'
#' \item{treat:}{ozone: grown under ozone environment, control: ozone free}
#'
#' }
#' @keywords datasets
#' @examples
#' 
#' data(sitka89)
#' 
"sitka89"

#' Log-size of 79 Sitka spruce trees
#' 
#' The \code{spruce} data frame has 1027 rows and 6 columns. The data consists
#' of measurements on 79 sitka spruce trees over two growing seasons. The trees
#' were grown in four controlled environment chambers, of which the first two,
#' containing 27 trees each, were treated with introduced ozone at 70 ppb whilst
#' the remaining two, containing 12 and 13 trees, were controls.
#' 
#' 
#' @format This data frame contains the following columns:
#'
#' \describe{
#'
#' \item{chamber}{a numeric vector of chamber numbers}
#'
#' \item{ozone}{a factor with levels \code{enriched} and \code{normal}}
#'
#' \item{id}{a numeric vector of tree id}
#'
#' \item{time}{a numeric vector of the time when the
#'     measurements were taken, measured in days since Jan. 1, 1988}
#'
#' \item{wave}{a numeric vector of the measurement number} \item{logsize}{a
#'     numeric vector of the log-size}
#'
#' }
#' 
#' @source Diggle, P.J., Liang, K.Y., and Zeger, S.L. (1994) Analysis of
#'     Longitudinal Data, Clarendon Press.
#' @keywords datasets
#' @examples
#' 
#' data(spruce)
#' spruce$contr <- ifelse(spruce$ozone=="enriched", 0, 1)
#' sitka88 <- spruce[spruce$wave <= 5,]
#' sitka89 <- spruce[spruce$wave > 5,]
#' fit.88 <- geese(logsize ~ as.factor(wave) + contr +
#'                           I(time/100*contr) - 1,
#'                 id=id, data=sitka88, corstr="ar1")
#' summary(fit.88)
#' 
#' fit.89 <- geese(logsize ~ as.factor(wave) + contr - 1,
#'                 id=id, data=sitka89, corstr="ar1")
#' summary(fit.89)
#' 
"spruce"