Nothing
NB_mov <-
function(Z_mat=Z_mat, first.order=first.order,home.field=home.field, control=control){
if(home.field){
y_fixed_effects <- formula(~1)
}else{
y_fixed_effects <- formula(~1)
}
r_fixed_effects <- formula(~neutral.site)
home_field<-home.field
#------------------
#First derivative of fn.eta (score)
gr.eta <- function(eta, R_X, R_Y, R_Z, rbetas, G.inv, n_eta,X, Y, Z, ybetas, R_inv) {
gr.y <- crossprod(Z, R_inv) %*% (Y - X %*% ybetas - Z %*% eta)
gr.r <- colSums(R_Z * as.vector((-1)^(1 - R_Y) * rder1((-1)^(1 - R_Y) * (R_X %*% rbetas + R_Z %*% eta))))
gr.p.eta <- -G.inv %*% eta
-as.vector(gr.y + gr.r + gr.p.eta)
}
#--------------------
#Second derivative of fn.eta (Hessian)
H.eta <- function(eta, rbetas, R_X, R_Y, R_Z,G.inv, n_eta,Z,R_inv) {
h.eta <- G.inv
h.y <- crossprod(Z, R_inv) %*% Z
temp <- -rder2((-1)^(1 - R_Y) * (R_X %*% rbetas + R_Z %*% eta))
h.r <- Matrix(crossprod(R_Z, temp * R_Z))
Matrix(h.eta +h.y+ h.r)
}
#---------------------------------------------------
#ltriangle: extract lower triangle
#and rebuild from elements
#note ltriangle(ltriangle(x))=x
ltriangle <- function(x) {
if (!is.null(dim(x)[2])) {
resA <- as.vector(x[lower.tri(x, diag = TRUE)])
resA
} else {
nx <- length(x)
d <- 0.5 * (-1 + sqrt(1 + 8 * nx))
resB <- Diagonal(d)
resB[lower.tri(resB, diag = TRUE)] <- x
if (nx > 1) {
resB <- resB + t(resB) - diag(diag(resB))
}
resB
}
}
#--------------
#These functions are derivatives of the standard normal CDF that are used in the missing data mechanism
rder0 <- function(q) {
q <- as.vector(q)
pnorm(q, log.p = TRUE)
}
rder1 <- function(q) {
q <- as.vector(q)
dnorm(q)/pmax(pnorm(q), 1e-15)
}
rder2 <- function(q) {
q <- as.vector(q)
(-(q/sqrt(2 * pi) * exp(-q^2/2)) * pnorm(q) - dnorm(q)^2)/pmax(pnorm(q)^2, 1e-15)
}
rder3 <- function(q) {
q <- as.vector(q)
((q^2 - 1)/sqrt(2 * pi) * exp(-q^2/2) * pnorm(q)^2 + 3 * (q/sqrt(2 * pi) * exp(-q^2/2)) * pnorm(q) * dnorm(q) + 2 * dnorm(q)^3)/pmax(pnorm(q)^3, 1e-15)
}
rder4 <- function(q) {
q <- as.vector(q)
((-q * (q^2 - 3)/sqrt(2 * pi) * exp(-q^2/2)) * pnorm(q)^3 - 4 * ((q^2 - 1)/sqrt(2 * pi) * exp(-q^2/2)) * pnorm(q)^2 * dnorm(q) - 12 * (q/sqrt(2 * pi) * exp(-q^2/2)) * pnorm(q) * dnorm(q)^2 - 3 * (q/sqrt(2 * pi) * exp(-q^2/2))^2 * pnorm(q)^2 - 6 *
dnorm(q)^4)/pmax(pnorm(q)^4, 1e-15)
}
reduce.G<-function(G) ltriangle(as.matrix(G[1:2,1:2]))
#-------------------
#finds the values of the random effects that maximize the
#EM-complete data likelihood. These are the EBLUPS (must be
#corrected if non-normal data used)
update.eta <- function(eta, R_X, R_Y, R_Z, rbetas, G, n_eta, cons.logLik,X,Y,Z,cross_Z,R_inv,ybetas) {
G.chol <- chol(G)
#For G, chol2inv is faster than solve
G.inv <- chol2inv(G.chol)
eta <- as.vector(eta)
H <- H.eta(eta = eta, rbetas = rbetas, R_X = R_X, R_Y = R_Y, R_Z = R_Z, G.inv = G.inv, n_eta = n_eta,Z=Z,R_inv=R_inv)
#For H, solve is much faster than chol2inv
var.eta <- as.matrix(solve(H))
product <- matrix(rep(1, n_eta), n_eta, 1)
gr <- rep(1, n_eta)
while (as.numeric(gr %*% product) > 1e-08) {
gr <- gr.eta(eta = eta, R_X = R_X, R_Y = R_Y, R_Z = R_Z, rbetas = rbetas, G.inv = G.inv, n_eta = n_eta,X=X, Y=Y, Z=Z, ybetas=ybetas, R_inv=R_inv)
product <- var.eta %*% gr
eta <- eta - product
H <- H.eta(eta = eta, rbetas = rbetas, R_X = R_X, R_Y = R_Y, R_Z = R_Z, G.inv = G.inv, n_eta = n_eta,Z=Z,R_inv=R_inv)
var.eta <- as.matrix(solve(H))
}
rm(product, gr)
chol.H <- chol(H)
log.p.eta <- -(length(eta)/2) * log(2 * pi) - sum(log(diag(G.chol))) - 0.5 * crossprod(eta, as(G.inv,"generalMatrix")) %*% eta
log.p.r <- sum(pnorm(as.vector((-1)^(1 - R_Y) * (R_X %*% rbetas + R_Z %*% eta)), log.p = TRUE))
log.p.y <- -((Ny)/2) * log(2 * pi) + sum(log(diag(chol(R_inv)))) - 0.5 * crossprod(Y - X %*% ybetas - Z %*% eta, R_inv) %*% (Y - X %*% ybetas - Z %*% eta)
res <- var.eta
attr(res, "likelihood") <- as.vector(cons.logLik + log.p.eta +log.p.y+ log.p.r - 0.5 * (2 * sum(log(diag(chol.H)))))
attr(res, "eta") <- eta
res
}
#-----------------
Sc.rbetas.f <- function(eta, rbetas, R_X, R_Y, R_Z, n_eta, Svar, Svar2) {
E.rbetas <- ((-1)^(1 - R_Y) * rder1((-1)^(1 - R_Y) * (R_X %*% rbetas + R_Z %*% eta)))
R2 <- rder2((-1)^(1 - R_Y) * (R_X %*% rbetas + R_Z %*% eta))
R3 <- (-1)^(1 - R_Y) * rder3((-1)^(1 - R_Y) * (R_X %*% rbetas + R_Z %*% eta))
temp.C <- (R2 * R_Z)
block <- (Svar %*% t(temp.C)) * R3
trc.rbetas <- rowSums(Svar2 * R3) + colSums(rowSums(Svar2) * block)
score.rbetas <- as.vector(t(R_X) %*% (E.rbetas + 0.5 * trc.rbetas))
rm(temp.C, block)
score.rbetas
}
Sc.rbetas.f.first.order <- function(eta, rbetas, R_X, R_Y, R_Z) {
E.rbetas <- ((-1)^(1 - R_Y) * rder1((-1)^(1 - R_Y) * (R_X %*% rbetas + R_Z %*% eta)))
score.rbetas <- as.vector(t(R_X) %*% E.rbetas )
score.rbetas
}
#update rbetas
#update for fixed effects in missing data mechansim
#requires var.eta, not var.eta.hat
update.rbetas <- function(eta, var.eta, rbetas, R_X, R_Y, R_Z, n_eta) {
Svar <- as.matrix(R_Z %*% var.eta)
Svar2 <- Svar * R_Z
product <- matrix(rep(1, length(rbetas)), length(rbetas), 1)
scrbetas <- rep(1, length(rbetas))
while (as.numeric(scrbetas %*% product) > 1e-08) {
Hrbetas <- as.matrix(jacobian(Sc.rbetas.f, rbetas, method = "simple", eta = eta, R_X = R_X, R_Y = R_Y, R_Z = R_Z, n_eta = n_eta, Svar = Svar, Svar2 = Svar2))
scrbetas <- Sc.rbetas.f(eta, rbetas, R_X, R_Y, R_Z, n_eta, Svar = Svar, Svar2 = Svar2)
product <- c(solve(Hrbetas, scrbetas))
rbetas <- rbetas - product
}
rm(Svar, Svar2, scrbetas, product)
rbetas
}
update.rbetas.first.order <- function(eta, rbetas, R_X, R_Y, R_Z, n_eta) {
product <- matrix(rep(1, length(rbetas)), length(rbetas), 1)
scrbetas <- rep(1, length(rbetas))
while (as.numeric(scrbetas %*% product) > 1e-08) {
Hrbetas <- as.matrix(jacobian(Sc.rbetas.f.first.order, rbetas, method = "simple", eta = eta, R_X = R_X, R_Y = R_Y, R_Z = R_Z))
scrbetas <- Sc.rbetas.f.first.order(eta, rbetas, R_X, R_Y, R_Z)
product <- c(solve(Hrbetas, scrbetas))
rbetas <- rbetas - product
}
rm( scrbetas, product)
rbetas
}
update.ybeta <- function(X, Y, Z, R_inv, eta.hat) {
A.ybeta <- crossprod(X, R_inv) %*% X
B.ybeta <- crossprod(X, R_inv) %*% (Y - Z %*% eta.hat)
as.vector(solve(A.ybeta, B.ybeta))
}
Score <- function(thetas) {
ybetas <- thetas[1:n_ybeta]
if(home.field){
rbetas <- thetas[(n_ybeta + 1):(n_ybeta + 1)]
if(dim(R_X)[2]==2) rbetas<-c(rbetas,0)
sigup<-R.tri<-R.i.parm <- thetas[(n_ybeta+2):(n_ybeta+2)]
}else{
ybetas<-numeric(n_ybeta)
rbetas <- rep(0,ncol(R_X))
sigup<-R.tri<-R.i.parm <- thetas[(n_ybeta+1):(n_ybeta+1)]
}
#R_i.parm.constrained <- R.i.parm[-LRI]
R_i<-sigup
R<-suppressMessages(sigup*(Diagonal(Ny)))
R_inv<-suppressMessages((1/sigup)*(Diagonal(Ny)))
if(home.field){
G <- thetas[(n_ybeta+3):length(thetas)]
}else{
G <- thetas[(n_ybeta+2):length(thetas)]
}
G<-suppressMessages(kronecker(Diagonal(length(teams)),ltriangle(G)))
#update.eta returns new var.eta with eta and likelihood as attr()
new.eta <- update.eta(eta = eta.hat, R_X = R_X, R_Y = R_Y, R_Z = R_Z,rbetas = rbetas, G = G, n_eta = n_eta, cons.logLik = cons.logLik,X=X,Y=Y,Z=Z,cross_Z=cross_Z,R_inv=R_inv,ybetas=ybetas)
eta <- attr(new.eta, "eta")
eta.hat<-eta
var.eta <- var.eta.hat <- new.eta
eta.hat <- as.vector(eta)
temp_mat <- var.eta.hat + tcrossprod(eta.hat, eta.hat)
# temp_mat_R <- attr(new.eta, "h.inv") + tcrossprod(eta.hat,
# eta.hat)
rm(new.eta)
A.ybeta <- crossprod(X, R_inv) %*% X
B.ybeta <- crossprod(X, R_inv) %*% (Y - Z %*% eta.hat)
score.y <- as.vector(B.ybeta - A.ybeta %*% ybetas)
if(home.field) score.r <- Sc.rbetas.f.first.order(eta = eta, rbetas = rbetas, R_X = R_X, R_Y = R_Y, R_Z = R_Z)[1]
score.R <- -.5*(Ny/sigup-(1/sigup^2)*crossprod(Y-X%*%ybetas-Z%*%eta.hat)-(1/sigup^2)*sum(diag(crossprod(Z)%*%var.eta.hat)))
score.R<-as.numeric(score.R)
gam_t_sc <- list()
index1 <- 0
score.G <- Matrix(0, 0, 0)
gam_t_sc <- matrix(0, 2,2)
index2 <- c(1)
for (k in 1:nteams) {
gam_t_sc <- gam_t_sc + temp_mat[(index2):(index2 +
1), (index2):(index2 + 1)]
index2 <- index2 + 2
}
gam_t <- G[1:2, 1:2]
sv_gam_t <- chol2inv(chol(gam_t))
der <- -0.5 * (nteams * sv_gam_t - sv_gam_t %*%
gam_t_sc %*% sv_gam_t)
if (is.numeric(drop(sv_gam_t))) {
score.eta.t <- der
}
else {
score.eta.t <- 2 * der - diag(diag(der))
}
# for (k in 1:nteams) {
# score.G <- bdiag(score.G, score.eta.t)
# }
score.G<-ltriangle(score.eta.t)
if(home.field){
-c(score.y, score.r, score.R, score.G)
}else{
-c( score.R, score.G)
}
}
#save(list = ls(all = TRUE), file = "test.RData",envir=environment())
#-------------------------------
#Data format
Z_mat$home<-as.character(Z_mat$home)
Z_mat$away<-as.character(Z_mat$away)
teams <- sort(unique(c(Z_mat$home,Z_mat$away)))
nteams<-length(teams)
#R_mat contains data for missing data mechanism
R_mat <- Z_mat
#number of measured scores
Nr <- length(R_mat$home_win)
Ny<-Nr
Y<-Z_mat$Score.For-Z_mat$Score.Against
RE_mat <- Matrix(0,Ny,length(teams))
colnames(RE_mat)<-rep(teams)
R_RE_mat <- Matrix(0,Nr,length(teams))
colnames(R_RE_mat)<-teams
for(i in 1:length(teams)){
R_RE_mat[R_mat$home==teams[i],i]<-rep(1,length(R_RE_mat[R_mat$home==teams[i],i]))
R_RE_mat[R_mat$away==teams[i],i]<-rep(-1,length(R_RE_mat[R_mat$away==teams[i],i]))
}
#populate the X matrix for missing data model
R_X_mat <- sparse.model.matrix(r_fixed_effects, R_mat, drop.unused.levels = TRUE)
#drop 0 columns from X_mat
R_X_mat <- R_X_mat[, !(colSums(abs(R_X_mat)) == 0), drop = FALSE]
if (rankMatrix(R_X_mat,method = 'qrLINPACK')[1] != dim(R_X_mat)[2]) {
stop("WARNING: Fixed-effects design matrix not full-rank")
}
n_eta <- 2*length(teams)
n_rbeta <- dim(R_X_mat)[2]
R_X <- Matrix(R_X_mat)
R_Y <- as.vector(R_mat$home_win)
RE_mat<-R_RE_mat
if(any(R_Y==2)){
tie.indx<-which(R_Y==2)
X.tie<-R_X[tie.indx,,drop=FALSE]
Z.tie<-R_RE_mat[tie.indx,,drop=FALSE]
R_Y<-R_Y[-tie.indx]
R_X<-R_X[-tie.indx,,drop=FALSE]
R_RE_mat<-R_RE_mat[-tie.indx,,drop=FALSE]
for(i in 1:length(tie.indx)){
R_Y<-c(R_Y,1,0)
R_X<-rbind(R_X,X.tie[i,,drop=FALSE],X.tie[i,,drop=FALSE])
R_RE_mat<-rbind(R_RE_mat,Z.tie[i,,drop=FALSE],Z.tie[i,,drop=FALSE])
}
Nr <- length(R_Y)
}
#offense then defense
# joffense<-c(t(cbind(Z_mat$home,Z_mat$away)))
# jdefense<-c(t(cbind(Z_mat$away,Z_mat$home)))
# J_mat<-cbind(as.numeric(Y),joffense,jdefense)
# J_mat<-as.data.frame(J_mat)
# templ<-rep(Z_mat$neutral.site,each=2)
# templ2<-rep("Neutral Site",length(templ))
# for(i in 1:(2*Ny)){
# if(templ[i]==0&i%%2==1)
# templ2[i]<-"Home"
# if(templ[i]==0&i%%2==0)
# templ2[i]<-"Away"
# }
# J_mat<-cbind(J_mat,templ2)
# colnames(J_mat)<-c("J_Y","offense","defense","Location")
# if(control$OT.flag){
# J_mat<-cbind(J_mat,rep(Z_mat$OT,each=2))
# colnames(J_mat)<-c("J_Y","offense","defense","Location","OT")
# }
J_mat<-as.data.frame(R_mat)
#J_mat$fcs<-as.factor(J_mat$fcs)
J_mat$J_Y<-as.numeric(Y)
#jreo<-sparse.model.matrix(as.formula(~offense+0),data=J_mat)
#jred<--1*sparse.model.matrix(as.formula(~defense+0),data=J_mat)
X_mat <- sparse.model.matrix(y_fixed_effects, R_mat, drop.unused.levels = TRUE)
X_mat<-X_mat[,colSums(abs(X_mat))!=0,drop=FALSE]
if (rankMatrix(X_mat,method = 'qrLINPACK')[1] != dim(X_mat)[2]) {
stop("WARNING: Fixed-effects design matrix for scores not full-rank. May need
to remove home field effect.")
}
if(any(Z_mat$neutral.site==1))X_mat[Z_mat$neutral.site==1,]<-0
n_ybeta<-ncol(X_mat)
new_yz <- Matrix(0, Ny, n_eta)
new_rz <- Matrix(0, Nr, n_eta)
y.indicator <- rep(c(1,0),length(teams))
y_i <- y.indicator * (1:n_eta)
y_i <- y_i[y_i != 0]
eta.label <- character(n_eta)
new_yz[, y_i] <- RE_mat
eta.label[y_i] <- teams
r_i <- (1 - y.indicator) * (1:n_eta)
r_i <- r_i[r_i != 0]
new_rz[, r_i] <- R_RE_mat
#eta.label[r_i] <- c(R_t_effects)
#The results are loaded into the Z matricies
#Z[[]] and R_Z[[]] below -----------------------
FE.count<-0
R_Z <- Matrix(new_rz)
t_R_Z <- t(R_Z)
cross_R_Z <- crossprod(R_Z)
X <- Matrix(X_mat)
Y <- as.numeric(as.vector(J_mat$J_Y))
Z <- Matrix(new_yz)
cross_Z<-crossprod(Z)
#initialize parameters
eta.hat <- trc.y1 <- numeric(n_eta)
var.eta.hat <- Matrix(0, n_eta, n_eta)
G <- Diagonal(n_eta)
cons.logLik <- 0.5 * n_eta * log(2 * pi)
#Partition desigin matrices by year and
#calculate initial parameter values
# from data
rbetas<-rbetasn <- rep(0,ncol(R_X))
#these next few lines are used to populate
#comp.list, a list of components needed for
#the E-step update (not all n_eta^2 are needed)
dummy_mat <- kronecker(Diagonal(length(teams)),matrix(1,2,2))
dummy_mat<-dummy_mat + t(Z)%*%Z
dummy_mat <- drop0(triu(dummy_mat))
comp.list <- which(abs(dummy_mat) > 1e-10, arr.ind = TRUE)
comp.list <- unique(comp.list)
iter <- control$iter.EM
y.mat <- Matrix(0, iter, n_ybeta)
r.mat <- Matrix(0, iter, n_rbeta)
time.mat <- Matrix(0, iter, 1)
G.mat <- Matrix(0, iter, 6)
R<-R_inv<-Diagonal(Ny)
ybetas <- update.ybeta(X=X, Y=Y, Z=Z, R_inv=R_inv, eta.hat=eta.hat)
if(!home.field) ybetas<-0
names(ybetas)<-colnames(X_mat)
R.mat<-Matrix(0,iter,1)
lgLik <- numeric(iter)
L1.conv <- FALSE
L2.conv <- FALSE
L1.conv.it <- 0
#Begin EM algorithm
for (it in 1:iter) {
ptm <- proc.time()
rm(var.eta.hat)
new.eta <- update.eta(eta = eta.hat, R_X = R_X, R_Y = R_Y, R_Z = R_Z,rbetas = rbetas, G = G, n_eta = n_eta, cons.logLik = cons.logLik,X=X,Y=Y,Z=Z,cross_Z=cross_Z,R_inv=R_inv,ybetas=ybetas)
#save parameter values in matrix
y.mat[it,] <- c(ybetas)
r.mat[it, ] <- c(rbetas)
lgLik[it] <- attr(new.eta, "likelihood")
trc.y1 <- numeric(n_eta)
trc.y2 <- Matrix(0, n_eta, n_eta)
G.mat[it, ] <- reduce.G(G)
R.mat[it,]<-R[1,1]
eta <- as.vector(attr(new.eta, "eta"))
var.eta <- new.eta
rm(new.eta)
if(home.field){
thets1 <- c(G.mat[it - 1, ],R.mat[it - 1, ],y.mat[it - 1, ],r.mat[it - 1,1])
thets2 <- c(G.mat[it, ],R.mat[it, ],y.mat[it, ],r.mat[it,1])
}else{
thets1 <- c(G.mat[it - 1, ],R.mat[it - 1, ],y.mat[it - 1, ])
thets2 <- c(G.mat[it, ],R.mat[it, ],y.mat[it, ])
}
# print results if verbose
if ((control$verbose) & (it > 1)) {
cat("\n\niter:", it, "\n")
cat("log-likelihood:", lgLik[it], "\n")
cat("max % change in parm.", 100 * max(round(abs((thets2 - thets1)/(thets1+1e-6) * as.numeric(abs(thets1) > .00001)), 5)), "%\n")
cat("b.mean:", round(rbetas, 4), "\n")
cat("n.mean:", round(ybetas, 4), "\n")
cat("G:", reduce.G(G),"\n")
cat("R:", R.mat[it,],"\n")
}
#check for convergence of first order Laplace approximation
if ((it > 5) & (L1.conv == FALSE)) {
check.parm1 <- max(abs(thets2 - thets1) * as.numeric(abs(thets1) <= .00001)) < control$tol1
check.parm2 <- max(abs((thets2 - thets1)/(thets1+1e-6) * as.numeric(abs(thets1) > .00001))) < control$tol1
if (check.parm1 & check.parm2) {
L1.conv <- TRUE
L1.conv.it <- it
eblup.L1 <- round(cbind(eta, sqrt(diag(var.eta))), 4)
if (control$verbose) {
cat("\n First order Laplace has converged \n")
cat("log-likelihood:", lgLik[it], "\n")
cat("max % change in parm.", 100 * round(max(abs(thets2 - thets1)/abs(thets1) * as.numeric(abs(thets1) > .00001)), 5), "%\n")
cat("b.mean:", round(rbetas, 4), "\n")
cat("n.mean:", round(ybetas, 4), "\n")
cat("G:", reduce.G(G),"\n")
cat("R:", R.mat[it,],"\n")
}
# eblup<-eblup[rownames(eblup)%in%fbs_list,]
first.order.eblup<-cbind(1:length(teams),eblup[order(eblup[,1],decreasing=TRUE),])
if(first.order) break
}
}
#E-step
#Fully exponential corrections, calculated after 1st order
#Laplace approximation converges
if (L1.conv == TRUE) {
Svar <- as.matrix(R_Z %*% var.eta)
temp.trc.D <- as.vector(rder4((-1)^(1 - R_Y) * (R_X %*% rbetas + R_Z %*% eta)))
temp.trc.C <- (-1)^(1 - R_Y) * rder3((-1)^(1 - R_Y) * (R_X %*% rbetas + R_Z %*% eta))
trc.y1 <- rep(0,n_eta)
check.parmFE1 <- max(abs(thets2 - thets1) * as.numeric(abs(thets1) <= 0.0001)) < control$tolFE
check.parmFE2 <- max(abs((thets2 - thets1)/thets1 * as.numeric(abs(thets1) > 0.0001))) < control$tolFE
#calculate corrections to var.eta.hat after only calculating corrections to eta.hat for a while
#compute the trace corrections for var.eta
#The function trace.calc2 is used to calculate the trace corrections
Trace.calc2 <- function(comp.k,comp.l,dsig.dc.indx5, indx.5) {
if (comp.k !=comp.l) {
if(comp.k!=indx.5) comp2<-comp.k
if(comp.l!=indx.5) comp2<-comp.l
q<-var.eta%*%(dsig.dc.indx5%*%var.eta[,comp2])
d2.sig<- t_R_Z%*%(R_Z*(as.vector(R_Z%*%q)*temp.trc.C+ Svar[,indx.5]*Svar[,comp2]*temp.trc.D))
dsig.dc.comp2<- t_R_Z%*%(R_Z*Svar[,comp2]*temp.trc.C)
res<-sum(diag(var.eta%*%d2.sig)) + sum((t(dsig.dc.indx5)%*%var.eta)*(var.eta%*%dsig.dc.comp2))
}else{
q<-var.eta%*%(dsig.dc.indx5%*%var.eta[,indx.5])
d2.sig<- t_R_Z%*%(R_Z*(as.vector(R_Z%*%q)*temp.trc.C+ Svar[,indx.5]*Svar[,indx.5]*temp.trc.D))
res<-sum(diag(var.eta%*%d2.sig)) + sum((t(dsig.dc.indx5)%*%var.eta)*(var.eta%*%dsig.dc.indx5))
}
res
}
temp.comp <- comp.list
length.comp <- dim(comp.list)[1]
var.corrections <- matrix(0, 0, 3)
for (indx.5 in n_eta:1) {
ptm.cor <- proc.time()[3]
guide1 <- unique(which(temp.comp == indx.5, arr.ind = TRUE)[, 1])
guide2 <- comp.list[guide1, , drop = FALSE]
if (length(guide1) > 0) {
if(indx.5==n_eta)cat("Calculating FE corrections for random effects vector...\n")
dsig.dc.indx5<- t_R_Z%*%(R_Z*Svar[,indx.5]*temp.trc.C)
trc.y1[indx.5]<- sum(diag(var.eta%*%dsig.dc.indx5))
if (check.parmFE1 & check.parmFE2 | FE.count > 0) {
if(indx.5==n_eta) cat("Calculating FE corrections for random effects covariance matrix...\n")
FE.count <- FE.count + 1
res.temp <- cbind(guide2, mapply(Trace.calc2, comp.k = guide2[, 1], comp.l = guide2[, 2], MoreArgs = list(dsig.dc.indx5, indx.5 = indx.5)))
temp.comp <- temp.comp[-(guide1), , drop = FALSE]
var.corrections <- rbind(var.corrections, res.temp)
}
}
# cat(1-dim(temp.comp)[1]/length.comp,'%,',indx.5,',',proc.time()[3]-ptm.cor,'\n')
}
rm(indx.5)
if (check.parmFE1 & check.parmFE2| FE.count > 0) {
trc.y2 <- sparseMatrix(i = var.corrections[, 1], j = var.corrections[, 2], x = var.corrections[, 3], dims = c(n_eta, n_eta))
trc.y2 <- trc.y2 + t(trc.y2) - diag(diag(trc.y2))
}
rm(Svar,dsig.dc.indx5)
}
eta.hat <- as.vector(eta + 0.5 * trc.y1)
flush.console()
ptm.rbet <- proc.time()[3]
if(home_field){
if(first.order==FALSE&L1.conv==TRUE){
rbetasn <- update.rbetas(eta = eta, var.eta = var.eta, rbetas = rbetas, R_X=R_X, R_Y=R_Y, R_Z=R_Z, n_eta=n_eta)
}else{
rbetasn <- update.rbetas.first.order(eta = eta, rbetas = rbetas, R_X=R_X, R_Y=R_Y, R_Z=R_Z, n_eta=n_eta)
}
}
rm(eta)
var.eta <- var.eta + 0.5 * trc.y2
rm(trc.y2)
var.eta.hat <- var.eta
eblup <- as.matrix(cbind(eta.hat, sqrt(diag(var.eta.hat))))
colnames(eblup) <- c("eblup", "std. error")
rownames(eblup) <- rep(teams,each=2)
rm(var.eta)
if(first.order==TRUE&L1.conv==TRUE){
if (control$verbose) {
cat("\nFirst-order Model has converged!\n")
cat("\n\niter:", it, "\n")
cat("log-likelihood:", lgLik[it], "\n")
cat("max % change in parm.", 100 * round(max(abs((thets2 - thets1)/thets1) * as.numeric(abs(thets1) > .00001)), 5), "%\n")
cat("b.mean:", round(rbetas, 4), "\n")
cat("n.mean:", round(ybetas, 4), "\n")
cat("G:", reduce.G(G),"\n")
cat("R:", R.mat[it,],"\n")
}
break
}
# check convergence of Fully exponential model
if ((L1.conv == TRUE) & (it > L1.conv.it) ) {
check.parm1 <- max((thets2 - thets1) * as.numeric(abs(thets1) <= .00001)) < control$tol2
check.parm2 <- max(abs((thets2 - thets1)/thets1) * as.numeric(abs(thets1) > .00001)) < control$tol2
if (check.parm1 & check.parm2 ) {
L2.conv <- TRUE
if (control$verbose) {
cat("\nFully Exponential Model has converged!\n")
}
break
}
}
# M-step
#The following steps update the G
# matrix
temp_mat <- var.eta.hat + tcrossprod(eta.hat, eta.hat)
gt1<-matrix(0,2,2)
for(i in 1:length(teams)){
gt1<-gt1+temp_mat[(2*(i-1)+1):(2*i),(2*(i-1)+1):(2*i)]
}
gt1<-symmpart(gt1/length(teams))
Gn<-as(kronecker(Diagonal(length(teams)),gt1),"generalMatrix")
sigup<-(1/Ny)*(crossprod(Y-X%*%ybetas-Z%*%eta.hat)+sum(diag(crossprod(Z)%*%var.eta.hat)))
R<-suppressMessages(sigup*(Diagonal(Ny)))
R_inv<-suppressMessages((1/sigup)*(Diagonal(Ny)))
ybetasn<-update.ybeta(X=X, Y=Y, Z=Z, R_inv=R_inv, eta.hat=eta.hat)
ybetas<-ybetasn
if(!home.field) ybetas<-0
rbetas <- rbetasn
if(home_field){
rbetas[colnames(R_X)=="neutral.site"]<-0
}else{
rbetas<-numeric(length(rbetas))
}
G <- Gn
rm(Gn)
it.time <- (proc.time() - ptm)[3]
time.mat[it, ] <- c(it.time)
cat("Iteration", it, "took", it.time, "\n")
eblup <- cbind(eta.hat, sqrt(diag(var.eta.hat)))
colnames(eblup) <- c("eblup", "std. error")
rownames(eblup) <- rep(teams,each=2)
#write.csv(eblup,file="NB_mvglmmRank_ratings.csv")
} #end EM
if(home.field){
thetas <- c(ybetas,rbetas[1], as.numeric(sigup), reduce.G(G))
names(thetas)<-c("Mean","Binary mean","R[1,1]","G[1,1]","G[2,1]","G[2,2]")
}else{
thetas <- c( as.numeric(sigup), reduce.G(G))
names(thetas)<-c("R[1,1]","G[1,1]","G[2,1]","G[2,2]")
}
Hessian<-NULL
if(control$Hessian){
cat("\nCalculating Hessian with a central difference approximation...\n")
flush.console()
Hessian <- symmpart(jacobian(Score, thetas, method="simple"))
rownames(Hessian)<-colnames(Hessian)<-names(thetas)
#std_errors <- c(sqrt(diag(solve(Hessian))))
if(inherits(try(chol(Hessian),silent=TRUE), "try-error")) cat("\nWarning: Hessian not positive-definite\n")
}
G.res<-as.matrix(G[1:2,1:2])
colnames(G.res)<-c("Margin of Victory","Win Propensity")
G.res.cor<-cov2cor(G.res)
R.res<-as.matrix(R[1,1])
colnames(R.res)<-c("Variance")
R.res.cor<-cov2cor(R.res)
names(ybetas)<-"LocationHome"
names(rbetas)[1]<-c("LocationHome")
res<-list(n.ratings.mov=eblup[seq(1,2*nteams,by=2),1],n.ratings.offense=NULL,n.ratings.defense=NULL,p.ratings.offense=NULL,p.ratings.defense=NULL,b.ratings=eblup[seq(2,2*nteams,by=2),1],n.mean=ybetas,p.mean=NULL,b.mean=rbetas[1],G=G.res,G.cor=G.res.cor,R=R.res,R.cor=R.res.cor,home.field=home.field,actual=Y,pred=X%*%ybetas+Z%*%eta.hat,Hessian=Hessian,parameters=thetas)
}
Any scripts or data that you put into this service are public.
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.