Nothing
R/glm.fda.R
In fda: Functional Data Analysis
Defines functions
constrain
glm.fda
glm.fda <- function(basismat, y, family, lamRmat, wtvec=NULL,
bvec0=NULL, addterm=NULL) {
#GLM.FDA Fits a generalized linear model with regularization.
# This function is called by function smooth.GLM
# Arguments
#
# BASISMAT An N by NBASIS matrix of values of basis functions
# Y May be
# a N by NCURVE matrix of data to be fitted
# or, in the binomial case with local sample sizes M.i,
# a list array of length 2, the first of which cantains
# the matrix above containing observed frequencies,
# and the second of which contains the corresponding
# sample sizes. Note that in the binary or Bernoulli case,
# Y may be a matrix of 1"s and 0"s and the M"s are
# taken to be 1"s.
# FAMILY A string indicating which of the five GLM family members
# is assumed
# "normal" or "gaussian" or "Gaussian"
# "binomial" or "binary" or "Bernoulli"
# "poisson"
# "gamma"
# "inverse gaussian" or "inverse Gaussian"
# or a list array of length(N) with each list containing
# a specification of the GLM family of a single observation.
# LAMRMAT a \lambda R, that is, a roughness penalty matrix R of
# order equal to the number of basis functions used or number
# of columns of basismat multiplied by a scalar roughness
# penalty parameter \lambda
# wtvec a vector of prior weights, such as the inverses of the
# relative variance of each observation.
# BVEC0 starting values for regresscion coefficients
# ADDTERM a addterm with a coefficient fixed at 1.0.
#
# Returns
# BVEC Final estimate of coefficients
# DEVIANCE Deviance values
#
# Last modified 17 May 2018 by Jim Ramsay
#--------------------------------------------------------------------------
# Check arguments
#--------------------------------------------------------------------------
# dimensions of basismat
basismatDim <- dim(basismat)
n <- basismatDim[1]
nbasis <- basismatDim[2]
if (is.list(y)) {
yDim <- dim(as.matrix(y[[1]]))
ntmp <- yDim[1]
ncurve <- yDim[2]
} else {
y <- as.matrix(y)
yDim <- dim(y)
ntmp <- yDim[1]
ncurve <- yDim[2]
}
if (n != ntmp) {
stop("basismat and y do not have the same number of rows.")
}
# define default weight vector wtvec and check for positivity
if (is.null(wtvec)) {
wtvec <- matrix(1,n,1)
}
if (any(wtvec <= 0)) {
stop("Non-positive values of wtvec found.")
}
#--------------------------------------------------------------------------
# Process y and define anonymous functions according to the
# distribution of y
# devFn the deviance or loss function,
# called after convergence is achieved
# stdFn the scale factor multiplying D eta
# called second inside loop
# linkFn link function, eta <- linkFn(mu),
# called prior to loop, maps data space into real line
# DlinkFn derivative of the link function wrt to mu
# called first inside loop
# IlinkFn the inverse of the link function IlinkFn[eta] <- mu,
# called last inside loop, maps eta into data space
# Then set a starting value for the mean mu, avoiding boundary values.
#--------------------------------------------------------------------------
M <- NULL
if (is.character(family)) {
# --------------------------------------------------------------------
# All observations are in the same family, family is a string
# --------------------------------------------------------------------
if (!(family == "normal" ||
family == "binomial" ||
family == "poisson" ||
family == "gamma" ||
family == "inverse gaussian")) {
stop("The distribution is not valid.")
}
if (family == "normal") {
# Note y can be any real number, no restrictions
devFn <- function(mu,y) (y - mu)^2
stdFn <- function(mu) matrix(1,dim(mu))
linkFn <- function(mu) mu
DlinkFn <- function(mu) matrix(1,dim(mu))
IlinkFn <- function(eta) eta
mu <- y
}
# --------------------------------------------------------------------
if (family == "binomial") {
if (is.numeric(y)) {
# If y a matrix, M is taken to be 1 (set below)
# and it must be a binary matrix containing only 0"s and 1"s
if (any(y < 0 | y > 1)) {
stop(c("For binomial case, y a single column but ",
" contains values other than 0 or 1."))
}
M <- matrix(1,n,ncurve)
} else {
if (is.list(y) && length(y) == 2) {
# If y is a list array of length 2, then first list
# contains a matrix containing the number of successes and
# the second list either contains a matrix of the same
# size as the matrix in y{1} or a single positive
# integer.
# These values or this value is the number of trials M
# for a binomial or bernoulli distribution.
# M must be a positive integer.
Freq <- y[[1]]
M <- y[[2]]
if (length(M) == 1) {
M <- M*matrix(1,n,ncurve)
}
if (!all(dim(M) == dim(Freq))) {
stop(c("FAMILY is binomial and matrix M is not the same ",
"size as matrix FREQ"))
}
if (any(M < 0)) {
stop(c("FAMILY is binomial and one or more values in M ",
"have nonpositive values"))
}
if (any(any(floor(M) != M))) {
stop(c("FAMILY is binomial and one or more values in M ",
"have noninteger values."))
}
# Redefine y is the proportion of sucesses
y <- Freq/M
} else {
stop(c("FAMILY is binomial and y has incorrect dimensions ",
" or is of wrong type."))
}
devFn <- function(mu,y) 2*M*(y*log((y+(y==0))/mu) +
(1-y)*log((1-y+(y==1))/(1-mu)))
stdFn <- function(mu) sqrt(mu*(1-mu)/M)
linkFn <- function(mu) log(mu/(1-mu))
DlinkFn <- function(mu) 1/(mu*(1-mu))
loBnd <- -16
upBnd <- -loBnd
IlinkFn <- function(eta) 1/(1 + exp(-constrain(eta,loBnd,upBnd)))
mu <- (M*y + 0.5)/(M + 1)
}
}
# --------------------------------------------------------------------
if (family == "poisson") {
# Note y must not contain negative numbers
if (any(y < 0)) {
stop("FAMILY is poisson and y contains negative values")
}
devFn <- function(mu,y) 2*(y*(log((y+(y==0))/mu)) -
(y - mu))
stdFn <- function(mu) sqrt(mu)
linkFn <- function(mu) log(mu)
DlinkFn <- function(mu) 1/mu
loBnd <- -16
upBnd <- -loBnd
IlinkFn <- function(eta) exp(constrain(eta,loBnd,upBnd))
mu <- y + 0.25
}
# --------------------------------------------------------------------
if (family == "gamma") {
# Note y must contain only positive numbers
if (any(y <= 0)) {
stop("FAMILY is gamma and Y contains nonpositive values")
}
devFn <- function(mu,y) 2*(-log(y/mu) + (y - mu)/mu)
stdFn <- function(mu) mu
linkFn <- function(mu) 1/mu
DlinkFn <- function(mu) -1/mu^2
loBnd <- -16
upBnd <- 1/loBnd
IlinkFn <- function(eta) 1/constrain(eta,loBnd,upBnd)
mu <- max(y, eps)
}
# --------------------------------------------------------------------
if (family == "inverse gaussian") {
# Note y must contain only positive numbers
if (any(y <= 0)) {
stop(c("FAMILY is inverse gaussian and Y contains ",
"nonpositive values"))
}
devFn <- function(mu,y) ((y - mu)/mu)^2/ y
stdFn <- function(mu) mu^(3/2)
loBnd <- -8
upBnd <- 1/loBnd
linkFn <- function(mu) constrain(mu,loBnd,upBnd)^(-2)
DlinkFn <- function(mu) -2*mu^(-3)
IlinkFn <- function(eta) constrain(eta,loBnd,upBnd)^(-1/2)
mu <- y
}
}
# } else {
# if (is.list(family) && length(family) == n) {
# # --------------------------------------------------------------------
# # Observations can be in different families, family is a list array.
# # --------------------------------------------------------------------
# mu <- matrix(0,n,1)
# loBnd <- matrix(0,n,1)
# upBnd <- matrix(0,n,1)
# devFn <- vector("list",n)
# stdFn <- vector("list",n)
# linkFn <- vector("list",n)
# DlinkFn <- vector("list",n)
# IlinkFn <- vector("list",n)
# # Dealing with the presence of some binomial observations y has
# # to be a list with n rows and 2 columns for all data. Ugh!
# binomwrd <- is.list(y) && all(dim(y) == c(n,2))
# }
# for (i in 1:n) {
# familyi <- family[[i]]
# if (!is.character(familyi)) {
# stop("A distribution specification is not a string.")
# }
# if (family == "normal") {
# # Note y can be any real number, no restrictions
# devFn[[i]] <- function(mu,y) (y - mu)^2
# stdFn[[i]] <- function(mu) matrix(1,dim(mu))
# linkFn[[i]] <- function(mu) mu
# DlinkFn[[i]] <- function(mu) matrix(1,dim(mu))
# IlinkFn[[i]] <- function(eta) eta
# mu[i,] <- y[i,]
# }
# if (family == "binomial") {
# if (all(isnumeric(y[i,]))) {
# # If y a matrix, M is taken to be 1 (set below)
# # and it must be a binary matrix containing only
# #0"s and 1"s
# if (any(y[i,] < 0 | y[i,] > 1)) {
# stop(c("For binomial case, y a single column but ",
# " contains values other than 0 or 1."))
# }
# } else {
# if (binomwrd) {
# Freqi <- y[[i,1]]
# Mi <- y[[i,2]]
# if (length(Mi) == 1) {
# Mi <- Mi*matrix(1,1,ncurve)
# }
# if (!all(dim(Mi) == dim(Freqi))) {
# stop(paste("FAMILY is binomial and matrix M is not the same ",
# "dim as matrix FREQ"))
# }
# if (any(any(Mi < 0))) {
# stop(c("FAMILY is binomial and one or more values in M ",
# "have nonpositive values"))
# }
# if (any(any(floor(Mi) != Mi))) {
# stop(paste("FAMILY is binomial and one or more values in M ",
# "have noninteger values."))
# }
# # Redefine y is the proportion of sucesses
# y[i,] <- (Freqi/Mi)
# } else {
# stop(paste("FAMILY is binomial and y has incorrect dimensions ",
# " or is of wrong type."))
# }
# devFn[[i]] <- function(mu,y) 2*M*(y*log((y+(y==0))/mu) +
# (1-y)*log((1-y+(y==1))/(1-mu)))
# stdFn[[i]] <- function(mu) sqrt(mu*(1-mu)/M)
# linkFn[[i]] <- function(mu) log(mu/(1-mu))
# DlinkFn[[i]] <- function(mu) 1/(mu*(1-mu))
# loBnd[i] <- log(eps)
# upBnd[i] <- -loBnd[i]
# IlinkFn[[i]] <- function(eta) 1/(1 + exp(-constrain(eta,loBnd,upBnd)))
# mu[i] <- (M[i]*y[i] + 0.5)/(M[i] + 1)
# }
# if (family == "gamma") {
# # Note y must contain only positive numbers
# if (any(y[i] <= 0)) {
# stop("FAMILY is gamma and Y contains nonpositive values")
# }
# devFn[[i]] <- function(mu,y) 2*(-log(y/mu) + (y - mu)/mu)
# stdFn[[i]] <- function(mu) mu
# linkFn[[i]] <- function(mu) 1/mu
# DlinkFn[[i]] <- function(mu) -1/mu^2
# loBnd[i] <- eps
# upBnd[i] <- 1/loBnd[i]
# IlinkFn[[i]] <- function(eta) 1/constrain(eta,loBnd,upBnd)
# mu[i,] <- max(y[i,], eps)
# }
# if (family == "inverse gaussian") {
# # Note y must contain only positive numbers
# if (any(y[i,] <= 0)) {
# stop(c("FAMILY is inverse gaussian and Y contains ",
# "nonpositive values"))
# }
# devFn[[i]] <- function(mu,y) ((y - mu)/mu)^2/ y
# stdFn[[i]] <- function(mu) mu^(3/2)
# loBnd[i] <- eps^(1/2)
# upBnd[i] <- 1/loBnd[i]
# linkFn[[i]] <- function(mu) constrain(mu,loBnd,upBnd)^(-2)
# DlinkFn[[i]] <- function(mu) -2*mu^(-3)
# IlinkFn[[i]] <- function(eta) constrain(eta,loBnd,upBnd)^(-1/2)
# mu[i,] <- y[i,]
# }
# }
# }
#--------------------------------------------------------------------------
# Initialize mu and eta from y.
#--------------------------------------------------------------------------
# compute eta <- E(y) from mu
if (is.character(family)) {
eta <- linkFn(mu)
# } else {
# eta <- matrix(0,n,nurve)
# Deta <- matrix(0,n,nurve)
# stdm <- matrix(0,n,nurve)
# for (i in 1:n) {
# linkFni <- linkFn[[i]]
# eta[i,] <- linkFni(mu[i,])
# }
}
#--------------------------------------------------------------------------
# Set up for iterations
#--------------------------------------------------------------------------
iter <- 0
iterLim <- 100
seps <- sqrt(eps)
convcrit <- 1e-6
sqrtwt <- sqrt(wtvec)
# set up starting value bvec0 if required
if (is.null(bvec0)) {
bvec0 <- matrix(0,nbasis,ncurve)
}
bvec <- bvec0
# Enforce limits on mu to guard against an inverse linkFn that doesn"t map
# into the support of the distribution.
if (family == "binomial") {
# mu is a probability, so order one is the natural scale, and eps is a
# reasonable lower limit on that scale (plus it"s symmetric).
eps <- 1e-16
muLims <- c(eps, 1-eps)
}
if (family == "poisson" || family == "gamma" || family == "inverse gaussian") {
# Here we don"t know the natural scale for mu, so make the lower limit
# small. This choice keeps mu^4 from underflowing. No upper limit.
muLims <- 1e-4
}
#--------------------------------------------------------------------------
# Start of GLM iteration loop
#--------------------------------------------------------------------------
while (iter <= iterLim) {
iter <- iter+1
# Compute adjusted dep}ent variable for least squares fit
if (is.character(family)) {
Deta <- DlinkFn(mu)
stdm <- stdFn(mu)
# } else {
# for (i in 1:n) {
# DlinkFni <- DlinkFn[[i]]
# stdFni <- stdFn[[i]]
# mui <- mu[i,]
# Deta[i,] <- DlinkFni(mui)
# stdm[i,] <- stdFni(mui)
# }
}
Zvec <- eta + (y - mu)*Deta
# Compute IRLS weights the inverse of the variance function
sqrtw <- (sqrtwt %*% matrix(1,1,ncurve))/(abs(Deta)*stdm)
# Compute coefficient estimates for this iteration - the IRLS step
bvec.old <- bvec
if (!is.null(addterm)) {
ytmp <- Zvec - addterm
} else {
ytmp <- Zvec
}
yw <- ytmp*sqrtw
basismatw <- basismat*(sqrtwt %*% matrix(1,1,nbasis))
if (is.null(lamRmat)) {
Mmat <- crossprod(basismatw)
} else {
Mmat <- crossprod(basismatw) + lamRmat
}
bvec <- solve(Mmat,t(basismatw)) %*% yw
if (!is.null(addterm)) {
eta <- basismat %*% bvec + addterm
} else {
eta <- basismat %*% bvec
}
if (is.character(family)) {
mu <- IlinkFn(eta)
# } else {
# for (i in 1:n) {
# IlinkFni <- IlinkFn[[i]]
# mu[i,] <- IlinkFni(eta[i,])
# }
}
# Force mean in bounds, in case the linkFn function is faulty
if (is.character(family)) {
if (family == "binomial") {
if (any(mu < muLims[1] | muLims[2] < mu)) {
for (j in 1:n) {
mu[,j] <- max(min(mu[,j],muLims[2]),muLims[1])
}
}
}
if (family == "poisson" ||
family == "gamma" ||
family == "inverse gaussian") {
if (any(mu < muLims[1])) {
for (j in 1:n) {
mu[j] <- max(mu[j],muLims[1])
}
}
}
# } else {
# for (i in 1:n) {
# familyi <- family[[i]]
# if (family == "binomial") {
# if (any(mu[i,] < muLims[1] | muLims(2) < mu[i,])) {
# for (j in 1:m) {
# mu[i,j] <- max(min(mu[i,j],muLims[2]),muLims[1])
# }
# }
# }
# if (family == "poisson" || family == "gamma" ||
# family == "inverse gaussian") {
# if (any(mu[i,] < muLims[1])) {
# for (j in 1:m) {
# mu[i,j]q() <- max(mu[i,j],muLims[1])
# }
# }
# }
# }
}
# Check stopping conditions
print(max(abs(bvec-bvec.old)))
if (max(abs(bvec-bvec.old)) <
convcrit*max(max(abs(bvec.old))) ) {
break
}
}
#--------------------------------------------------------------------------
# end of GLM iteration loop
#--------------------------------------------------------------------------
if (iter > iterLim) {
warning("Iteration limit reached.")
}
# Sum components of deviance to get the total deviance.
if (is.character(family)) {
di <- devFn(mu,y)
Deviance <- sum((wtvec %*% matrix(1,1,ncurve))*di)
# } else {
# Deviance <- matrix(0,n,ncurve)
# for (i in 1:n) {
# devFni <- devFn[[i]]
# di <- devFni(mu[i,],y[,i])
# Deviance[i,] <- sum((wtvec[i]*matrix(1,1,ncurve))*di)
# }
}
return(list(bvec=bvec, Deviance=Deviance))
}
constrain <- function(eta, loBnd, upBnd) {
eta[eta<loBnd] <- loBnd
eta[eta>upBnd] <- upBnd
return(eta)
}
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Defines functions constrain glm.fda
glm.fda <- function(basismat, y, family, lamRmat, wtvec=NULL,
bvec0=NULL, addterm=NULL) {
#GLM.FDA Fits a generalized linear model with regularization.
# This function is called by function smooth.GLM
# Arguments
#
# BASISMAT An N by NBASIS matrix of values of basis functions
# Y May be
# a N by NCURVE matrix of data to be fitted
# or, in the binomial case with local sample sizes M.i,
# a list array of length 2, the first of which cantains
# the matrix above containing observed frequencies,
# and the second of which contains the corresponding
# sample sizes. Note that in the binary or Bernoulli case,
# Y may be a matrix of 1"s and 0"s and the M"s are
# taken to be 1"s.
# FAMILY A string indicating which of the five GLM family members
# is assumed
# "normal" or "gaussian" or "Gaussian"
# "binomial" or "binary" or "Bernoulli"
# "poisson"
# "gamma"
# "inverse gaussian" or "inverse Gaussian"
# or a list array of length(N) with each list containing
# a specification of the GLM family of a single observation.
# LAMRMAT a \lambda R, that is, a roughness penalty matrix R of
# order equal to the number of basis functions used or number
# of columns of basismat multiplied by a scalar roughness
# penalty parameter \lambda
# wtvec a vector of prior weights, such as the inverses of the
# relative variance of each observation.
# BVEC0 starting values for regresscion coefficients
# ADDTERM a addterm with a coefficient fixed at 1.0.
#
# Returns
# BVEC Final estimate of coefficients
# DEVIANCE Deviance values
#
# Last modified 17 May 2018 by Jim Ramsay
#--------------------------------------------------------------------------
# Check arguments
#--------------------------------------------------------------------------
# dimensions of basismat
basismatDim <- dim(basismat)
n <- basismatDim[1]
nbasis <- basismatDim[2]
if (is.list(y)) {
yDim <- dim(as.matrix(y[[1]]))
ntmp <- yDim[1]
ncurve <- yDim[2]
} else {
y <- as.matrix(y)
yDim <- dim(y)
ntmp <- yDim[1]
ncurve <- yDim[2]
}
if (n != ntmp) {
stop("basismat and y do not have the same number of rows.")
}
# define default weight vector wtvec and check for positivity
if (is.null(wtvec)) {
wtvec <- matrix(1,n,1)
}
if (any(wtvec <= 0)) {
stop("Non-positive values of wtvec found.")
}
#--------------------------------------------------------------------------
# Process y and define anonymous functions according to the
# distribution of y
# devFn the deviance or loss function,
# called after convergence is achieved
# stdFn the scale factor multiplying D eta
# called second inside loop
# linkFn link function, eta <- linkFn(mu),
# called prior to loop, maps data space into real line
# DlinkFn derivative of the link function wrt to mu
# called first inside loop
# IlinkFn the inverse of the link function IlinkFn[eta] <- mu,
# called last inside loop, maps eta into data space
# Then set a starting value for the mean mu, avoiding boundary values.
#--------------------------------------------------------------------------
M <- NULL
if (is.character(family)) {
# --------------------------------------------------------------------
# All observations are in the same family, family is a string
# --------------------------------------------------------------------
if (!(family == "normal" ||
family == "binomial" ||
family == "poisson" ||
family == "gamma" ||
family == "inverse gaussian")) {
stop("The distribution is not valid.")
}
if (family == "normal") {
# Note y can be any real number, no restrictions
devFn <- function(mu,y) (y - mu)^2
stdFn <- function(mu) matrix(1,dim(mu))
linkFn <- function(mu) mu
DlinkFn <- function(mu) matrix(1,dim(mu))
IlinkFn <- function(eta) eta
mu <- y
}
# --------------------------------------------------------------------
if (family == "binomial") {
if (is.numeric(y)) {
# If y a matrix, M is taken to be 1 (set below)
# and it must be a binary matrix containing only 0"s and 1"s
if (any(y < 0 | y > 1)) {
stop(c("For binomial case, y a single column but ",
" contains values other than 0 or 1."))
}
M <- matrix(1,n,ncurve)
} else {
if (is.list(y) && length(y) == 2) {
# If y is a list array of length 2, then first list
# contains a matrix containing the number of successes and
# the second list either contains a matrix of the same
# size as the matrix in y{1} or a single positive
# integer.
# These values or this value is the number of trials M
# for a binomial or bernoulli distribution.
# M must be a positive integer.
Freq <- y[[1]]
M <- y[[2]]
if (length(M) == 1) {
M <- M*matrix(1,n,ncurve)
}
if (!all(dim(M) == dim(Freq))) {
stop(c("FAMILY is binomial and matrix M is not the same ",
"size as matrix FREQ"))
}
if (any(M < 0)) {
stop(c("FAMILY is binomial and one or more values in M ",
"have nonpositive values"))
}
if (any(any(floor(M) != M))) {
stop(c("FAMILY is binomial and one or more values in M ",
"have noninteger values."))
}
# Redefine y is the proportion of sucesses
y <- Freq/M
} else {
stop(c("FAMILY is binomial and y has incorrect dimensions ",
" or is of wrong type."))
}
devFn <- function(mu,y) 2*M*(y*log((y+(y==0))/mu) +
(1-y)*log((1-y+(y==1))/(1-mu)))
stdFn <- function(mu) sqrt(mu*(1-mu)/M)
linkFn <- function(mu) log(mu/(1-mu))
DlinkFn <- function(mu) 1/(mu*(1-mu))
loBnd <- -16
upBnd <- -loBnd
IlinkFn <- function(eta) 1/(1 + exp(-constrain(eta,loBnd,upBnd)))
mu <- (M*y + 0.5)/(M + 1)
}
}
# --------------------------------------------------------------------
if (family == "poisson") {
# Note y must not contain negative numbers
if (any(y < 0)) {
stop("FAMILY is poisson and y contains negative values")
}
devFn <- function(mu,y) 2*(y*(log((y+(y==0))/mu)) -
(y - mu))
stdFn <- function(mu) sqrt(mu)
linkFn <- function(mu) log(mu)
DlinkFn <- function(mu) 1/mu
loBnd <- -16
upBnd <- -loBnd
IlinkFn <- function(eta) exp(constrain(eta,loBnd,upBnd))
mu <- y + 0.25
}
# --------------------------------------------------------------------
if (family == "gamma") {
# Note y must contain only positive numbers
if (any(y <= 0)) {
stop("FAMILY is gamma and Y contains nonpositive values")
}
devFn <- function(mu,y) 2*(-log(y/mu) + (y - mu)/mu)
stdFn <- function(mu) mu
linkFn <- function(mu) 1/mu
DlinkFn <- function(mu) -1/mu^2
loBnd <- -16
upBnd <- 1/loBnd
IlinkFn <- function(eta) 1/constrain(eta,loBnd,upBnd)
mu <- max(y, eps)
}
# --------------------------------------------------------------------
if (family == "inverse gaussian") {
# Note y must contain only positive numbers
if (any(y <= 0)) {
stop(c("FAMILY is inverse gaussian and Y contains ",
"nonpositive values"))
}
devFn <- function(mu,y) ((y - mu)/mu)^2/ y
stdFn <- function(mu) mu^(3/2)
loBnd <- -8
upBnd <- 1/loBnd
linkFn <- function(mu) constrain(mu,loBnd,upBnd)^(-2)
DlinkFn <- function(mu) -2*mu^(-3)
IlinkFn <- function(eta) constrain(eta,loBnd,upBnd)^(-1/2)
mu <- y
}
}
# } else {
# if (is.list(family) && length(family) == n) {
# # --------------------------------------------------------------------
# # Observations can be in different families, family is a list array.
# # --------------------------------------------------------------------
# mu <- matrix(0,n,1)
# loBnd <- matrix(0,n,1)
# upBnd <- matrix(0,n,1)
# devFn <- vector("list",n)
# stdFn <- vector("list",n)
# linkFn <- vector("list",n)
# DlinkFn <- vector("list",n)
# IlinkFn <- vector("list",n)
# # Dealing with the presence of some binomial observations y has
# # to be a list with n rows and 2 columns for all data. Ugh!
# binomwrd <- is.list(y) && all(dim(y) == c(n,2))
# }
# for (i in 1:n) {
# familyi <- family[[i]]
# if (!is.character(familyi)) {
# stop("A distribution specification is not a string.")
# }
# if (family == "normal") {
# # Note y can be any real number, no restrictions
# devFn[[i]] <- function(mu,y) (y - mu)^2
# stdFn[[i]] <- function(mu) matrix(1,dim(mu))
# linkFn[[i]] <- function(mu) mu
# DlinkFn[[i]] <- function(mu) matrix(1,dim(mu))
# IlinkFn[[i]] <- function(eta) eta
# mu[i,] <- y[i,]
# }
# if (family == "binomial") {
# if (all(isnumeric(y[i,]))) {
# # If y a matrix, M is taken to be 1 (set below)
# # and it must be a binary matrix containing only
# #0"s and 1"s
# if (any(y[i,] < 0 | y[i,] > 1)) {
# stop(c("For binomial case, y a single column but ",
# " contains values other than 0 or 1."))
# }
# } else {
# if (binomwrd) {
# Freqi <- y[[i,1]]
# Mi <- y[[i,2]]
# if (length(Mi) == 1) {
# Mi <- Mi*matrix(1,1,ncurve)
# }
# if (!all(dim(Mi) == dim(Freqi))) {
# stop(paste("FAMILY is binomial and matrix M is not the same ",
# "dim as matrix FREQ"))
# }
# if (any(any(Mi < 0))) {
# stop(c("FAMILY is binomial and one or more values in M ",
# "have nonpositive values"))
# }
# if (any(any(floor(Mi) != Mi))) {
# stop(paste("FAMILY is binomial and one or more values in M ",
# "have noninteger values."))
# }
# # Redefine y is the proportion of sucesses
# y[i,] <- (Freqi/Mi)
# } else {
# stop(paste("FAMILY is binomial and y has incorrect dimensions ",
# " or is of wrong type."))
# }
# devFn[[i]] <- function(mu,y) 2*M*(y*log((y+(y==0))/mu) +
# (1-y)*log((1-y+(y==1))/(1-mu)))
# stdFn[[i]] <- function(mu) sqrt(mu*(1-mu)/M)
# linkFn[[i]] <- function(mu) log(mu/(1-mu))
# DlinkFn[[i]] <- function(mu) 1/(mu*(1-mu))
# loBnd[i] <- log(eps)
# upBnd[i] <- -loBnd[i]
# IlinkFn[[i]] <- function(eta) 1/(1 + exp(-constrain(eta,loBnd,upBnd)))
# mu[i] <- (M[i]*y[i] + 0.5)/(M[i] + 1)
# }
# if (family == "gamma") {
# # Note y must contain only positive numbers
# if (any(y[i] <= 0)) {
# stop("FAMILY is gamma and Y contains nonpositive values")
# }
# devFn[[i]] <- function(mu,y) 2*(-log(y/mu) + (y - mu)/mu)
# stdFn[[i]] <- function(mu) mu
# linkFn[[i]] <- function(mu) 1/mu
# DlinkFn[[i]] <- function(mu) -1/mu^2
# loBnd[i] <- eps
# upBnd[i] <- 1/loBnd[i]
# IlinkFn[[i]] <- function(eta) 1/constrain(eta,loBnd,upBnd)
# mu[i,] <- max(y[i,], eps)
# }
# if (family == "inverse gaussian") {
# # Note y must contain only positive numbers
# if (any(y[i,] <= 0)) {
# stop(c("FAMILY is inverse gaussian and Y contains ",
# "nonpositive values"))
# }
# devFn[[i]] <- function(mu,y) ((y - mu)/mu)^2/ y
# stdFn[[i]] <- function(mu) mu^(3/2)
# loBnd[i] <- eps^(1/2)
# upBnd[i] <- 1/loBnd[i]
# linkFn[[i]] <- function(mu) constrain(mu,loBnd,upBnd)^(-2)
# DlinkFn[[i]] <- function(mu) -2*mu^(-3)
# IlinkFn[[i]] <- function(eta) constrain(eta,loBnd,upBnd)^(-1/2)
# mu[i,] <- y[i,]
# }
# }
# }
#--------------------------------------------------------------------------
# Initialize mu and eta from y.
#--------------------------------------------------------------------------
# compute eta <- E(y) from mu
if (is.character(family)) {
eta <- linkFn(mu)
# } else {
# eta <- matrix(0,n,nurve)
# Deta <- matrix(0,n,nurve)
# stdm <- matrix(0,n,nurve)
# for (i in 1:n) {
# linkFni <- linkFn[[i]]
# eta[i,] <- linkFni(mu[i,])
# }
}
#--------------------------------------------------------------------------
# Set up for iterations
#--------------------------------------------------------------------------
iter <- 0
iterLim <- 100
seps <- sqrt(eps)
convcrit <- 1e-6
sqrtwt <- sqrt(wtvec)
# set up starting value bvec0 if required
if (is.null(bvec0)) {
bvec0 <- matrix(0,nbasis,ncurve)
}
bvec <- bvec0
# Enforce limits on mu to guard against an inverse linkFn that doesn"t map
# into the support of the distribution.
if (family == "binomial") {
# mu is a probability, so order one is the natural scale, and eps is a
# reasonable lower limit on that scale (plus it"s symmetric).
eps <- 1e-16
muLims <- c(eps, 1-eps)
}
if (family == "poisson" || family == "gamma" || family == "inverse gaussian") {
# Here we don"t know the natural scale for mu, so make the lower limit
# small. This choice keeps mu^4 from underflowing. No upper limit.
muLims <- 1e-4
}
#--------------------------------------------------------------------------
# Start of GLM iteration loop
#--------------------------------------------------------------------------
while (iter <= iterLim) {
iter <- iter+1
# Compute adjusted dep}ent variable for least squares fit
if (is.character(family)) {
Deta <- DlinkFn(mu)
stdm <- stdFn(mu)
# } else {
# for (i in 1:n) {
# DlinkFni <- DlinkFn[[i]]
# stdFni <- stdFn[[i]]
# mui <- mu[i,]
# Deta[i,] <- DlinkFni(mui)
# stdm[i,] <- stdFni(mui)
# }
}
Zvec <- eta + (y - mu)*Deta
# Compute IRLS weights the inverse of the variance function
sqrtw <- (sqrtwt %*% matrix(1,1,ncurve))/(abs(Deta)*stdm)
# Compute coefficient estimates for this iteration - the IRLS step
bvec.old <- bvec
if (!is.null(addterm)) {
ytmp <- Zvec - addterm
} else {
ytmp <- Zvec
}
yw <- ytmp*sqrtw
basismatw <- basismat*(sqrtwt %*% matrix(1,1,nbasis))
if (is.null(lamRmat)) {
Mmat <- crossprod(basismatw)
} else {
Mmat <- crossprod(basismatw) + lamRmat
}
bvec <- solve(Mmat,t(basismatw)) %*% yw
if (!is.null(addterm)) {
eta <- basismat %*% bvec + addterm
} else {
eta <- basismat %*% bvec
}
if (is.character(family)) {
mu <- IlinkFn(eta)
# } else {
# for (i in 1:n) {
# IlinkFni <- IlinkFn[[i]]
# mu[i,] <- IlinkFni(eta[i,])
# }
}
# Force mean in bounds, in case the linkFn function is faulty
if (is.character(family)) {
if (family == "binomial") {
if (any(mu < muLims[1] | muLims[2] < mu)) {
for (j in 1:n) {
mu[,j] <- max(min(mu[,j],muLims[2]),muLims[1])
}
}
}
if (family == "poisson" ||
family == "gamma" ||
family == "inverse gaussian") {
if (any(mu < muLims[1])) {
for (j in 1:n) {
mu[j] <- max(mu[j],muLims[1])
}
}
}
# } else {
# for (i in 1:n) {
# familyi <- family[[i]]
# if (family == "binomial") {
# if (any(mu[i,] < muLims[1] | muLims(2) < mu[i,])) {
# for (j in 1:m) {
# mu[i,j] <- max(min(mu[i,j],muLims[2]),muLims[1])
# }
# }
# }
# if (family == "poisson" || family == "gamma" ||
# family == "inverse gaussian") {
# if (any(mu[i,] < muLims[1])) {
# for (j in 1:m) {
# mu[i,j]q() <- max(mu[i,j],muLims[1])
# }
# }
# }
# }
}
# Check stopping conditions
print(max(abs(bvec-bvec.old)))
if (max(abs(bvec-bvec.old)) <
convcrit*max(max(abs(bvec.old))) ) {
break
}
}
#--------------------------------------------------------------------------
# end of GLM iteration loop
#--------------------------------------------------------------------------
if (iter > iterLim) {
warning("Iteration limit reached.")
}
# Sum components of deviance to get the total deviance.
if (is.character(family)) {
di <- devFn(mu,y)
Deviance <- sum((wtvec %*% matrix(1,1,ncurve))*di)
# } else {
# Deviance <- matrix(0,n,ncurve)
# for (i in 1:n) {
# devFni <- devFn[[i]]
# di <- devFni(mu[i,],y[,i])
# Deviance[i,] <- sum((wtvec[i]*matrix(1,1,ncurve))*di)
# }
}
return(list(bvec=bvec, Deviance=Deviance))
}
constrain <- function(eta, loBnd, upBnd) {
eta[eta<loBnd] <- loBnd
eta[eta>upBnd] <- upBnd
return(eta)
}
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