## ----setup, include = FALSE---------------------------------------------------
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

## ----ttest_ex1, eval=FALSE----------------------------------------------------
#  # load the bain package which includes the simulated sesamesim data set
#  library(bain)
#  # collect the data for the boys in the vector x and for the girls in the
#  # vector y
#  x<-sesamesim$postnumb[which(sesamesim$sex==1)]
#  y<-sesamesim$postnumb[which(sesamesim$sex==2)]
#  # execute student's t-test
#  ttest <- t_test(x,y,paired = FALSE, var.equal = TRUE)
#  # set a seed value
#  set.seed(100)
#  # test hypotheses with bain. The names of the means are x and y.
#  results <- bain(ttest, "x = y; x > y; x < y")
#  # display the results
#  results
#  # obtain the descriptives table
#  summary(results, ci = 0.95)

## ----ttest_ex2, eval=FALSE----------------------------------------------------
#  # load the bain package which includes the simulated sesamesim data set
#  library(bain)
#  # collect the data for the boys in the vector x and for the girs in the
#  # vector y
#  x<-sesamesim$postnumb[which(sesamesim$sex==1)]
#  y<-sesamesim$postnumb[which(sesamesim$sex==2)]
#  # execute student's t-test
#  ttest <- t_test(x,y,paired = FALSE, var.equal = FALSE)
#  # set a seed value
#  set.seed(100)
#  # test hypotheses with bain. The names of the means are x and y.
#  results <- bain(ttest, "x = y; x > y; x < y")
#  # display the results
#  print(results)
#  # obtain the descriptives table
#  summary(results, ci = 0.95)

## ----ttest_ex3, eval=FALSE----------------------------------------------------
#  # load the bain package which includes the simulated sesamesim data set
#  library(bain)
#  # compare the pre with the post measurements
#  ttest <- t_test(sesamesim$prenumb,sesamesim$postnumb,paired = TRUE)
#  # set a seed value
#  set.seed(100)
#  # test hypotheses with bain. Use difference to refer to the difference between means
#  results <- bain(ttest, "difference=0; difference>0; difference<0")
#  # display the results
#  print(results)
#  # obtain the descriptives table
#  summary(results, ci = 0.95)

## ----ttest_ex4, eval=FALSE----------------------------------------------------
#  # load the bain package which includes the simulated sesamesim data se
#  library(bain)
#  # compare post measurements with the reference value 30
#  ttest <- t_test(sesamesim$postnumb)
#  # Check name of estimate
#  set.seed(100)
#  # test hypotheses with bain versus the reference value 30. Use x to refer to the mean
#  results <- bain(ttest, "x=30; x>30; x<30")
#  # display the results
#  print(results)
#  # obtain the descriptives table
#  summary(results, ci = 0.95)

## ----ttest_ex5, eval=FALSE----------------------------------------------------
#  # load the bain package which includes the simulated sesamesim data set
#  library(bain)
#  # collect the data for the boys in the vector x and for the girs in the
#  # vector y
#  x<-sesamesim$postnumb[which(sesamesim$sex==1)]
#  y<-sesamesim$postnumb[which(sesamesim$sex==2)]
#  # execute student's t-test
#  ttest <- t_test(x,y,paired = FALSE, var.equal = TRUE)
#  # compute the pooled within standard deviation using the variance of x
#  # (ttest$v[1]) and y (ttest$v[2])
#  pwsd <- sqrt(((length(x) -1) * ttest$v[1] + (length(y)-1) * ttest$v[2])/
#  ((length(x) -1) + (length(y) -1)))
#  # print pwsd in order to be able to include it in the hypothesis. Its value
#  # is 12.60
#  print(pwsd)
#  # set a seed value
#  set.seed(100)
#  # test hypotheses (the means of boy and girl differ less than .2 * pwsd =
#  # 2.52 VERSUS the means differ more than .2 * pwsd = 2.52) with bain
#  # note that, .2 is a value for Cohen's d reflecting a "small" effect, that
#  # is, the means differ less or more than .2 pwsd.
#  # use x and y to refer to the means.
#  results <- bain(ttest, "x - y > -2.52 & x - y < 2.52")
#  # display the results
#  print(results)
#  # obtain the descriptives table
#  summary(results, ci = 0.95)

## ----ttest_ex6, eval=FALSE----------------------------------------------------
#  # load the bain package which includes the simulated sesamesim data set
#  library(bain)
#  # make a factor of variable site
#  sesamesim$site <- as.factor(sesamesim$site)
#  # execute an analysis of variance using lm() which, due to the -1, returns
#  # estimates of the means per group
#  anov <- lm(postnumb~site-1,sesamesim)
#  # take a look at the estimated means and their names
#  coef(anov)
#  # set a seed value
#  set.seed(100)
#  # test hypotheses with bain
#  results <- bain(anov, "site1=site2=site3=site4=site5; site2>site5>site1>
#  site3>site4")
#  # display the results
#  print(results)
#  # obtain the descriptives table
#  summary(results, ci = 0.95)

## ----ttest_ex7, eval=FALSE----------------------------------------------------
#  # load the bain package which includes the simulated sesamesim data se
#  library(bain)
#  # make a factor of variable site
#  sesamesim$site <- as.factor(sesamesim$site)
#  # Center the covariate. If centered the coef() command below displays the
#  # adjusted means. If not centered the intercepts are displayed.
#  sesamesim$prenumb <- sesamesim$prenumb - mean(sesamesim$prenumb)
#  # execute an analysis of covariance using lm() which, due to the -1, returns
#  # estimates of the adjusted means per group
#  ancov <- lm(postnumb~site+prenumb-1,sesamesim)
#  # take a look at the estimated adjusted means, the regression coefficient
#  # of the covariate and their names
#  coef(ancov)
#  # set a seed value
#  set.seed(100)
#  # test hypotheses with bain
#  results <- bain(ancov, "site1=site2=site3=site4=site5;
#                          site2>site5>site1>site3>site4")
#  # display the results
#  print(results)
#  # obtain the descriptives table
#  summary(results, ci = 0.95)

## ----ttest_ex8, eval=FALSE----------------------------------------------------
#  # load the bain package which includes the simulated sesamesim data set
#  library(bain)
#  # execute a multiple regression using lm()
#  regr <- lm(postnumb ~ age + peabody + prenumb,sesamesim)
#  # take a look at the estimated regression coefficients and their names
#  coef(regr)
#  # set a seed value
#  set.seed(100)
#  # test hypotheses with bain. Note that standardize = FALSE denotes that the
#  # hypotheses are in terms of unstandardized regression coefficients
#  results<-bain(regr, "age = 0 & peab=0 & pre=0 ; age > 0 & peab > 0 & pre > 0"
#  , standardize = FALSE)
#  # display the results
#  print(results)
#  # obtain the descriptives table
#  summary(results, ci = 0.95)
#  # Since it is only meaningful to compare regression coefficients if they are
#  # measured on the same scale, bain can also evaluate standardized regression
#  # coefficients (based on the seBeta function by Jeff Jones and Niels Waller):
#  # set a seed value
#  set.seed(100)
#  # test hypotheses with bain. Note that standardize = TRUE denotes that the
#  # hypotheses are in terms of standardized regression coefficients
#  results<-bain(regr, "age = peab = pre ; pre > age > peab",standardize = TRUE)
#  # display the results
#  print(results)
#  # obtain the descriptives table
#  summary(results, ci = 0.95)

## ----ttest_ex9, eval=FALSE----------------------------------------------------
#  # load the bain package which includes the simulated sesamesim data set
#  library(bain)
#  # make a factor of variable site
#  sesamesim$site <- as.factor(sesamesim$site)
#  # execute an analysis of variance using lm() which, due to the -1, returns
#  # estimates of the means per group
#  anov <- lm(postnumb~site-1,sesamesim)
#  # take a look at the estimated means and their names
#  coef(anov)
#  # set a seed value
#  set.seed(100)
#  # test hypotheses with bain
#  results1 <- bain(anov, "site1=site2=site3=site4=site5; site2>site5>site1>
#  site3>site4", fraction = 1)
#  # display the results
#  print(results1)
#  # obtain the descriptives table
#  summary(results1, ci = 0.95)
#  # execute a sensitivity analysis. See Hoijtink, Mulder,
#  # van Lissa, and Gu (2019) for elaborations.
#  set.seed(100)
#  results2 <- bain(anov, "site1=site2=site3=site4=site5; site2>site5>site1>
#  site3>site4",fraction = 2)
#  print(results2)
#  set.seed(100)
#  results3 <- bain(anov, "site1=site2=site3=site4=site5; site2>site5>site1>
#  site3>site4",fraction = 3)
#  print(results3)

## ----ttest_ex20, eval=FALSE---------------------------------------------------
#  # load the bain package which includes the simulated sesamesim data set
#  library(bain)
#  
#  # load mice (multiple imputation of missing data)
#  # inspect the mice help file to obtain further information
#  library(mice)
#  
#  # create missing values in four variables from the sesamesim data set
#  misdat <- cbind(sesamesim$prenumb,sesamesim$postnumb,sesamesim$funumb,sesamesim$peabody)
#  colnames(misdat) <- c("prenumb","postnumb","funumb","peabody")
#  misdat <- as.data.frame(misdat)
#  
#  set.seed(1)
#  pmis <- .80
#  #
#  for (i in 1:240){
#    uni<-runif(1)
#    if (pmis < uni) {
#      misdat$funumb[i]<-NA
#    }
#    uni<-runif(1)
#    if (pmis < uni) {
#      misdat$prenumb[i]<-NA
#      misdat$postnumb[i]<-NA
#    }
#    uni<-runif(1)
#    if (pmis < uni) {
#      misdat$peabody[i]<-NA
#    }
#  }
#  # print data summaries - note the missing values (NAs)
#  summary(misdat)
#  
#  # use mice to create 1000 imputed data matrices. Note that, the approach used
#  # below # is only one manner in which mice can be instructed. Many other
#  # options are available.
#  M <- 1000
#  out <- mice(data = misdat, m = M, seed=999, meth=c("norm","norm","norm","norm"), diagnostics = FALSE, printFlag = FALSE)
#  
#  # create vectors in which 1000 fits and complexities can be stored for each
#  # of two hypotheses and their complement
#  fits1 <- vector("numeric",1000)
#  compls1 <- vector("numeric",1000)
#  fits2 <- vector("numeric",1000)
#  compls2 <- vector("numeric",1000)
#  fitscomplement <- vector("numeric",1000)
#  complscomplement <- vector("numeric",1000)
#  
#  # analyse each imputed data set with lm and bain, store the resulting
#  # fits and complexities
#  set.seed(100)
#  for(i in 1:M) {
#  regr <- lm(funumb~prenumb+postnumb,complete(out,i))
#  result <- bain(regr,"prenumb=0 & postnumb=0;prenumb>0 & postnumb>0")
#  fits1[i]<-result$fit$Fit[1]
#  compls1[i]<-result$fit$Com[1]
#  fits2[i]<-result$fit$Fit[2]
#  compls2[i]<-result$fit$Com[2]
#  fitscomplement[i]<-result$fit$Fit[4]
#  complscomplement[i]<-result$fit$Com[4]
#  }
#  
#  # compute the Bayes factor from the imputed fits and complexities
#  # see Equation 23 in Hoijtink, H., Gu, X., Mulder, J., and Rosseel, Y. (2019).
#  # Computing Bayes Factors from Data with Missing Values.
#  # Psychological Methods, 24, 253-268.
#  
#  BF1u <- sum(fits1)/sum(compls1)
#  BF2u <- sum(fits2)/sum(compls2)
#  BFcomplementu <- sum(fitscomplement)/sum(complscomplement)
#  
#  # compute PMPc
#  PMPcH1 <- BF1u/(BF1u + BF2u + BFcomplementu)
#  PMPcH2 <- BF2u/(BF1u + BF2u + BFcomplementu)
#  PMPcHcomplement <- BFcomplementu/(BF1u + BF2u + BFcomplementu)

## ----ttest_ex10, eval=FALSE---------------------------------------------------
#  # Load the bain and lavaan libraries. Visit www.lavaan.org for
#  # lavaan mini-tutorials, examples, and elaborations
#  library(bain)
#  library(lavaan)
#  
#  #  Specify and fit the confirmatory factor model
#  model1 <- '
#      A =~ Ab + Al + Af + An + Ar + Ac
#      B =~ Bb + Bl + Bf + Bn + Br + Bc
#  '
#  # Use the lavaan sem function to execute the confirmatory factor analysis
#  fit1 <- sem(model1, data = sesamesim, std.lv = TRUE)
#  
#  # Inspect the parameter names
#  coef(fit1)
#  
#  # Formulate hypotheses, call bain, obtain summary stats
#  hypotheses1 <-
#  " A=~Ab > .6 & A=~Al > .6 & A=~Af > .6 & A=~An > .6 & A=~Ar > .6 & A=~Ac >.6 &
#  B=~Bb > .6 & B=~Bl > .6 & B=~Bf > .6 & B=~Bn > .6 & B=~Br > .6 & B=~Bc >.6"
#  set.seed(100)
#  y <- bain(fit1,hypotheses1,fraction=1,standardize=TRUE)
#  sy <- summary(y, ci = 0.95)
#  

## ----ttest_ex11, eval=FALSE---------------------------------------------------
#  # Load the bain and lavaan libraries. Visit www.lavaan.org for
#  # lavaan mini-tutorials, examples, and elaborations
#  library(bain)
#  library(lavaan)
#  
#  # Specify and fit the latent regression model
#  model2 <- '
#      A  =~ Ab + Al + Af + An + Ar + Ac
#      B =~ Bb + Bl + Bf + Bn + Br + Bc
#  
#      A ~ B + age + peabody
#  '
#  fit2 <- sem(model2, data = sesamesim, std.lv = TRUE)
#  
#  # Inspect the parameter names
#  coef(fit2)
#  
#  # Formulate hypotheses, call bain, obtain summary stats
#  
#  hypotheses2 <- "A~B > A~peabody = A~age = 0;
#                 A~B > A~peabody > A~age = 0;
#  A~B > A~peabody > A~age > 0"
#  set.seed(100)
#  y1 <- bain(fit2, hypotheses2, fraction = 1, standardize = TRUE)
#  sy1 <- summary(y1, ci = 0.99)

## ----ttest_ex12, eval=FALSE---------------------------------------------------
#  # Load the bain and lavaan libraries. Visit www.lavaan.org for
#  # lavaan mini-tutorials, examples, and elaborations
#  library(bain)
#  library(lavaan)
#  
#  # Specify A multiple group regression model
#  model3 <- '
#      postnumb ~ prenumb + peabody
#  '
#  # Assign labels to the groups to be used when formulating
#  # hypotheses
#  sesamesim$sex <- factor(sesamesim$sex, labels = c("boy", "girl"))
#  # Fit the multiple group regression model
#  fit3 <- sem(model3, data = sesamesim, std.lv = TRUE, group = "sex")
#  # Inspect the parameter names
#  coef(fit3)
#  
#  # Formulate and evaluate the hypotheses
#  hypotheses3 <-
#  "postnumb~prenumb.boy = postnumb~prenumb.girl & postnumb~peabody.boy = postnumb~peabody.girl;
#   postnumb~prenumb.boy < postnumb~prenumb.girl & postnumb~peabody.boy < postnumb~peabody.girl
#  "
#  set.seed(100)
#  y1 <- bain(fit3, hypotheses3, standardize = TRUE)
#  sy1 <- summary(y1, ci = 0.95)

## ----ttest_ex13, eval=FALSE---------------------------------------------------
#  # load the bain package which includes the simulated sesamesim data se
#  library(bain)
#  # make a factor of variable site
#  sesamesim$site <- as.factor(sesamesim$site)
#  # execute an analysis of variance using lm() which, due to the -1, returns
#  # estimates of the means per group
#  anov <- lm(postnumb~site-1,sesamesim)
#  # take a look at the estimated means and their names
#  coef(anov)
#  # collect the estimates means in a vector
#  estimate <- coef(anov)
#  # give names to the estimates in anov
#  names(estimate) <- c("site1", "site2", "site3","site4","site5")
#  # create a vector containing the sample size of each group
#  # (in case of missing values in the variables used, the command
#  # below has to be modified such that only the cases without
#  # missing values are counted)
#  ngroup <- table(sesamesim$site)
#  # compute for each group the covariance matrix of the parameters
#  # of that group and collect these in a list
#  # for the ANOVA this is simply a list containing for each group the variance
#  # of the mean note that, the within group variance as estimated using lm is
#  # used to compute the variance of each of the means! See, Hoijtink, Gu, and
#  # Mulder (2019) for further elaborations.
#  var <- summary(anov)$sigma**2
#  cov1 <- matrix(var/ngroup[1], nrow=1, ncol=1)
#  cov2 <- matrix(var/ngroup[2], nrow=1, ncol=1)
#  cov3 <- matrix(var/ngroup[3], nrow=1, ncol=1)
#  cov4 <- matrix(var/ngroup[4], nrow=1, ncol=1)
#  cov5 <- matrix(var/ngroup[5], nrow=1, ncol=1)
#  covlist <- list(cov1, cov2, cov3, cov4,cov5)
#  # set a seed value
#  set.seed(100)
#  # test hypotheses with bain. Note that there are multiple groups
#  # characterized by one mean, therefore group_parameters=0. Note that are no
#  # joint parameters, therefore, joint_parameters=0.
#  results <- bain(estimate,
#  "site1=site2=site3=site4=site5; site2>site5>site1>site3>site4",
#  n=ngroup,Sigma=covlist,group_parameters=1,joint_parameters = 0)
#  # display the results
#  print(results)
#  # obtain the descriptives table
#  summary(results, ci = 0.95)

## ----ttest_ex21, eval=FALSE---------------------------------------------------
#  # Load the bain library
#  library(bain)
#  
#  # make a factor of variable site
#  sesamesim$site <- as.factor(sesamesim$site)
#  
#  # collect the estimated means in a vector
#  estimates <- aggregate(sesamesim$postnumb,list(sesamesim$site),mean)[,2]
#  # give names to the estimates
#  names(estimates) <- c("site1", "site2", "site3","site4","site5")
#  
#  # create a vector containing the sample sizes of each group
#  ngroup <- table(sesamesim$site)
#  
#  # compute the variances in each group and subquently the squared standard errors
#  vars <- aggregate(sesamesim$postnumb,list(sesamesim$site),var)
#  vargroup <- vars[,2]/ngroup
#  
#  # collect the variances of the means in a covariance listcov1 <- matrix(vargroup[1], nrow=1, ncol=1)
#  cov2 <- matrix(vargroup[2], nrow=1, ncol=1)
#  cov3 <- matrix(vargroup[3], nrow=1, ncol=1)
#  cov4 <- matrix(vargroup[4], nrow=1, ncol=1)
#  cov5 <- matrix(vargroup[5], nrow=1, ncol=1)
#  covlist <- list(cov1, cov2, cov3, cov4,cov5)
#  
#  # set a seed value
#  set.seed(100)
#  # test hypotheses using bain. Note that there are multiple groups
#  # characterized by one mean, therefore group_parameters=1. Note that
#  # there are no joint parameters, therefore, joint_parameters=0.
#  results <- bain(estimates,
#                  "site1=site2=site3=site4=site5;site2>site5>site1>site4>site3",
#                  n=ngroup,Sigma=covlist,group_parameters=1,joint_parameters = 0)
#  print(results)
#  
#  # obtain the descriptives table
#  summary(results, ci = 0.95)

## ----ttest_ex19, eval=FALSE---------------------------------------------------
#  # load the bain package which includes the simulated sesamesim data set
#  library(bain)
#  # load the WRS2 package which renders the trimmed sample mean and
#  # corresponding standard error
#  library(WRS2)
#  # make a factor of variable site
#  sesamesim$site <- as.factor(sesamesim$site)
#  # create a vector containing the sample sizes of each group
#  # (in case of missing values in the variables used, the command
#  # below has to be modified such that only the cases without
#  # missing values are counted)
#  ngroup <- table(sesamesim$site)
#  # Compute the 20\% sample trimmed mean for each site
#  estimates <- c(mean(sesamesim$postnumb[sesamesim$site == 1], tr = 0.2),
#                 mean(sesamesim$postnumb[sesamesim$site == 2], tr = 0.2),
#                 mean(sesamesim$postnumb[sesamesim$site == 3], tr = 0.2),
#                 mean(sesamesim$postnumb[sesamesim$site == 4], tr = 0.2),
#                 mean(sesamesim$postnumb[sesamesim$site == 5], tr = 0.2))
#  # give names to the estimates
#  names(estimates) <- c("s1", "s2", "s3","s4","s5")
#  # display the estimates and their names
#  print(estimates)
#  # Compute the sample trimmed mean standard error for each site
#  se <- c(trimse(sesamesim$postnumb[sesamesim$site == 1]),
#          trimse(sesamesim$postnumb[sesamesim$site == 2]),
#          trimse(sesamesim$postnumb[sesamesim$site == 3]),
#          trimse(sesamesim$postnumb[sesamesim$site == 4]),
#          trimse(sesamesim$postnumb[sesamesim$site == 5]))
#  # Square the standard errors to obtain the variances of the sample
#  # trimmed means
#  var <- se^2
#  # Store the variances in a list of matrices
#  covlist <- list(matrix(var[1]),matrix(var[2]),
#  matrix(var[3]),matrix(var[4]), matrix(var[5]))
#  # set a seed value
#  set.seed(100)
#  # test hypotheses with bain
#  results <- bain(estimates,"s1=s2=s3=s4=s5;s2>s5>s1>s3>s4",
#  n=ngroup,Sigma=covlist,group_parameters=1,joint_parameters= 0)
#  # display the results
#  print(results)
#  # obtain the descriptives table
#  summary(results, ci = 0.95)

## ----ttest_ex14, eval=FALSE---------------------------------------------------
#  # load the bain package which includes the simulated sesamesim data se
#  library(bain)
#  # make a factor of variable site
#  sesamesim$site <- as.factor(sesamesim$site)
#  # center the covariate. If centered the coef() command below displays the
#  # adjusted means. If not centered the intercepts are displayed.
#  sesamesim$prenumb <- sesamesim$prenumb - mean(sesamesim$prenumb)
#  # execute an analysis of covariance using lm() which, due to the -1, returns
#  # estimates of the adjusted means per group
#  ancov2 <- lm(postnumb~site+prenumb-1,sesamesim)
#  # take a look at the estimated adjusted means and their names
#  coef(ancov2)
#  # collect the estimates of the adjusted means and regression coefficient of
#  # the covariate in a vector (the vector has to contain first the
#  # adjusted means and next the regression coefficients of the covariates)
#  estimates <- coef(ancov2)
#  # assign names to the estimates
#  names(estimates)<- c("v.1", "v.2", "v.3", "v.4","v.5", "pre")
#  # compute the sample size per group
#  # (in case of missing values in the variables used, the command
#  # below has to be modified such that only the cases without
#  # missing values are counted)
#  ngroup <- table(sesamesim$site)
#  # compute for each group the covariance matrix of the parameters of that
#  # group and collect these in a list note that, the residual variance as
#  # estimated using lm is used to compute these covariance matrices
#  var <- (summary(ancov2)$sigma)**2
#  # below, for each group, the covariance matrix of the adjusted mean and
#  # covariate is computed
#  # see Hoijtink, Gu, and Mulder (2019) for further explanation and elaboration
#  cat1 <- subset(cbind(sesamesim$site,sesamesim$prenumb), sesamesim$site == 1)
#  cat1[,1] <- 1
#  cat1 <- as.matrix(cat1)
#  cov1 <- var * solve(t(cat1) %*% cat1)
#  #
#  cat2 <- subset(cbind(sesamesim$site,sesamesim$prenumb), sesamesim$site == 2)
#  cat2[,1] <- 1
#  cat2 <- as.matrix(cat2)
#  cov2 <- var * solve(t(cat2) %*% cat2)
#  #
#  cat3 <- subset(cbind(sesamesim$site,sesamesim$prenumb), sesamesim$site == 3)
#  cat3[,1] <- 1
#  cat3 <- as.matrix(cat3)
#  cov3 <- var * solve(t(cat3) %*% cat3)
#  #
#  cat4 <- subset(cbind(sesamesim$site,sesamesim$prenumb), sesamesim$site == 4)
#  cat4[,1] <- 1
#  cat4 <- as.matrix(cat4)
#  cov4 <- var * solve(t(cat4) %*% cat4)
#  #
#  cat5 <- subset(cbind(sesamesim$site,sesamesim$prenumb), sesamesim$site == 5)
#  cat5[,1] <- 1
#  cat5 <- as.matrix(cat5)
#  cov5 <- var * solve(t(cat5) %*% cat5)
#  #
#  covariances <- list(cov1, cov2, cov3, cov4,cov5)
#  # set a seed value
#  set.seed(100)
#  # test hypotheses with bain. Note that there are multiple groups
#  # characterized by one adjusted mean, therefore group_parameters=1 Note that
#  # there is one covariate, therefore, joint_parameters=1.
#  results2<-bain(estimates,"v.1=v.2=v.3=v.4=v.5;v.2 > v.5 > v.1 > v.3 >v.4;",
#  n=ngroup,Sigma=covariances,group_parameters=1,joint_parameters = 1)
#  # display the results
#  print(results2)
#  # obtain the descriptives table
#  summary(results2, ci = 0.95)

## ----ttest_ex15, eval=FALSE---------------------------------------------------
#  # load the bain package which includes the simulated sesamesim data set
#  library(bain)
#  # estimate the means of three repeated measures of number knowledge
#  # the 1 denotes that these means have to be estimated
#  within <- lm(cbind(prenumb,postnumb,funumb)~1, data=sesamesim)
#  # take a look at the estimated means and their names
#  coef(within)
#  # note that the model specified in lm has three dependent variables.
#  # Consequently, the estimates rendered by lm are collected in a "matrix".
#  # Since bain needs a named vector containing the estimated means, the [1:3]
#  # code is used to select the three means from a matrix and store them in a
#  # vector.
#  estimate <- coef(within)[1:3]
#  # give names to the estimates in anov
#  names(estimate) <- c("pre", "post", "fu")
#  # compute the sample size
#  # (in case of missing values in the variables used, the command
#  # below has to be modified such that only the cases without
#  # missing values are counted)
#  ngroup <- nrow(sesamesim)
#  # compute the covariance matrix of the three means
#  covmatr <- list(vcov(within))
#  # set a seed value
#  set.seed(100)
#  # test hypotheses with bain. Note that there is one group, with three
#  # means therefore group_parameters=3.
#  results <- bain(estimate,"pre = post = fu; pre < post < fu", n=ngroup,
#  Sigma=covmatr, group_parameters=3, joint_parameters = 0)
#  # display the results
#  print(results)
#  # obtain the descriptives table
#  summary(results, ci = 0.95)

## ----ttest_ex16, eval=FALSE---------------------------------------------------
#  # load the bain package which includes the simulated sesamesim data set
#  library(bain)
#  # make a factor of the variable sex
#  sesamesim$sex <- factor(sesamesim$sex)
#  # estimate the means of prenumb, postnumb, and funumb for boys and girls
#  # the -1 denotes that the means have to estimated
#  bw <- lm(cbind(prenumb, postnumb, funumb)~sex-1, data=sesamesim)
#  # take a look at the estimated means and their names
#  coef(bw)
#  # collect the estimated means in a vector
#  est1 <-coef(bw)[1,1:3] # the three means for sex = 1
#  est2 <-coef(bw)[2,1:3] # the three means for sex = 2
#  estimate <- c(est1,est2)
#  # give names to the estimates in anov
#  names(estimate) <- c("pre1", "post1", "fu1","pre2", "post2", "fu2")
#  # determine the sample size per group
#  # (in case of missing values in the variables used, the command
#  # below has to be modified such that only the cases without
#  # missing values are counted)
#  ngroup<-table(sesamesim$sex)
#  # cov1 has to contain the covariance matrix of the three means in group 1.
#  # cov2 has to contain the covariance matrix in group 2
#  # typing vcov(bw) in the console pane highlights the structure of
#  # the covariance matrix of all 3+3=6 means
#  # it has to be dissected in to cov1 and cov2
#  cov1 <- c(vcov(bw)[1,1],vcov(bw)[1,3],vcov(bw)[1,5],vcov(bw)[3,1],
#  vcov(bw)[3,3],vcov(bw)[3,5],vcov(bw)[5,1],vcov(bw)[5,3],vcov(bw)[5,5])
#  cov1 <- matrix(cov1,3,3)
#  cov2 <- c(vcov(bw)[2,2],vcov(bw)[2,4],vcov(bw)[2,6],vcov(bw)[4,2],
#  vcov(bw)[4,4],vcov(bw)[4,6],vcov(bw)[6,2],vcov(bw)[6,4],vcov(bw)[6,6])
#  cov2 <- matrix(cov2,3,3)
#  covariance<-list(cov1,cov2)
#  # set a seed value
#  set.seed(100)
#  # test hypotheses with bain. Note that there are multiple groups
#  # characterized by three means, therefore group_parameters=3. Note that there
#  # are no additional parameters, therefore, joint_parameters=0.
#  results <-bain(estimate, "pre1 - pre2 = post1 - post2 = fu1 -fu2;
#  pre1 - pre2 > post1 - post2 > fu1 -fu2"  , n=ngroup, Sigma=covariance,
#  group_parameters=3, joint_parameters = 0)
#  # display the results
#  print(results)
#  # obtain the descriptives table
#  summary(results, ci = 0.95)

## ----ttest_ex17, eval=FALSE---------------------------------------------------
#  # load the bain package which includes the simulated sesamesim data set
#  library(bain)
#  # regression coefficients can only be mutually compared if the
#  # corresponding predictors are measured on the same scale, therefore the
#  # predictors are standardized
#  sesamesim$age <- (sesamesim$age - mean(sesamesim$age))/sd(sesamesim$age)
#  sesamesim$peabody <- (sesamesim$peabody - mean(sesamesim$peabody))/
#  sd(sesamesim$peabody)
#  sesamesim$prenumb <- (sesamesim$prenumb - mean(sesamesim$prenumb))/
#  sd(sesamesim$prenumb)
#  # estimate the logistic regression coefficients
#  logreg <- glm(viewenc ~ age + peabody + prenumb, family=binomial,
#  data=sesamesim)
#  # take a look at the estimates and their names
#  coef(logreg)
#  # collect the estimated intercept and regression coefficients in a vector
#  estimate <- coef(logreg)
#  # give names to the estimates
#  names(estimate) <- c("int", "age", "peab" ,"pre" )
#  # compute the sample size. Note that, this is an analysis with ONE group
#  # (in case of missing values in the variables used, the command
#  # below has to be modified such that only the cases without
#  # missing values are counted)
#  ngroup <- nrow(sesamesim)
#  # compute the covariance matrix of the intercept and regression coefficients
#  covmatr <- list(vcov(logreg))
#  # set a seed value
#  set.seed(100)
#  # test hypotheses with bain. Note that there is one group, with four
#  # parameters (intercept plus three regression coefficients) therefore
#  # group_parameters=4.
#  results <- bain(estimate, "age = peab = pre; age > pre > peab", n=ngroup,
#  Sigma=covmatr, group_parameters=4, joint_parameters = 0)
#  # display the results
#  print(results)
#  # obtain the descriptives table
#  summary(results, ci = 0.95)

## ----ttest_ex18, eval=FALSE---------------------------------------------------
#  # load the bain package which includes the simulated sesamesim data set
#  library(bain)
#  # load the numDeriv package which will be used to compute the covariance
#  # matrix of the adjusted group coefficients and regression coefficient of age
#  # for the boys and the girls # using the estimates obtained using the data for
#  # the boys AND the girls.
#  library(numDeriv)
#  # make a factor of the variable sex
#  sesamesim$sex <- factor(sesamesim$sex)
#  # center the covariate age
#  sesamesim$age <- sesamesim$age - mean(sesamesim$age)
#  # determine sample size per sex group
#  # (in case of missing values in the variables used, the command
#  # below has to be modified such that only the cases without
#  # missing values are counted)
#  ngroup <- table(sesamesim$sex)
#  # execute the logistic regression, -1 ensures that the coefficients
#  # for boys and girl are estimated adjusted for the covariate age
#  anal <- glm(viewenc ~ sex + age - 1, family=binomial, data=sesamesim)
#  # take a look at the estimates and their names
#  coef(anal)
#  # collect the estimates obtained using the data of the boys AND the
#  # girls in a vector. This vector contains first the group specific
#  # parameters followed by the regression coefficient of the covariate.
#  estimates <-coef(anal)
#  # give names to the estimates
#  names(estimates) <- c("boys", "girls", "age")
#  # use numDeriv to compute the Hessian matrix and subsequently the
#  # covariance matrix for each of the two (boys and girls) groups.
#  # The vector f should contain the regression coefficient of the group
#  # at hand and the regression coefficient of the covariate.
#  #
#  # the first group
#  data <- subset(cbind(sesamesim$sex,sesamesim$age,sesamesim$viewenc),
#  sesamesim$sex==1)
#  f <- 1
#  f[1] <- estimates[1] # the regression coefficient of boys
#  f[2] <- estimates[3] # the regression coefficient of age
#  #
#  # within the for loop below the log likelihood of the logistic
#  # regression model is computed using the data for the boys
#  logist1 <- function(x){
#    out <- 0
#    for (i in 1:ngroup[1]){
#      out <- out + data[i,3]*(x[1] + x[2]*data[i,2]) - log (1 +
#      exp(x[1] + x[2]*data[i,2]))
#    }
#    return(out)
#  }
#  hes1 <- hessian(func=logist1, x=f)
#  # multiply with -1 and invert to obtain the covariance matrix for the
#  # first group
#  cov1 <- -1 * solve(hes1)
#  #
#  # the second group
#  data <- subset(cbind(sesamesim$sex,sesamesim$age,sesamesim$viewenc),
#  sesamesim$sex==2)
#  f[1] <- estimates[2] # the regression coefficient of girls
#  f[2] <- estimates[3] # the regression coefficient of age
#  
#  # within the for loop below the log likelihood of the logistic
#  # regression model is computed using the data for the girls
#  logist2 <- function(x){
#    out <- 0
#    for (i in 1:ngroup[2]){
#      out <- out + data[i,3]*(x[1] + x[2]*data[i,2]) - log (1 +
#      exp(x[1] + x[2]*data[i,2]))
#    }
#    return(out)
#  }
#  hes2 <- hessian(func=logist2, x=f)
#  # multiply with -1 and invert to obtain the covariance matrix
#  cov2 <- -1 * solve(hes2)
#  #
#  #make a list of covariance matrices
#  covariance<-list(cov1,cov2)
#  #
#  # set a seed value
#  set.seed(100)
#  # test hypotheses with bain. Note that there are multiple groups
#  # characterized by one adjusted group coefficient,
#  # therefore group_parameters=1. Note that there is one covariate,
#  # therefore, joint_parameters=1.
#  results <- bain(estimates, "boys < girls & age > 0", n=ngroup,
#  Sigma=covariance, group_parameters=1, joint_parameters = 1)
#  # display the results
#  print(results)
#  # obtain the descriptives table
#  summary(results, ci = 0.95)

## ---- eval = FALSE------------------------------------------------------------
#  library(bain)
#  library(lavaan)
#  model1 <- 'A =~ Ab + Al + Af + An + Ar + Ac
#             B =~ Bb + Bl + Bf + Bn + Br + Bc'
#  fit1 <- sem(model1, data = sesamesim, std.lv = TRUE)

## ---- eval = FALSE------------------------------------------------------------
#  hypotheses <- "(Ab, Al, Af, An, Ar, Ac) >.6 &
#                 (Bb, Bl, Bf, Bn, Br, Bc) >.6"

## ---- eval = FALSE------------------------------------------------------------
#  # Extract standardized parameter estimates (argument x)
#  PE1 <- parameterEstimates(fit1, standardized = TRUE)
#  # Identify which parameter estimates are factor loadings
#  loadings <- which(PE1$op == "=~")
#  # Collect the standardized "std.all" factor loadings "=~"
#  estimates <- PE1$std.all[loadings]
#  # Assign names to the standardized factor loadings
#  names(estimates) <- c("Ab", "Al", "Af", "An", "Ar", "Ac",
#                        "Bb", "Bl", "Bf", "Bn", "Br", "Bc")
#  
#  # Extract sample size (argument n)
#  n <- nobs(fit1)
#  
#  # Extract the standardized model parameter covariance matrix,
#  # selecting only the rows and columns for the loadings
#  covariance <- lavInspect(fit1, "vcov.std.all")[loadings, loadings]
#  
#  # Give the covariance matrix the same names as the estimate
#  dimnames(covariance) <- list(names(estimates), names(estimates))
#  
#  # Put the covariance matrix in a list
#  covariance <- list(covariance)
#  
#  # Specify number of group parameters; this simply means that there
#  # are 12 parameters in the estimate.
#  group_parameters <- 12
#  
#  # Then, the number of joint parameters. This is always 0 for evaluations of
#  # SEM hypotheses:
#  joint_parameters <- 0

## ---- eval = FALSE------------------------------------------------------------
#  res <- bain(x = estimates,
#              hypothesis = hypotheses,
#              n = n,
#              Sigma = covariance,
#              group_parameters = group_parameters,
#              joint_parameters = joint_parameters)
#  res

## ---- eval = FALSE------------------------------------------------------------
#  sres <- summary(res, ci = 0.95)
#  sres

