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smsn.mmix.R
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smsn.mmix.R
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##############################################################################################
########### ALGORITMO EM MULTIVARIADO PARA MISTURAS DE DISTRI SMSN ################
########### Alteracoes feitas em 03/05/2010 por Celso Romulo ################
########### Esta eh a versao utilizada no artigo submetido ao CSDA ################
smsn.mmix <- function(y, nu=1, mu = NULL, Sigma = NULL, shape = NULL, pii = NULL, g = NULL, get.init = TRUE, criteria = TRUE,
group = FALSE, family = "Skew.normal", error = 0.0001, iter.max = 100, uni.Gama = FALSE, calc.im=FALSE,
obs.prob= FALSE, kmeans.param = NULL){
#mu, Sigma, shape devem ser do tipo list(). O numero de entradas no list eh o numero g de componentes de misturas
#cada entrada do list deve ser de tamanho igual ao numero de colunas da matriz de dados y
y <- as.matrix(y)
dimnames(y) <- NULL
if(!is.matrix(y)) stop("The response is not in a matrix format\n")
if(ncol(y) <= 1) stop("For the univariate case use the smsn.mix function\n")
if((family != "t") && (family != "slash") && (family != "Skew.t") && (family != "Skew.cn") && (family != "Skew.slash") && (family != "Skew.normal") && (family != "Normal")) stop(paste("Family",family,"not recognized.\n",sep=" "))
if((length(g) == 0) && ((length(mu)==0) || (length(Sigma)==0) || (length(shape)==0) || (length(pii)==0))) stop("The model is not specified correctly.\n")
if(get.init == FALSE){
g <- length(mu)
if((length(mu) != length(Sigma)) || (length(mu) != length(pii))) stop("The size of the initial values are not compatibles.\n")
if((family == "Skew.t" || family == "Skew.cn" || family == "Skew.slash" || family == "Skew.normal") & (length(mu) != length(shape))) stop("The size of the initial values are not compatibles.\n")
if(sum(pii) != 1) stop("probability of pii does not sum to 1.\n")
for (j in 1:g){
dimnames(Sigma[[j]]) <- NULL
names(mu[[j]]) <- NULL
names(shape[[j]]) <- NULL
}
}
if((length(g)!= 0) && (g < 1)) stop("g must be greater than 0.\n")
p <- ncol(y)
n <- nrow(y)
if (get.init == TRUE){
key.mu <- key.sig <- key.shp <- TRUE
if(length(g) == 0) stop("g is not specified correctly.\n")
if(length(mu) > 0) key.mu <- FALSE
if(length(Sigma) > 0) key.sig <- FALSE
if(length(shape) > 0) key.shp <- FALSE
if(((!key.mu) & (length(mu) != g)) | ((!key.sig) & (length(Sigma) != g)) | ((!key.shp) & (length(shape) != g))) stop("The size of the initial values are not compatibles.\n")
k.iter.max <- 50
n.start <- 1
algorithm <- "Hartigan-Wong"
if(length(kmeans.param) > 0){
if(length(kmeans.param$iter.max) > 0 ) k.iter.max <- kmeans.param$iter.max
if(length(kmeans.param$n.start) > 0 ) n.start <- kmeans.param$n.start
if(length(kmeans.param$algorithm) > 0 ) algorithm <- kmeans.param$algorithm
}
if(g > 1){
if(key.mu) init <- kmeans(y,g,k.iter.max,n.start,algorithm)
else init <- kmeans(y,mu,k.iter.max,n.start,algorithm)
pii <- init$size/length(y)
mu <- shape <- Sigma <- list()
for (j in 1:g){
if(key.mu) mu[[j]] <- init$centers[j,]
if(key.shp) shape[[j]] <- sign( apply( (y[init$cluster == j, ] - matrix(rep(mu[[j]], nrow(y[init$cluster == j, ])), nrow = nrow(y[init$cluster == j, ]), ncol=p, byrow = TRUE))^3, 2, sum))
if(key.sig) Sigma[[j]] <- var(y[init$cluster == j,])
dimnames(Sigma[[j]]) <- NULL
names(mu[[j]]) <- NULL
names(shape[[j]]) <- NULL
}
}
else{
pii <- 1
if(key.mu) mu[[1]] <- colMeans(y)
if(key.sig) Sigma[[1]] <- var(y)
if(key.shp) shape[[1]] <- sign( apply( (y - matrix(rep(mu[[1]], nrow(y)), nrow(y), p, byrow = TRUE) )^3, 2, sum ))
dimnames(Sigma[[1]]) <- NULL
names(mu[[1]]) <- NULL
names(shape[[1]]) <- NULL
}
}
if (family == "t"){
delta <- Delta <- Gama <- list()
# teta <- c()
for (k in 1:g){
Delta[[k]] <- shape[[k]] <- rep(0,p)
Gama[[k]] <- Sigma[[k]] - Delta[[k]]%*%t(Delta[[k]])
# teta <- c(teta, mu[[k]], Gama[[k]][upper.tri(Gama[[k]], diag = TRUE)], Delta[[k]])
}
# teta <- c(teta, pii, nu) #teta para nu desconhecido
if(uni.Gama){
Gama.uni <- Gama[[1]]
if(g > 1) for(k in 2:g) Gama.uni <- Gama.uni + Gama[[k]]
Gama.uni <- Gama.uni / g
for(k in 1:g) Gama[[k]] <- Gama.uni
}
mu.old <- mu
Delta.old <- Delta
Gama.old <- Gama
criterio <- 1
count <- 0
lkante <- 1
while((criterio > error) && (count <= iter.max)){
count <- count + 1
tal <- matrix(0, n, g)
S1 <- matrix(0, n, g)
S2 <- matrix(0, n, g)
S3 <- matrix(0, n, g)
for (j in 1:g){
### E-step: calculando ui, tui, tui2 ###
Dif <- y - matrix(rep(mu[[j]], n), n, p, byrow = TRUE)
Mtij2 <- as.numeric( 1/(1 + t(Delta[[j]])%*%solve(Gama[[j]])%*%Delta[[j]]) )
Mtij <- sqrt(Mtij2)
mutij <- apply( matrix(rep( Mtij2*t(Delta[[j]])%*%solve(Gama[[j]]),n), n, p, byrow = TRUE ) * Dif, 1, sum)
A <- mutij / Mtij
dj <- mahalanobis(y, mu[[j]], Sigma[[j]])
E = (2*(nu)^(nu/2)*gamma((p+nu+1)/2)*((dj + nu + A^2))^(-(p+nu+1)/2)) / (gamma(nu/2)*(sqrt(pi))^(p+1)*sqrt(det(Sigma[[j]]))*dmvt.ls(y, mu[[j]], Sigma[[j]], shape[[j]] ,nu))
u = ((4*(nu)^(nu/2)*gamma((p+nu+2)/2)*(dj + nu)^(-(p+nu+2)/2)) / (gamma(nu/2)*sqrt(pi^p)*sqrt(det(Sigma[[j]]))*dmvt.ls(y, mu[[j]], Sigma[[j]], shape[[j]] ,nu)) )*pt(sqrt((p+nu+2)/(dj+nu))*A,p+nu+2)
d1 <- dmvt.ls(y, mu[[j]], Sigma[[j]], shape[[j]], nu)
if(length(which(d1 == 0)) > 0) d1[which(d1 == 0)] <- .Machine$double.xmin
d2 <- d.mixedmvST(y, pii, mu, Sigma, shape, nu)
if(length(which(d2 == 0)) > 0) d2[which(d2 == 0)] <- .Machine$double.xmin
tal[,j] <- d1*pii[j] / d2
S1[,j] <- tal[,j]*u
S2[,j] <- tal[,j]*(mutij*u + Mtij*E)
S3[,j] <- tal[,j]*(mutij^2*u + Mtij2 + Mtij*mutij*E)
### M-step: atualizar mu, Delta, Gama, sigma2 ###
pii[j] <- (1/n)*sum(tal[,j])
mu[[j]] <- apply(S1[,j]*y - S2[,j] * matrix(rep(Delta.old[[j]], n), n, p, byrow = TRUE), 2, sum) / sum(S1[,j])
Dif <- y - matrix(rep(mu[[j]], n), n, p, byrow = TRUE)
Delta[[j]] <- rep(0,p)
sum2 <- matrix(0,p,p)
for (i in 1:n) sum2 <- sum2 + (S1[i,j]*(y[i,] - mu[[j]])%*%t(y[i,] - mu[[j]]) - S2[i,j]*Delta[[j]]%*%t(y[i,] - mu[[j]]) - S2[i,j]*(y[i,] - mu[[j]])%*%t(Delta[[j]]) + S3[i,j]*Delta[[j]]%*%t(Delta[[j]]))
Gama[[j]] <- sum2 / sum(tal[,j])
if(!uni.Gama){
Sigma[[j]] <- Gama[[j]] + Delta[[j]]%*%t(Delta[[j]])
shape[[j]] <- rep(0,p)
}
}
if(uni.Gama){
GS <- 0
for (j in 1:g) GS <- GS+kronecker(tal[,j],Gama[[j]])
Gama.uni <- t(rowSums(array(t(GS),dim=c(p,p,n)),dims=2))/n
for (j in 1:g){
Gama[[j]] <- Gama.uni
Sigma[[j]] <- Gama[[j]] + Delta[[j]]%*%t(Delta[[j]])
shape[[j]] <- rep(0,p)
}
}
#aqui comecam as alteracoes para estimar o valor de nu
logvero.ST <- function(nu) sum(log( d.mixedmvST(y, pii, mu, Sigma, shape, nu) ))
nu <- optimize(logvero.ST, c(0,100), tol = 0.000001, maximum = TRUE)$maximum
pii[g] <- 1 - (sum(pii) - pii[g])
zero.pos <- NULL
zero.pos <- which(pii == 0)
if(length(zero.pos) != 0){
pii[zero.pos] <- 1e-10
pii[which(pii == max(pii))] <- max(pii) - sum(pii[zero.pos])
}
# param <- teta
# teta <- c()
# for (k in 1:g) teta <- c(teta, mu[[k]], Gama[[k]][upper.tri(Gama[[k]], diag = TRUE)], Delta[[k]])
# teta <- c(teta, pii, nu) #teta para nu desconhecido
lk <- sum(log( d.mixedmvST(y, pii, mu, Sigma, shape, nu) ))
criterio <- abs((lk/lkante)-1)
lkante <- lk
mu.old <- mu
Delta.old <- Delta
Gama.old <- Gama
}
if (criteria == TRUE){
cl <- apply(tal, 1, which.max)
icl <- 0
for (j in 1:g) icl <- icl+sum(log(pii[j]*dmvt.ls(y[cl==j,], mu[[j]], Sigma[[j]], shape[[j]], nu)))
#icl=-2*icl+4*g*log(n)
}
}
if (family == "Skew.t"){
delta <- Delta <- Gama <- list()
# teta <- c()
for (k in 1:g){
delta[[k]] <- shape[[k]] / as.numeric(sqrt(1 + t(shape[[k]])%*%shape[[k]]))
Delta[[k]] <- as.vector(matrix.sqrt(Sigma[[k]])%*%delta[[k]])
Gama[[k]] <- Sigma[[k]] - Delta[[k]]%*%t(Delta[[k]])
# teta <- c(teta, mu[[k]], Gama[[k]][upper.tri(Gama[[k]], diag = TRUE)], Delta[[k]])
}
# teta <- c(teta, pii, nu) #teta para nu desconhecido
if(uni.Gama){
Gama.uni <- Gama[[1]]
if(g > 1) for(k in 2:g) Gama.uni <- Gama.uni + Gama[[k]]
Gama.uni <- Gama.uni / g
for(k in 1:g) Gama[[k]] <- Gama.uni
}
mu.old <- mu
Delta.old <- Delta
Gama.old <- Gama
criterio <- 1
count <- 0
lkante <- 1
while((criterio > error) && (count <= iter.max)){
count <- count + 1
tal <- matrix(0, n, g)
S1 <- matrix(0, n, g)
S2 <- matrix(0, n, g)
S3 <- matrix(0, n, g)
for (j in 1:g){
### E-step: calculando ui, tui, tui2 ###
Dif <- y - matrix(rep(mu[[j]], n), n, p, byrow = TRUE)
Mtij2 <- as.numeric( 1/(1 + t(Delta[[j]])%*%solve(Gama[[j]])%*%Delta[[j]]) )
Mtij <- sqrt(Mtij2)
mutij <- apply( matrix(rep( Mtij2*t(Delta[[j]])%*%solve(Gama[[j]]),n), n, p, byrow = TRUE ) * Dif, 1, sum)
A <- mutij / Mtij
dj <- mahalanobis(y, mu[[j]], Sigma[[j]])
E = (2*(nu)^(nu/2)*gamma((p+nu+1)/2)*((dj + nu + A^2))^(-(p+nu+1)/2)) / (gamma(nu/2)*(sqrt(pi))^(p+1)*sqrt(det(Sigma[[j]]))*dmvt.ls(y, mu[[j]], Sigma[[j]], shape[[j]] ,nu))
u = ((4*(nu)^(nu/2)*gamma((p+nu+2)/2)*(dj + nu)^(-(p+nu+2)/2)) / (gamma(nu/2)*sqrt(pi^p)*sqrt(det(Sigma[[j]]))*dmvt.ls(y, mu[[j]], Sigma[[j]], shape[[j]] ,nu)) )*pt(sqrt((p+nu+2)/(dj+nu))*A,p+nu+2)
d1 <- dmvt.ls(y, mu[[j]], Sigma[[j]], shape[[j]], nu)
if(length(which(d1 == 0)) > 0) d1[which(d1 == 0)] <- .Machine$double.xmin
d2 <- d.mixedmvST(y, pii, mu, Sigma, shape, nu)
if(length(which(d2 == 0)) > 0) d2[which(d2 == 0)] <- .Machine$double.xmin
tal[,j] <- d1*pii[j] / d2
S1[,j] <- tal[,j]*u
S2[,j] <- tal[,j]*(mutij*u + Mtij*E)
S3[,j] <- tal[,j]*(mutij^2*u + Mtij2 + Mtij*mutij*E)
### M-step: atualizar mu, Delta, Gama, sigma2 ###
pii[j] <- (1/n)*sum(tal[,j])
mu[[j]] <- apply(S1[,j]*y - S2[,j] * matrix(rep(Delta.old[[j]], n), n, p, byrow = TRUE), 2, sum) / sum(S1[,j])
Dif <- y - matrix(rep(mu[[j]], n), n, p, byrow = TRUE)
Delta[[j]] <- apply(S2[,j]*Dif, 2, sum) / sum(S3[,j])
sum2 <- matrix(0,p,p)
for (i in 1:n) sum2 <- sum2 + (S1[i,j]*(y[i,] - mu[[j]])%*%t(y[i,] - mu[[j]]) - S2[i,j]*Delta[[j]]%*%t(y[i,] - mu[[j]]) - S2[i,j]*(y[i,] - mu[[j]])%*%t(Delta[[j]]) + S3[i,j]*Delta[[j]]%*%t(Delta[[j]]))
Gama[[j]] <- sum2 / sum(tal[,j])
if(!uni.Gama){
Sigma[[j]] <- Gama[[j]] + Delta[[j]]%*%t(Delta[[j]])
shape[[j]] <- (solve(matrix.sqrt(Sigma[[j]]))%*%Delta[[j]]) / as.numeric( (1 - t(Delta[[j]])%*%solve(Sigma[[j]])%*%Delta[[j]]) )^(1/2)
}
}
if(uni.Gama){
GS <- 0
for (j in 1:g) GS <- GS+kronecker(tal[,j],Gama[[j]])
Gama.uni <- t(rowSums(array(t(GS),dim=c(p,p,n)),dims=2))/n
for (j in 1:g){
Gama[[j]] <- Gama.uni
Sigma[[j]] <- Gama[[j]] + Delta[[j]]%*%t(Delta[[j]])
shape[[j]] <- (solve(matrix.sqrt(Sigma[[j]]))%*%Delta[[j]]) / as.numeric( (1 - t(Delta[[j]])%*%solve(Sigma[[j]])%*%Delta[[j]]) )^(1/2)
}
}
#aqui comecam as alteracoes para estimar o valor de nu
logvero.ST <- function(nu) sum(log( d.mixedmvST(y, pii, mu, Sigma, shape, nu) ))
nu <- optimize(logvero.ST, c(0,100), tol = 0.000001, maximum = TRUE)$maximum
pii[g] <- 1 - (sum(pii) - pii[g])
zero.pos <- NULL
zero.pos <- which(pii == 0)
if(length(zero.pos) != 0){
pii[zero.pos] <- 1e-10
pii[which(pii == max(pii))] <- max(pii) - sum(pii[zero.pos])
}
# param <- teta
# teta <- c()
# for (k in 1:g) teta <- c(teta, mu[[k]], Gama[[k]][upper.tri(Gama[[k]], diag = TRUE)], Delta[[k]])
# teta <- c(teta, pii, nu) #teta para nu desconhecido
lk <- sum(log( d.mixedmvST(y, pii, mu, Sigma, shape, nu) ))
criterio <- abs((lk/lkante)-1)
lkante <- lk
mu.old <- mu
Delta.old <- Delta
Gama.old <- Gama
}
if (criteria == TRUE){
cl <- apply(tal, 1, which.max)
icl <- 0
for (j in 1:g) icl <- icl+sum(log(pii[j]*dmvt.ls(y[cl==j,], mu[[j]], Sigma[[j]], shape[[j]], nu)))
#icl=-2*icl+4*g*log(n)
}
}
if (family == "Skew.cn"){
if(length(nu) != 2) stop("The Skew.cn need a vector of two components in nu both between (0,1).")
delta <- Delta <- Gama <- list()
# teta <- c()
for (k in 1:g){
delta[[k]] <- shape[[k]] / as.numeric(sqrt(1 + t(shape[[k]])%*%shape[[k]]))
Delta[[k]] <- as.vector(matrix.sqrt(Sigma[[k]])%*%delta[[k]])
Gama[[k]] <- Sigma[[k]] - Delta[[k]]%*%t(Delta[[k]])
## teta <- c(teta, mu[[k]], Gama[[k]][upper.tri(Gama[[k]], diag = TRUE)], Delta[[k]])
}
## teta <- c(teta, pii, nu) #teta para nu desconhecido
if(uni.Gama){
Gama.uni <- Gama[[1]]
if(g > 1) for(k in 2:g) Gama.uni <- Gama.uni + Gama[[k]]
Gama.uni <- Gama.uni / g
for(k in 1:g) Gama[[k]] <- Gama.uni
}
mu.old <- mu
Delta.old <- Delta
Gama.old <- Gama
nu.old <- nu
criterio <- 1
count <- 0
lkante <- 1
while((criterio > error) && (count <= iter.max)){
count <- count + 1
tal <- matrix(0, n, g)
S1 <- matrix(0, n, g)
S2 <- matrix(0, n, g)
S3 <- matrix(0, n, g)
for (j in 1:g){
### E-step: calculando ui, tui, tui2 ###
Dif <- y - matrix(rep(mu[[j]], n), n, p, byrow = TRUE)
Mtij2 <- as.numeric( 1/(1 + t(Delta[[j]])%*%solve(Gama[[j]])%*%Delta[[j]]) )
Mtij <- sqrt(Mtij2)
mutij <- apply( matrix(rep( Mtij2*t(Delta[[j]])%*%solve(Gama[[j]]),n), n, p, byrow = TRUE ) * Dif, 1, sum)
A <- mutij / Mtij
dj <- mahalanobis(y, mu[[j]], Sigma[[j]])
u = (2/dmvSNC(y,mu[[j]],Sigma[[j]],shape[[j]],nu))*(nu[1]*nu[2]*dmvnorm(y,mu[[j]],Sigma[[j]]/nu[2])*pnorm(sqrt(nu[2])*A,0,1)+(1-nu[1])*dmvnorm(y,mu[[j]],Sigma[[j]])*pnorm(A,0,1))
E = (2/dmvSNC(y,mu[[j]],Sigma[[j]],shape[[j]],nu))*(nu[1]*sqrt(nu[2])*dmvnorm(y,mu[[j]],Sigma[[j]]/nu[2])*dnorm(sqrt(nu[2])*A,0,1)+(1-nu[1])*dmvnorm(y,mu[[j]],Sigma[[j]])*dnorm(A,0,1))
d1 <-dmvSNC(y, mu[[j]], Sigma[[j]], shape[[j]], nu)
if(length(which(d1 == 0)) > 0) d1[which(d1 == 0)] <- .Machine$double.xmin
d2 <- d.mixedmvSNC(y, pii, mu, Sigma, shape, nu)
if(length(which(d2 == 0)) > 0) d2[which(d2 == 0)] <- .Machine$double.xmin
tal[,j] <- d1*pii[j] / d2
S1[,j] <- tal[,j]*u
S2[,j] <- tal[,j]*(mutij*u + Mtij*E)
S3[,j] <- tal[,j]*(mutij^2*u + Mtij2 + Mtij*mutij*E)
### M-step: atualizar mu, Delta, Gama, sigma2 ###
pii[j] <- (1/n)*sum(tal[,j])
mu[[j]] <- apply(S1[,j]*y - S2[,j] * matrix(rep(Delta.old[[j]], n), n, p, byrow = TRUE), 2, sum) / sum(S1[,j])
Dif <- y - matrix(rep(mu[[j]], n), n, p, byrow = TRUE)
Delta[[j]] <- apply(S2[,j]*Dif, 2, sum) / sum(S3[,j])
sum2 <- matrix(0,p,p)
for (i in 1:n) sum2 <- sum2 + (S1[i,j]*(y[i,] - mu[[j]])%*%t(y[i,] - mu[[j]]) - S2[i,j]*Delta[[j]]%*%t(y[i,] - mu[[j]]) - S2[i,j]*(y[i,] - mu[[j]])%*%t(Delta[[j]]) + S3[i,j]*Delta[[j]]%*%t(Delta[[j]]))
Gama[[j]] <- sum2 / sum(tal[,j])
if(!uni.Gama){
Sigma[[j]] <- Gama[[j]] + Delta[[j]]%*%t(Delta[[j]])
shape[[j]] <- (solve(matrix.sqrt(Sigma[[j]]))%*%Delta[[j]]) / as.numeric( (1 - t(Delta[[j]])%*%solve(Sigma[[j]])%*%Delta[[j]]) )^(1/2)
}
}
if(uni.Gama){
GS <- 0
for (j in 1:g) GS <- GS+kronecker(tal[,j],Gama[[j]])
Gama.uni <- t(rowSums(array(t(GS),dim=c(p,p,n)),dims=2))/n
for (j in 1:g){
Gama[[j]] <- Gama.uni
Sigma[[j]] <- Gama[[j]] + Delta[[j]]%*%t(Delta[[j]])
shape[[j]] <- (solve(matrix.sqrt(Sigma[[j]]))%*%Delta[[j]]) / as.numeric( (1 - t(Delta[[j]])%*%solve(Sigma[[j]])%*%Delta[[j]]) )^(1/2)
}
}
#aqui comecam as alteracoes para estimar o valor de nu
logvero.SNC <- function(nu) sum(log( d.mixedmvSNC(y, pii, mu, Sigma, shape, nu) ))
nu <- optim(nu.old, logvero.SNC, control = list(fnscale = -1), method = "L-BFGS-B", lower = rep(0.01, 2), upper = rep(0.99,2))$par
pii[g] <- 1 - (sum(pii) - pii[g])
zero.pos <- NULL
zero.pos <- which(pii == 0)
if(length(zero.pos) != 0){
pii[zero.pos] <- 1e-10
pii[which(pii == max(pii))] <- max(pii) - sum(pii[zero.pos])
}
## param <- teta
## teta <- c()
## for (k in 1:g) teta <- c(teta, mu[[k]], Gama[[k]][upper.tri(Gama[[k]], diag = TRUE)], Delta[[k]])
## teta <- c(teta, pii, nu) #teta para nu desconhecido
lk <- sum(log( d.mixedmvSNC(y, pii, mu, Sigma, shape, nu) ))
criterio <- abs((lk/lkante)-1)
lkante <- lk
mu.old <- mu
Delta.old <- Delta
Gama.old <- Gama
nu.old <- nu
}
if (criteria == TRUE){
cl <- apply(tal, 1, which.max)
icl <- 0
for (j in 1:g) icl <- icl+sum(log(pii[j]*dmvSNC(y[cl==j,], mu[[j]], Sigma[[j]], shape[[j]], nu)))
#icl <- -2*icl+(4*g+1)*log(n)
}
}
if (family == "Skew.slash"){
cat("\nThe Skew.slash takes a long time to run.\n")
delta <- Delta <- Gama <- list()
# teta <- c()
for (k in 1:g){
delta[[k]] <- shape[[k]] / as.numeric(sqrt(1 + t(shape[[k]])%*%shape[[k]]))
Delta[[k]] <- as.vector(matrix.sqrt(Sigma[[k]])%*%delta[[k]])
Gama[[k]] <- Sigma[[k]] - Delta[[k]]%*%t(Delta[[k]])
# teta <- c(teta, mu[[k]], Gama[[k]][upper.tri(Gama[[k]], diag = TRUE)], Delta[[k]])
}
#teta <- c(teta, pii, nu) #teta para nu desconhecido
# teta <- c(teta, pii) #teta para nu desconhecido
if(uni.Gama){
Gama.uni <- Gama[[1]]
if(g > 1) for(k in 2:g) Gama.uni <- Gama.uni + Gama[[k]]
Gama.uni <- Gama.uni / g
for(k in 1:g) Gama[[k]] <- Gama.uni
}
mu.old <- mu
Delta.old <- Delta
Gama.old <- Gama
criterio <- 1
count <- 0
lkante <- 1
while((criterio > error) && (count <= iter.max)){
count <- count + 1
tal <- matrix(0, n, g)
S1 <- matrix(0, n, g)
S2 <- matrix(0, n, g)
S3 <- matrix(0, n, g)
for (j in 1:g){
### E-step: calculando ui, tui, tui2 ###
Dif <- y - matrix(rep(mu[[j]], n), n, p, byrow = TRUE)
Mtij2 <- as.numeric( 1/(1 + t(Delta[[j]])%*%solve(Gama[[j]])%*%Delta[[j]]) )
Mtij <- sqrt(Mtij2)
mutij <- apply( matrix(rep( Mtij2*t(Delta[[j]])%*%solve(Gama[[j]]),n), n, p, byrow = TRUE ) * Dif, 1, sum)
A <- mutij / Mtij
dj <- mahalanobis(y, mu[[j]], Sigma[[j]])
#int <- c()
#for (k in 1:n){ #melhorar se der
# f <- function(u) pnorm(u^(1/2)*A[k])*pgamma(u,(2*nu+p+2)/2,dj[k]/2)
# int[k] <- integrate(f,0,1)$value
#}
#u = ((2^(nu+2)*nu*gamma((2*nu+p+2)/(2)))/(dmvSS(y, mu[[j]], Sigma[[j]], shape[[j]], nu)*sqrt(pi^p)*det(Sigma[[j]])^(1/2)))*pgamma(1,(2*nu+p+2)/2,dj/2)*(dj^(-(2*nu+p+2)/2))*int
#E = ((2^(nu+1)*nu*gamma((2*nu+p+1)/(2)))/(dmvSS(y, mu[[j]], Sigma[[j]], shape[[j]], nu)*sqrt(pi)^(p+1)*det(Sigma[[j]])^(1/2)))*(dj + A^2)^(-(2*nu+p+1)/(2))*pgamma(1,(2*nu+p+1)/(2),(dj+A^2)/2)
u <- E <- c()
#===========================================================================================================
# Usando integracao de Monte Carlo para calcular kappa_1
# for(i in 1:n){
# U <- runif(2500)
# V <- pgamma(1,(2*nu + 3)/2, dj[i]/2)*U
# S <- qgamma(V,(2*nu + 3)/2, dj[i]/2)
# u[i] = ((2^(nu+2)*nu*gamma((2*nu+p+2)/(2)))/
# (dmvSS(y[i,], mu[[j]], Sigma[[j]], shape[[j]], nu)*sqrt(pi^p)*det(Sigma[[j]])^(1/2)))*
# pgamma(1,(2*nu+p+2)/2,dj[i]/2)*(dj[i]^(-(2*nu+p+2)/2))*mean(pnorm(S^(1/2)*A[i]))
# }
#============================================================================================================
#===========================================================================================================
# Usando integracao numerica para calcular kappa_1 (Introduzido por Celso Romulo)
for(i in 1:n){
faux <- function(u) u^(nu+p/2)*exp(-u*dj[i]/2)*pnorm(u^(1/2)*A[i])
aux22 <- integrate(faux,0,1)$value
u[i] = nu*2^(1-p/2)*pi^(-0.5*p)*det(Sigma[[j]])^(-1/2)*aux22/dmvSS(y[i,], mu[[j]], Sigma[[j]], shape[[j]], nu)
}
# faux <- function(u) u^(nu+p/2)*exp(-u*dj/2)*pnorm(u^(1/2)*A)
# aux22 <- integrate(faux,0,1)$value
# u = nu*2^(1-p/2)*pi^(-0.5*p)*det(Sigma[[j]])^(-1/2)*aux22/dmvSS(y, mu[[j]], Sigma[[j]], shape[[j]], nu)
#============================================================================================================
E = ((2^(nu+1)*nu*gamma((2*nu+p+1)/(2)))/(dmvSS(y, mu[[j]], Sigma[[j]], shape[[j]], nu)*sqrt(pi)^(p+1)*det(Sigma[[j]])^(1/2)))*
(dj + A^2)^(-(2*nu+p+1)/(2))*pgamma(1,(2*nu+p+1)/(2),(dj+A^2)/2)
d1 <- dmvSS(y, mu[[j]], Sigma[[j]], shape[[j]], nu)
if(length(which(d1 == 0)) > 0) d1[which(d1 == 0)] <- .Machine$double.xmin
d2 <- d.mixedmvSS(y, pii, mu, Sigma, shape, nu)
if(length(which(d2 == 0)) > 0) d2[which(d2 == 0)] <- .Machine$double.xmin
tal[,j] <- d1*pii[j] / d2
S1[,j] <- tal[,j]*u
S2[,j] <- tal[,j]*(mutij*u + Mtij*E)
S3[,j] <- tal[,j]*(mutij^2*u + Mtij2 + Mtij*mutij*E)
### M-step: atualizar mu, Delta, Gama, sigma2 ###
pii[j] <- (1/n)*sum(tal[,j])
mu[[j]] <- apply(S1[,j]*y - S2[,j] * matrix(rep(Delta.old[[j]], n), n, p, byrow = TRUE), 2, sum) / sum(S1[,j])
Dif <- y - matrix(rep(mu[[j]], n), n, p, byrow = TRUE)
Delta[[j]] <- apply(S2[,j]*Dif, 2, sum) / sum(S3[,j])
sum2 <- matrix(0,p,p)
for (i in 1:n) sum2 <- sum2 + (S1[i,j]*(y[i,] - mu[[j]])%*%t(y[i,] - mu[[j]]) - S2[i,j]*Delta[[j]]%*%t(y[i,] - mu[[j]]) - S2[i,j]*(y[i,] - mu[[j]])%*%t(Delta[[j]]) + S3[i,j]*Delta[[j]]%*%t(Delta[[j]]))
Gama[[j]] <- sum2 / sum(tal[,j])
# Sigma[[j]] <- Gama[[j]] + Delta[[j]]%*%t(Delta[[j]])
######## DISCUTIR ISSO AQUI
# if (any(!is.finite(Sigma[[j]]))) {
# print("infinite or missing values in Sigma")
#print(Sigma[[j]])
# obj.out <- list(Sigma=Sigma[[j]],iter = count,control=1)
# return(obj.out)
# }
if(!uni.Gama){
Sigma[[j]] <- Gama[[j]] + Delta[[j]]%*%t(Delta[[j]])
shape[[j]] <- (solve(matrix.sqrt(Sigma[[j]]))%*%Delta[[j]]) / as.numeric( (1 - t(Delta[[j]])%*%solve(Sigma[[j]])%*%Delta[[j]]) )^(1/2)
}
}
if(uni.Gama){
GS <- 0
for (j in 1:g) GS <- GS+kronecker(tal[,j],Gama[[j]])
Gama.uni <- t(rowSums(array(t(GS),dim=c(p,p,n)),dims=2))/n
for (j in 1:g){
Gama[[j]] <- Gama.uni
Sigma[[j]] <- Gama[[j]] + Delta[[j]]%*%t(Delta[[j]])
shape[[j]] <- (solve(matrix.sqrt(Sigma[[j]]))%*%Delta[[j]]) / as.numeric( (1 - t(Delta[[j]])%*%solve(Sigma[[j]])%*%Delta[[j]]) )^(1/2)
}
}
#aqui comecam as alteracoes para estimar o valor de nu
#===============================================
# Ative se desejar estimar nu
logvero.SS <- function(nu) sum(log( d.mixedmvSS(y, pii, mu, Sigma, shape, nu) ))
nu <- optimize(logvero.SS, c(0,100), tol = 0.000001, maximum = TRUE)$maximum
pii[g] <- 1 - (sum(pii) - pii[g])
zero.pos <- NULL
zero.pos <- which(pii == 0)
if(length(zero.pos) != 0){
pii[zero.pos] <- 1e-10
pii[which(pii == max(pii))] <- max(pii) - sum(pii[zero.pos])
}
# param <- teta
# teta <- c()
# for (k in 1:g) teta <- c(teta, mu[[k]], Gama[[k]][upper.tri(Gama[[k]], diag = TRUE)], Delta[[k]])
#teta <- c(teta, pii, nu) #teta para nu desconhecido
# teta <- c(teta, pii)
# criterio <- sqrt((teta-param)%*%(teta-param))
lk <- sum(log( d.mixedmvSS(y, pii, mu, Sigma, shape, nu) ))
criterio <- abs((lk/lkante)-1)
lkante <- lk
mu.old <- mu
Delta.old <- Delta
Gama.old <- Gama
}
if (criteria == TRUE){
cl <- apply(tal, 1, which.max)
icl <- 0
for (j in 1:g) icl <- icl+sum(log(pii[j]*dmvSS(y[cl==j,], mu[[j]], Sigma[[j]], shape[[j]], nu)))
#icl <- -2*icl+4*g*log(n)
}
}
if (family == "slash"){
cat("\nThe Slash takes a long time to run.\n")
delta <- Delta <- Gama <- list()
# teta <- c()
for (k in 1:g){
Delta[[k]] <- shape[[k]] <- rep(0,p)
Delta[[k]] <- as.vector(matrix.sqrt(Sigma[[k]])%*%delta[[k]])
Gama[[k]] <- Sigma[[k]] - Delta[[k]]%*%t(Delta[[k]])
# teta <- c(teta, mu[[k]], Gama[[k]][upper.tri(Gama[[k]], diag = TRUE)], Delta[[k]])
}
#teta <- c(teta, pii, nu) #teta para nu desconhecido
# teta <- c(teta, pii) #teta para nu desconhecido
if(uni.Gama){
Gama.uni <- Gama[[1]]
if(g > 1) for(k in 2:g) Gama.uni <- Gama.uni + Gama[[k]]
Gama.uni <- Gama.uni / g
for(k in 1:g) Gama[[k]] <- Gama.uni
}
mu.old <- mu
Delta.old <- Delta
Gama.old <- Gama
criterio <- 1
count <- 0
lkante <- 1
while((criterio > error) && (count <= iter.max)){
count <- count + 1
tal <- matrix(0, n, g)
S1 <- matrix(0, n, g)
S2 <- matrix(0, n, g)
S3 <- matrix(0, n, g)
for (j in 1:g){
### E-step: calculando ui, tui, tui2 ###
Dif <- y - matrix(rep(mu[[j]], n), n, p, byrow = TRUE)
Mtij2 <- as.numeric( 1/(1 + t(Delta[[j]])%*%solve(Gama[[j]])%*%Delta[[j]]) )
Mtij <- sqrt(Mtij2)
mutij <- apply( matrix(rep( Mtij2*t(Delta[[j]])%*%solve(Gama[[j]]),n), n, p, byrow = TRUE ) * Dif, 1, sum)
A <- mutij / Mtij
dj <- mahalanobis(y, mu[[j]], Sigma[[j]])
#int <- c()
#for (k in 1:n){ #melhorar se der
# f <- function(u) pnorm(u^(1/2)*A[k])*pgamma(u,(2*nu+p+2)/2,dj[k]/2)
# int[k] <- integrate(f,0,1)$value
#}
#u = ((2^(nu+2)*nu*gamma((2*nu+p+2)/(2)))/(dmvSS(y, mu[[j]], Sigma[[j]], shape[[j]], nu)*sqrt(pi^p)*det(Sigma[[j]])^(1/2)))*pgamma(1,(2*nu+p+2)/2,dj/2)*(dj^(-(2*nu+p+2)/2))*int
#E = ((2^(nu+1)*nu*gamma((2*nu+p+1)/(2)))/(dmvSS(y, mu[[j]], Sigma[[j]], shape[[j]], nu)*sqrt(pi)^(p+1)*det(Sigma[[j]])^(1/2)))*(dj + A^2)^(-(2*nu+p+1)/(2))*pgamma(1,(2*nu+p+1)/(2),(dj+A^2)/2)
u <- E <- c()
#===========================================================================================================
# Usando integracao de Monte Carlo para calcular kappa_1
# for(i in 1:n){
# U <- runif(2500)
# V <- pgamma(1,(2*nu + 3)/2, dj[i]/2)*U
# S <- qgamma(V,(2*nu + 3)/2, dj[i]/2)
# u[i] = ((2^(nu+2)*nu*gamma((2*nu+p+2)/(2)))/
# (dmvSS(y[i,], mu[[j]], Sigma[[j]], shape[[j]], nu)*sqrt(pi^p)*det(Sigma[[j]])^(1/2)))*
# pgamma(1,(2*nu+p+2)/2,dj[i]/2)*(dj[i]^(-(2*nu+p+2)/2))*mean(pnorm(S^(1/2)*A[i]))
# }
#============================================================================================================
#===========================================================================================================
# Usando integracao numerica para calcular kappa_1 (Introduzido por Celso Romulo)
for(i in 1:n){
faux <- function(u) u^(nu+p/2)*exp(-u*dj[i]/2)*pnorm(u^(1/2)*A[i])
aux22 <- integrate(faux,0,1)$value
u[i] = nu*2^(1-p/2)*pi^(-0.5*p)*det(Sigma[[j]])^(-1/2)*aux22/dmvSS(y[i,], mu[[j]], Sigma[[j]], shape[[j]], nu)
}
# faux <- function(u) u^(nu+p/2)*exp(-u*dj/2)*pnorm(u^(1/2)*A)
# aux22 <- integrate(faux,0,1)$value
# u = nu*2^(1-p/2)*pi^(-0.5*p)*det(Sigma[[j]])^(-1/2)*aux22/dmvSS(y, mu[[j]], Sigma[[j]], shape[[j]], nu)
#============================================================================================================
E = ((2^(nu+1)*nu*gamma((2*nu+p+1)/(2)))/(dmvSS(y, mu[[j]], Sigma[[j]], shape[[j]], nu)*sqrt(pi)^(p+1)*det(Sigma[[j]])^(1/2)))*
(dj + A^2)^(-(2*nu+p+1)/(2))*pgamma(1,(2*nu+p+1)/(2),(dj+A^2)/2)
d1 <- dmvSS(y, mu[[j]], Sigma[[j]], shape[[j]], nu)
if(length(which(d1 == 0)) > 0) d1[which(d1 == 0)] <- .Machine$double.xmin
d2 <- d.mixedmvSS(y, pii, mu, Sigma, shape, nu)
if(length(which(d2 == 0)) > 0) d2[which(d2 == 0)] <- .Machine$double.xmin
tal[,j] <- d1*pii[j] / d2
S1[,j] <- tal[,j]*u
S2[,j] <- tal[,j]*(mutij*u + Mtij*E)
S3[,j] <- tal[,j]*(mutij^2*u + Mtij2 + Mtij*mutij*E)
### M-step: atualizar mu, Delta, Gama, sigma2 ###
pii[j] <- (1/n)*sum(tal[,j])
mu[[j]] <- apply(S1[,j]*y - S2[,j] * matrix(rep(Delta.old[[j]], n), n, p, byrow = TRUE), 2, sum) / sum(S1[,j])
Dif <- y - matrix(rep(mu[[j]], n), n, p, byrow = TRUE)
Delta[[j]] <- rep(0,p)
sum2 <- matrix(0,p,p)
for (i in 1:n) sum2 <- sum2 + (S1[i,j]*(y[i,] - mu[[j]])%*%t(y[i,] - mu[[j]]) - S2[i,j]*Delta[[j]]%*%t(y[i,] - mu[[j]]) - S2[i,j]*(y[i,] - mu[[j]])%*%t(Delta[[j]]) + S3[i,j]*Delta[[j]]%*%t(Delta[[j]]))
Gama[[j]] <- sum2 / sum(tal[,j])
# Sigma[[j]] <- Gama[[j]] + Delta[[j]]%*%t(Delta[[j]])
######## DISCUTIR ISSO AQUI
# if (any(!is.finite(Sigma[[j]]))) {
# print("infinite or missing values in Sigma")
#print(Sigma[[j]])
# obj.out <- list(Sigma=Sigma[[j]],iter = count,control=1)
# return(obj.out)
# }
if(!uni.Gama){
Sigma[[j]] <- Gama[[j]] + Delta[[j]]%*%t(Delta[[j]])
shape[[j]] <- rep(0,p)
}
}
if(uni.Gama){
GS <- 0
for (j in 1:g) GS <- GS+kronecker(tal[,j],Gama[[j]])
Gama.uni <- t(rowSums(array(t(GS),dim=c(p,p,n)),dims=2))/n
for (j in 1:g){
Gama[[j]] <- Gama.uni
Sigma[[j]] <- Gama[[j]] + Delta[[j]]%*%t(Delta[[j]])
shape[[j]] <- rep(0,p)
}
}
#aqui comecam as alteracoes para estimar o valor de nu
#===============================================
# Ative se desejar estimar nu
logvero.SS <- function(nu) sum(log( d.mixedmvSS(y, pii, mu, Sigma, shape, nu) ))
nu <- optimize(logvero.SS, c(0,100), tol = 0.000001, maximum = TRUE)$maximum
pii[g] <- 1 - (sum(pii) - pii[g])
zero.pos <- NULL
zero.pos <- which(pii == 0)
if(length(zero.pos) != 0){
pii[zero.pos] <- 1e-10
pii[which(pii == max(pii))] <- max(pii) - sum(pii[zero.pos])
}
# param <- teta
# teta <- c()
# for (k in 1:g) teta <- c(teta, mu[[k]], Gama[[k]][upper.tri(Gama[[k]], diag = TRUE)], Delta[[k]])
#teta <- c(teta, pii, nu) #teta para nu desconhecido
# teta <- c(teta, pii)
# criterio <- sqrt((teta-param)%*%(teta-param))
lk <- sum(log( d.mixedmvSS(y, pii, mu, Sigma, shape, nu) ))
criterio <- abs((lk/lkante)-1)
lkante <- lk
mu.old <- mu
Delta.old <- Delta
Gama.old <- Gama
}
if (criteria == TRUE){
cl <- apply(tal, 1, which.max)
icl <- 0
for (j in 1:g) icl <- icl+sum(log(pii[j]*dmvSS(y[cl==j,], mu[[j]], Sigma[[j]], shape[[j]], nu)))
#icl <- -2*icl+4*g*log(n)
}
}
if (family == "Skew.normal"){
delta <- Delta <- Gama <- list()
# teta <- c()
for (k in 1:g){
delta[[k]] <- shape[[k]] / as.numeric(sqrt(1 + t(shape[[k]])%*%shape[[k]]))
Delta[[k]] <- as.vector(matrix.sqrt(Sigma[[k]])%*%delta[[k]])
Gama[[k]] <- Sigma[[k]] - Delta[[k]]%*%t(Delta[[k]])
# teta <- c(teta, mu[[k]], Gama[[k]][upper.tri(Gama[[k]], diag = TRUE)], Delta[[k]])
}
# teta <- c(teta, pii) #teta para nu conhecido
if(uni.Gama){
Gama.uni <- Gama[[1]]
if(g > 1) for(k in 2:g) Gama.uni <- Gama.uni + Gama[[k]]
Gama.uni <- Gama.uni / g
for(k in 1:g) Gama[[k]] <- Gama.uni
}
mu.old <- mu
Delta.old <- Delta
Gama.old <- Gama
criterio <- 1
count <- 0
lkante <- 1
while((criterio > error) && (count <= iter.max)){
count <- count + 1
tal <- matrix(0, n, g)
S1 <- matrix(0, n, g)
S2 <- matrix(0, n, g)
S3 <- matrix(0, n, g)
for (j in 1:g){
### E-step: calculando ui, tui, tui2 ###
Dif <- y - matrix(rep(mu[[j]], n), n, p, byrow = TRUE)
Mtij2 <- as.numeric( 1/(1 + t(Delta[[j]])%*%solve(Gama[[j]])%*%Delta[[j]]) )
Mtij <- sqrt(Mtij2)
mutij <- apply( matrix(rep( Mtij2*t(Delta[[j]])%*%solve(Gama[[j]]),n), n, p, byrow = TRUE ) * Dif, 1, sum)
A <- mutij / Mtij
prob <- pnorm(A)
if(length(which(prob == 0)) > 0) prob[which(prob == 0)] <- .Machine$double.xmin
E = dnorm(A) / prob
u = rep(1, n)
#print(Sigma)
#print(d.mixedmvSN(y, pii, mu, Sigma, shape))
#print("foi")
d1 <- dmvSN(y, mu[[j]], Sigma[[j]], shape[[j]])
if(length(which(d1 == 0)) > 0) d1[which(d1 == 0)] <- .Machine$double.xmin
d2 <- d.mixedmvSN(y, pii, mu, Sigma, shape)
if(length(which(d2 == 0)) > 0) d2[which(d2 == 0)] <- .Machine$double.xmin
tal[,j] <- d1*pii[j] / d2
S1[,j] <- tal[,j]*u
S2[,j] <- tal[,j]*(mutij*u + Mtij*E)
S3[,j] <- tal[,j]*(mutij^2*u + Mtij2 + Mtij*mutij*E)
### M-step: atualizar mu, Delta, Gama, sigma2 ###
pii[j] <- (1/n)*sum(tal[,j])
mu[[j]] <- apply(S1[,j]*y - S2[,j] * matrix(rep(Delta.old[[j]], n), n, p, byrow = TRUE), 2, sum) / sum(S1[,j])
Dif <- y - matrix(rep(mu[[j]], n), n, p, byrow = TRUE)
Delta[[j]] <- apply(S2[,j]*Dif, 2, sum) / sum(S3[,j])
sum2 <- matrix(0,p,p)
for (i in 1:n) sum2 <- sum2 + (S1[i,j]*(y[i,] - mu[[j]])%*%t(y[i,] - mu[[j]]) - S2[i,j]*Delta[[j]]%*%t(y[i,] - mu[[j]]) - S2[i,j]*(y[i,] - mu[[j]])%*%t(Delta[[j]]) + S3[i,j]*Delta[[j]]%*%t(Delta[[j]]))
Gama[[j]] <- sum2 / sum(tal[,j])
if(!uni.Gama){
Sigma[[j]] <- Gama[[j]] + Delta[[j]]%*%t(Delta[[j]])
shape[[j]] <- (solve(matrix.sqrt(Sigma[[j]]))%*%Delta[[j]]) / as.numeric( (1 - t(Delta[[j]])%*%solve(Sigma[[j]])%*%Delta[[j]]) )^(1/2)
}
}
if(uni.Gama){
GS <- 0
for (j in 1:g) GS <- GS+kronecker(tal[,j],Gama[[j]])
Gama.uni <- t(rowSums(array(t(GS),dim=c(p,p,n)),dims=2))/n
for (j in 1:g){
Gama[[j]] <- Gama.uni
Sigma[[j]] <- Gama[[j]] + Delta[[j]]%*%t(Delta[[j]])
shape[[j]] <- (solve(matrix.sqrt(Sigma[[j]]))%*%Delta[[j]]) / as.numeric( (1 - t(Delta[[j]])%*%solve(Sigma[[j]])%*%Delta[[j]]) )^(1/2)
}
}
#print("saiu do for g")
pii[g] <- 1 - (sum(pii) - pii[g])
zero.pos <- NULL
zero.pos <- which(pii == 0)
if(length(zero.pos) != 0){
pii[zero.pos] <- 1e-10
pii[which(pii == max(pii))] <- max(pii) - sum(pii[zero.pos])
}
# param <- teta
# teta <- c()
# for (k in 1:g) teta <- c(teta, mu[[k]], Gama[[k]][upper.tri(Gama[[k]], diag = TRUE)], Delta[[k]])
# teta <- c(teta, pii) #teta para nu conhecido
lk <- sum(log( d.mixedmvSN(y, pii, mu, Sigma, shape) ))
criterio <- abs((lk/lkante)-1)
lkante <- lk
mu.old <- mu
Delta.old <- Delta
Gama.old <- Gama
}
if (criteria == TRUE){
cl <- apply(tal, 1, which.max)
icl <- 0
for (j in 1:g) icl <- icl+sum(log(pii[j]*dmvSN(y[cl==j,], mu[[j]], Sigma[[j]], shape[[j]])))
#icl <- -2*icl+(4*g-1)*log(n)
}
}
if (family == "Normal"){
delta <- Delta <- Gama <- list()
# teta <- c()
for (k in 1:g){
Delta[[k]] <- shape[[k]] <- rep(0,p)
Gama[[k]] <- Sigma[[k]]
# teta <- c(teta, mu[[k]], Gama[[k]][upper.tri(Gama[[k]], diag = TRUE)])
}
# teta <- c(teta, pii) #teta para nu conhecido
if(uni.Gama){
Gama.uni <- Gama[[1]]
if(g > 1) for(k in 2:g) Gama.uni <- Gama.uni + Gama[[k]]
Gama.uni <- Gama.uni / g
for(k in 1:g) Gama[[k]] <- Gama.uni
}
mu.old <- mu
Delta.old <- Delta
Gama.old <- Gama
criterio <- 1
count <- 0
lkante <- 1
while((criterio > error) && (count <= iter.max)){
count <- count + 1
tal <- matrix(0, n, g)
S1 <- matrix(0, n, g)
S2 <- matrix(0, n, g)
S3 <- matrix(0, n, g)
for (j in 1:g){
### E-step: calculando ui, tui, tui2 ###
Dif <- y - matrix(rep(mu[[j]], n), n, p, byrow = TRUE)
Mtij2 <- as.numeric( 1/(1 + t(Delta[[j]])%*%solve(Gama[[j]])%*%Delta[[j]]) )
Mtij <- sqrt(Mtij2)
mutij <- apply( matrix(rep( Mtij2*t(Delta[[j]])%*%solve(Gama[[j]]),n), n, p, byrow = TRUE ) * Dif, 1, sum)
A <- mutij / Mtij
prob <- pnorm(A)
if(length(which(prob == 0)) > 0) prob[which(prob == 0)] <- .Machine$double.xmin
E = dnorm(A) / prob
u = rep(1, n)
d1 <- dmvSN(y, mu[[j]], Sigma[[j]], shape[[j]])
if(length(which(d1 == 0)) > 0) d1[which(d1 == 0)] <- .Machine$double.xmin
d2 <- d.mixedmvSN(y, pii, mu, Sigma, shape)
if(length(which(d2 == 0)) > 0) d2[which(d2 == 0)] <- .Machine$double.xmin
tal[,j] <- d1*pii[j] / d2
S1[,j] <- tal[,j]*u
S2[,j] <- tal[,j]*(mutij*u + Mtij*E)
S3[,j] <- tal[,j]*(mutij^2*u + Mtij2 + Mtij*mutij*E)
### M-step: atualizar mu, Delta, Gama, sigma2 ###
pii[j] <- (1/n)*sum(tal[,j])
mu[[j]] <- apply(S1[,j]*y - S2[,j] * matrix(rep(Delta.old[[j]], n), n, p, byrow = TRUE), 2, sum) / sum(S1[,j])
Dif <- y - matrix(rep(mu[[j]], n), n, p, byrow = TRUE)
Delta[[j]] <- rep(0,p)
sum2 <- matrix(0,p,p)
for (i in 1:n) sum2 <- sum2 + (S1[i,j]*(y[i,] - mu[[j]])%*%t(y[i,] - mu[[j]]))
Gama[[j]] <- sum2 / sum(tal[,j])
if(!uni.Gama){
Sigma[[j]] <- Gama[[j]] + Delta[[j]]%*%t(Delta[[j]])
shape[[j]] <- rep(0,p)
}
}
if(uni.Gama){
GS <- 0
for (j in 1:g) GS <- GS+kronecker(tal[,j],Gama[[j]])
Gama.uni <- t(rowSums(array(t(GS),dim=c(p,p,n)),dims=2))/n
for (j in 1:g){
Gama[[j]] <- Gama.uni
Sigma[[j]] <- Gama[[j]] + Delta[[j]]%*%t(Delta[[j]])
shape[[j]] <- rep(0,p)
}
}
pii[g] <- 1 - (sum(pii) - pii[g])
zero.pos <- NULL
zero.pos <- which(pii == 0)
if(length(zero.pos) != 0){
pii[zero.pos] <- 1e-10
pii[which(pii == max(pii))] <- max(pii) - sum(pii[zero.pos])
}
# param <- teta
# teta <- c()
# for (k in 1:g) teta <- c(teta, mu[[k]], Gama[[k]][upper.tri(Gama[[k]], diag = TRUE)])
# teta <- c(teta, pii) #teta para nu conhecido
lk <- sum(log( d.mixedmvSN(y, pii, mu, Sigma, shape) ))
criterio <- abs((lk/lkante)-1)
lkante <- lk
mu.old <- mu
Delta.old <- Delta
Gama.old <- Gama
#print(count)
#print(mu[[1]])
}
if (criteria == TRUE){
cl <- apply(tal, 1, which.max)
icl <- 0
for (j in 1:g) icl <- icl+sum(log(pii[j]*dmvSN(y[cl==j,], mu[[j]], Sigma[[j]], shape[[j]])))
#icl <- -2*icl+(3*g-1)*log(n)
}
}
if(criteria == TRUE){
if(uni.Gama){
if((family == "t") | (family == "Normal")) d <- g*p + length(Sigma[[1]][upper.tri(Sigma[[1]], diag = TRUE)]) + (g-1) #mu + Sigma + pi
else d <- g*2*p + length(Sigma[[1]][upper.tri(Sigma[[1]], diag = TRUE)]) + (g-1) #mu + shape + Sigma + pi
if((family == "t") | (family == "slash") | (family == "Skew.t") | (family == "Skew.slash")) d <- d+1 # add nu
if((family == "Skew.cn")) d <- d+2 # add nu
}
else{
if((family == "t") | (family == "Normal")) d <- g*(p + length(Sigma[[1]][upper.tri(Sigma[[1]], diag = TRUE)]) ) + (g-1) #mu + Sigma + pi
else d <- g*(2*p + length(Sigma[[1]][upper.tri(Sigma[[1]], diag = TRUE)]) ) + (g-1) #mu + shape + Sigma + pi
if((family == "t") | (family == "slash") | (family == "Skew.t") | (family == "Skew.slash")) d <- d+1 # add nu
if((family == "Skew.cn")) d <- d+2 # add nu
}
aic <- -2*lk + 2*d
bic <- -2*lk + log(n)*d
edc <- -2*lk + 0.2*sqrt(n)*d