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ConstrainedLogisticBiplot <- function(Y, X, dim=2, Scaling=5, tolerance = 1e-05, maxiter = 100, penalization = 0.1){
Y=as.matrix(Y)
n <- nrow(Y)
p <- ncol(Y)
q <- ncol(X)
r=min(p,q)
X=as.matrix(X)
Xo=X
ContinuousDataTransform = c("Raw Data", "Substract the global mean", "Double centering",
"Column centering", "Standardize columns", "Row centering",
"Standardize rows", "Divide by the column means and center",
"Normalized residuals from independence", "Divide by the range",
"Within groups standardization", "Ranks")
if (is.numeric(Scaling))
Scaling = ContinuousDataTransform[Scaling]
Data = InitialTransform(X, transform = Scaling)
X = Data$X
if (Scaling=="Within groups standardization") Biplot$Deviations = Data$ColStdDevs
Yh=matrix(0, n,p)
Betas=matrix(0, q+1, p)
X=cbind(rep(1,n),X)
for (i in 1:p){
ajuste=RidgeBinaryLogistic(Y[,i], X, tolerance = tolerance, maxiter = maxiter, penalization = penalization)
Yh[,i]=ajuste$linterm
Betas[,i]=ajuste$beta
}
Betas=t(Betas)
rownames(Betas)=colnames(Y)
colnames(Betas)=colnames(X)
colnames(Betas)[1]="Intercept"
Yh = InitialTransform(Yh, transform = 5)$X
SD = svd(Yh)
EV = SD$d[1:r]^2
Inertia = round((EV/sum(EV)) * 100, digits = 3)
CumInertia = cumsum(Inertia)
a = SD$u[,1:dim] %*% diag(SD$d[1:dim])
rownames(a)=rownames(Y)
freq = matrix(1, n, 1)
aa=cbind(matrix(1, n, 1), a)
b = matrix(0, p, dim + 1)
for (j in 1:p) {
b[j, ] = RidgeBinaryLogisticFit(Y[, j], aa, freq = matrix(1, n, 1), tolerance=tolerance, maxiter=maxiter)
}
rownames(b)=colnames(Y)
colnames(b)=c("intercept", paste("dim",1:dim))
esp = aa %*% t(b)
pred = exp(esp)/(1 + exp(esp))
loglikelyhood = sum(sum(Y * log(pred) + (1 - Y) * log(1 - pred)))
pred2 = matrix(as.numeric(pred > 0.5), n, p)
acier = matrix(as.numeric(Y == pred2), n, p)
acierfil = 100*apply(acier,1,sum)/p
aciercol = 100*apply(acier,2,sum)/n
presences=apply(Y, 2, sum)
absences=n-presences
sens = apply((acier==1) & (Y==1), 2, sum)/presences
spec = apply((acier==1) & (Y==0), 2, sum)/absences
totsens = sum((acier==1) & (Y==1))/sum(presences)
totspec = sum((acier==1) & (Y==0))/sum(absences)
gfit = (sum(sum(acier))/(n * p)) * 100
esp0 = freq %*% b[, 1]
pred0 = exp(esp0)/(1 + exp(esp0))
d1 = -2 * apply(Y * log(pred0) + (1 - Y) * log(1 - pred0),2,sum)
d2 = -2 * apply(Y * log(pred) + (1 - Y) * log(1 - pred),2,sum)
d = d1 - d2
ps = matrix(0, p, 1)
for (j in 1:p) ps[j] = 1 - pchisq(d[j], 1)
resid = Y - pred
r2 = 1 - (sum(sum(resid^2))/sum(sum(Y^2)))
pred2 = (esp > 0.5)
corrfil = acierfil
corrcol = aciercol
rownames(b)=colnames(Y)
Res=list()
Res$Biplot="Binary Logistic (Constrained)"
Res$Type= "Binary Logistic (Constrained)"
Res$Betas=Betas
Res$RowCoordinates=a
Res$ColumnParameters=b
Res$NullDeviances=d1
Res$ModelDeviances=d2
Res$Deviances=d
Res$Dfs=rep(dim, p)
Res$pvalues=ps
Res$CoxSnell=1-exp(-1*Res$Deviances/n)
Res$Nagelkerke=Res$CoxSnell/(1-exp((Res$NullDeviances/(-2)))^(2/n))
Res$MacFaden=1-(Res$ModelDeviances/Res$NullDeviances)
Res$TotalPercent=gfit
Res$ModelDevianceTotal=sum(Res$ModelDeviances)
Res$NullDevianceTotal=sum(Res$NullDeviances)
Res$DevianceTotal=sum(Res$Deviances)
dd = sqrt(rowSums(cbind(1,Res$ColumnParameters[, 2:(dim + 1)])^2))
Res$Loadings = solve(diag(dd)) %*% Res$ColumnParameters[, 2:(dim + 1)]
Res$Tresholds = Res$ColumnParameters[, 1]/d
Res$Communalities = rowSums(Res$Loadings^2)
nn=n*p
Res$TotCoxSnell=1-exp(-1*Res$DevianceTotal/nn)
Res$TotNagelkerke=Res$TotCoxSnell/(1-exp((Res$NullDevianceTotal/(-2)))^(2/nn))
Res$TotMacFaden=1-(Res$ModelDevianceTotal/Res$NullDevianceTotal)
Res$R2 = apply((Y-esp)^2,2, sum)/apply((Y)^2,2, sum)
Res$TotR2 = sum((Y-esp)^2) /sum((Y)^2)
pred= matrix(as.numeric(esp>0.5),n , p)
verdad = matrix(as.numeric(Y==pred),n , p)
Res$PercentsCorrec=apply(verdad, 2, sum)/n
Res$TotalPercent=sum(verdad)/(n*p)
Res$Sensitivity=sens
Res$Specificity=spec
Res$TotalSensitivity=totsens
Res$TotalSpecificity=totspec
Res$TotalDf = dim*p
Res$p=1-pchisq(Res$DevianceTotal, df = Res$TotalDf)
Res$ClusterType="us"
Res$Clusters = as.factor(matrix(1,n, 1))
Res$ClusterColors="blue"
Res$ClusterNames="ClusterTotal"
class(Res) = "Binary.Logistic.Biplot"
Res=AddContVars2Biplot(Res, Xo, dims=dim, Scaling = Scaling)
return(Res)
}
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