R/Z_latent_ex_5_1.R

In christianu7/BNPMIXcluster: Bayesian Nonparametric Model for Clustering with Mixed Scale Variables

#'
#' @docType data
#'
#' @name
#'     Z_latent_ex_5_1
#'
#' @title
#'     Simulated data for testing the \emph{BNPMIXcluster} package
#'
#' @description
#'     Simulated values for three continuous variables under the existence of three clusters.
#'
#'     The data consists of a three-variate Normal distribution with different mean and covariance matrix between clusters.
#'
#'     This can be assumed either as continuous data to be clustered Y=(Y_1,Y_2,Y_3); or also can be used as the underlying latent data that can be transformed into observable variables Y_i=f(Z_i), which can be continuous or categorical.
#'
#' @usage
#'     Z_latent_ex_5_1
#'
#' @format
#'     A data frame with 100 rows and 4 variables.
#'     \describe{
#'         \item{cluster}{Indicates the cluster for each row}
#'         \item{Z1,Z2,Z3}{Continuous values coming from a multivariate normal distribution, given the cluster}
#'     }
#'
#' @details
#'     A data frame with 100 rows and 4 variables.
#'
#' @examples
#'
#' ### Visualizing the simulated data for clustering ###
#' 
#' require(scatterplot3d)
#'
#' cluster_color <- c(rgb(1,0,0,alpha = 0.5),
#'                    rgb(0,0,1,alpha = 0.5),
#'                    rgb(0,0.5,0,alpha = 0.5))
#' cluster_color <- cluster_color[Z_latent_ex_5_1$cluster]
#' cluster_pch <- c(19,15,17)[Z_latent_ex_5_1$cluster]
#' par(mfrow=c(2,2))
#' par(mar=c(4,5,2,2))
#'
#' scatterplot3d::scatterplot3d(x=Z_latent_ex_5_1$Z1,y = Z_latent_ex_5_1$Z2, z=Z_latent_ex_5_1$Z3,
#'               color=cluster_color,pch=cluster_pch,
#'               xlab="Z1",ylab="Z2",zlab="Z3",
#'               main="Simulated data in 3 clusters"
#'               )
#' par(mar=c(4,5,2,2))
#' plot(Z_latent_ex_5_1[,c("Z2","Z3")],col=cluster_color,pch=cluster_pch,xlab="Z2",ylab="Z3")
#' par(mar=c(4,5,2,2))
#' plot(Z_latent_ex_5_1[,c("Z1","Z3")],col=cluster_color,pch=cluster_pch,xlab="Z1",ylab="Z3")
#' par(mar=c(4,5,2,2))
#' plot(Z_latent_ex_5_1[,c("Z1","Z2")],col=cluster_color,pch=cluster_pch,xlab="Z1",ylab="Z2")
#'
#'
#' ##############################
#' #        Exercise 5.1        #
#' #      Data definition       #
#' ##############################
#'
#' ### Code to generate the simulated data from scratch ###
#' require(MASS)
#' 
#' set.seed(0)
#' 
#' n.sim <- 100
#' n.cluster <- 3
#' p <- 3
#' 
#' mu_Z_latent <- matrix( c( 2 , 2 , 5 ,
#'                           6 , 4 , 2 ,
#'                           1 , 6 , 2 ),
#'                       nrow=n.cluster, ncol=p, byrow=TRUE)
#' 
#' sigma_Z_latent <- array(dim=c(3,3,3))
#' sigma_Z_latent[,,1] <- diag(3)
#' sigma_Z_latent[,,2] <- matrix( c( 0.1 , 0 , 0 ,
#'                                     0 , 2 , 0 ,
#'                                     0 , 0 , 0.1 ),
#'                               nrow=n.cluster, ncol=p, byrow=TRUE)
#' 
#' sigma_Z_latent[,,3] <- matrix( c( 2 , 0   , 0   ,
#'                                   0 , 0.1 , 0   ,
#'                                   0 , 0   , 0.1 ),
#'                                   nrow=n.cluster, ncol=p, byrow=TRUE)
#' 
#' Z_cluster <- data.frame(cluster=sample(x=1:n.cluster,size=n.sim,replace=TRUE))
#' 
#' Z_latent <- matrix(NA,nrow=n.sim,ncol=p)
#' 
#' for( i in unique(Z_cluster$cluster) ) {
#'     Z_latent[Z_cluster[,1]==i,] <- MASS::mvrnorm( n=sum(Z_cluster[,1]==i),
#'                                                   mu=mu_Z_latent[i,],
#'                                                   Sigma=sigma_Z_latent[,,i] )
#' }
#' colnames(Z_latent) <- paste("Z",1:ncol(Z_latent),sep="")
#' Z_latent_ex_5_1 <- cbind(Z_cluster,Z_latent)
#' Z_latent_ex_5_1
#'
#'
#' @seealso
#' \code{\link{MIXclustering}}
#'

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