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R/cphidden.r
In repeated: Non-Normal Repeated Measurements Models
Defines functions
cphidden
Documented in
cphidden
#
# repeated : A Library of Repeated Measurements Models
# Copyright (C) 1998, 1999, 2000, 2001 J.K. Lindsey
#
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public Licence as published by
# the Free Software Foundation; either version 2 of the Licence, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public Licence for more details.
#
# You should have received a copy of the GNU General Public Licence
# along with this program; if not, write to the Free Software
# Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
#
# SYNOPSIS
#
# cphidden(response=NULL, totals=NULL, times=NULL, distribution="Bernoulli",
# mu=NULL, cmu=NULL, tvmu=NULL, pgamma, pmu=NULL, pcmu=NULL, ptvmu=NULL,
# pshape=NULL, pfamily=NULL, par=NULL, pintercept=NULL, delta=NULL,
# envir=parent.frame(), print.level=0, ndigit=10, gradtol=0.00001,
# steptol=0.00001, fscale=1, iterlim=100, typsize=abs(p),
# stepmax=10*sqrt(p%*%p))
#
# DESCRIPTION
#
# A function to find a changepoint using a hidden Markov chain
# model in continuous time
##' Changepoint Location using a Continuous-time Two-state Hidden Markov Chain
##'
##' \code{cphidden} fits a two-state hidden Markov chain model with a variety
##' of distributions in continuous time in order to locate a changepoint in the
##' chosen distribution. All series on different individuals are assumed to
##' start at the same time point.
##'
##' For quantitative responses, specifying \code{par} allows an `observed'
##' autoregression to be fitted as well as the hidden Markov chain.
##'
##' All functions and formulae for the location parameter are on the
##' (generalized) logit scale for the Bernoulli, binomial, and multinomial
##' distributions.
##'
##' If \code{cmu} and \code{tvmu} are used, these two mean functions are
##' additive so that interactions between time-constant and time-varying
##' variables are not possible.
##'
##' The algorithm will run more quickly if the most frequently occurring time
##' step is scaled to be equal to unity.
##'
##' The object returned can be plotted to give the probabilities of being in
##' each hidden state at each time point. See \code{\link[repeated]{hidden}}
##' for details. For distributions other than the multinomial, proportional
##' odds, and continuation ratio, the (recursive) predicted values can be
##' plotted using \code{\link[rmutil]{mprofile}} and
##' \code{\link[rmutil]{iprofile}}.
##'
##'
##' @param response A list of two or three column matrices with counts or
##' category indicators, times, and possibly totals (if the distribution is
##' binomial), for each individual, one matrix or dataframe of counts, or an
##' object of class, \code{response} (created by
##' \code{\link[rmutil]{restovec}}) or \code{repeated} (created by
##' \code{\link[rmutil]{rmna}} or \code{\link[rmutil]{lvna}}). If the
##' \code{repeated} data object contains more than one response variable, give
##' that object in \code{envir} and give the name of the response variable to
##' be used here. If there is only one series, a vector of responses may be
##' supplied instead.
##'
##' Multinomial and ordinal categories must be integers numbered from 0.
##' @param totals If response is a matrix, a corresponding matrix of totals if
##' the distribution is binomial. Ignored if response has class,
##' \code{response} or \code{repeated}.
##' @param times If \code{response} is a matrix, a vector of corresponding
##' times, when they are the same for all individuals. Ignored if response has
##' class, \code{response} or \code{repeated}.
##' @param distribution Bernoulli, Poisson, multinomial, proportional odds,
##' continuation ratio, binomial, exponential, beta binomial, negative
##' binomial, normal, inverse Gauss, logistic, gamma, Weibull, Cauchy, Laplace,
##' Levy, Pareto, gen(eralized) gamma, gen(eralized) logistic, Hjorth, Burr,
##' gen(eralized) Weibull, gen(eralized) extreme value, gen(eralized) inverse
##' Gauss, power exponential, skew Laplace, or Student t. (For definitions of
##' distributions, see the corresponding [dpqr]distribution help.)
##' @param mu A general location function with two possibilities: (1) a list of
##' formulae (with parameters having different names) or functions (with one
##' parameter vector numbering for all of them) each returning one value per
##' observation; or (2) a single formula or function which will be used for all
##' states (and all categories if multinomial) but with different parameter
##' values in each so that pmu must be a vector of length the number of
##' unknowns in the function or formula times the number of states (times the
##' number of categories minus one if multinomial).
##' @param cmu A time-constant location function with three possibilities: (1)
##' a list of formulae (with parameters having different names) or functions
##' (with one parameter vector numbering for all of them) each returning one
##' value per individual; (2) a single formula or function which will be used
##' for all states (and all categories if multinomial) but with different
##' parameter values in each so that pcmu must be a vector of length the number
##' of unknowns in the function or formula times the number of states (times
##' the number of categories minus one if multinomial); or (3) a function
##' returning an array with one row for each individual, one column for each
##' state of the hidden Markov chain, and, if multinomial, one layer for each
##' category but the last. If used, this function or formula should contain the
##' intercept. Ignored if \code{mu} is supplied.
##' @param tvmu A time-varying location function with three possibilities: (1)
##' a list of formulae (with parameters having different names) or functions
##' (with one parameter vector numbering for all of them) each returning one
##' value per time point; (2) a single formula or function which will be used
##' for all states (and all categories if multinomial) but with different
##' parameter values in each so that ptvmu must be a vector of length the
##' number of unknowns in the function or formula times the number of states
##' (times the number of categories minus one if multinomial); or (3) a
##' function returning an array with one row for each time point, one column
##' for each state of the hidden Markov chain, and, if multinomial, one layer
##' for each category but the last. This function or formula is usually a
##' function of time; it is the same for all individuals. It only contains the
##' intercept if \code{cmu} does not. Ignored if \code{mu} is supplied.
##' @param pgamma An initial estimate of the transition intensity between the
##' two states in the continuous-time hidden Markov chain.
##' @param pmu Initial estimates of the unknown parameters in \code{mu}.
##' @param pcmu Initial estimates of the unknown parameters in \code{cmu}.
##' @param ptvmu Initial estimates of the unknown parameters in \code{tvmu}.
##' @param pshape Initial estimate(s) of the dispersion parameter, for those
##' distributions having one. This can be one value or a vector with a
##' different value for each state.
##' @param pfamily Initial estimate of the family parameter, for those
##' distributions having one.
##' @param par Initial estimate of the autoregression parameter.
##' @param pintercept For multinomial, proportional odds, and continuation
##' ratio models, \code{p-2} initial estimates for intercept contrasts from the
##' first intercept, where \code{p} is the number of categories.
##' @param delta Scalar or vector giving the unit of measurement (always one
##' for discrete data) for each response value, set to unity by default. For
##' example, if a response is measured to two decimals, delta=0.01. If the
##' response is transformed, this must be multiplied by the Jacobian. For
##' example, with a log transformation, \code{delta=1/response}. Ignored if
##' response has class, \code{response} or \code{repeated}.
##' @param envir Environment in which model formulae are to be interpreted or a
##' data object of class, \code{repeated}, \code{tccov}, or \code{tvcov}; the
##' name of the response variable should be given in \code{response}. If
##' \code{response} has class \code{repeated}, it is used as the environment.
##' @param print.level Arguments for nlm.
##' @param typsize Arguments for nlm.
##' @param ndigit Arguments for nlm.
##' @param gradtol Arguments for nlm.
##' @param stepmax Arguments for nlm.
##' @param steptol Arguments for nlm.
##' @param iterlim Arguments for nlm.
##' @param fscale Arguments for nlm.
##' @return A list of classes \code{hidden} and \code{recursive} (unless
##' multinomial, proportional odds, or continuation ratio) is returned that
##' contains all of the relevant information calculated, including error codes.
##' @author J.K. Lindsey
### @seealso \code{\link[repeated]{chidden}}, \code{\link[repeated]{gar}},
### \code{\link[repeated]{gnlmm}}, \code{\link[repeated]{hidden}},
### \code{\link[rmutil]{iprofile}}, \code{\link[repeated]{kalcount}},
### \code{\link[rmutil]{mexp}}, \code{\link[rmutil]{mprofile}},
### \code{\link[repeated]{nbkal}}, \code{\link[rmutil]{read.list}},
### \code{\link[rmutil]{restovec}}, \code{\link[rmutil]{rmna}}.
##' @keywords models
##' @examples
##'
##' # model for one randomly-generated binary series
##' y <- c(rbinom(10,1,0.1), rbinom(10,1,0.9))
##' mu <- function(p) array(p, c(1,2))
##' print(z <- cphidden(y, times=1:20, dist="Bernoulli",
##' pgamma=0.1,cmu=mu, pcmu=c(-2,2)))
##' # or equivalently
##' print(z <- cphidden(y, times=1:20, dist="Bernoulli",
##' pgamma=0.2,cmu=~1, pcmu=c(-2,2)))
##' # or
##' print(z <- cphidden(y, times=1:20, dist="Bernoulli",
##' pgamma=0.2,mu=~rep(a,20), pmu=c(-2,2)))
##' mexp(z$gamma)
##' par(mfcol=c(2,2))
##' plot(z)
##' plot(iprofile(z), lty=2)
##' print(z <- cphidden(y, times=(1:20)*2, dist="Bernoulli",
##' pgamma=0.1,cmu=~1, pcmu=c(-2,2)))
##' mexp(z$gamma) %*% mexp(z$gamma)
##' plot(z)
##' plot(iprofile(z), lty=2)
##'
##' @export cphidden
<- function(response=NULL, totals=NULL, times=NULL,
distribution="Bernoulli", mu=NULL, cmu=NULL, tvmu=NULL, pgamma,
pmu=NULL, pcmu=NULL, ptvmu=NULL, pshape=NULL, pfamily=NULL,
par=NULL, pintercept=NULL, delta=NULL, envir=parent.frame(),
print.level=0, ndigit=10, gradtol=0.00001, steptol=0.00001,
fscale=1, iterlim=100, typsize=abs(p),stepmax=10*sqrt(p%*%p)){
#
# likelihood function for nlm
#
likel <- function(p){
if(ord)for(i in 1:states){
if(!all(diff(p[np4+l*(i-1)+(1:l)])>0))
p[np4+l*(i-1)+(1:l)] <- p[np4+l*(i-1)+1]*seq(1,1.1,length=l)}
if(is.function(muf))pmu0 <- muf(p[nm1:nmu])
if(is.function(cmuf))pmu1 <- cmuf(p[nm1:ncmu])
if(is.function(tvmuf))pmu2 <- tvmuf(p[ncmu1:np])
if(np>np1){
if(np3-np1==1)pshape <- rep(p[np3],states)
else pshape <- p[np2:np3]}
z <- .Fortran("cphidden_f",
x=as.double(p),
as.integer(states),
iq=as.integer(nosubj),
nobs=as.integer(nobs(response)),
mobs=as.integer(mobs),
s=as.double(if(mdl==4)y else response$response$y),
n=as.integer(response$response$n),
times=as.double(response$response$times),
l=as.integer(l),
pgamma=as.double(pgamma),
gamma=double(states*states),
gamma2=double(states*states),
val=double(states),
vec=double(states*states),
invec=double(states*states),
model=as.integer(mdl),
lgam=as.double(lgam),
ismu=as.logical(ismu),
pmu=as.double(pmu0),
pcmu=as.double(pmu1),
ptvmu=as.double(pmu2),
pshape=as.double(pshape),
pfam=as.double(p[np5]),
ppar=as.logical(!is.null(par)),
par=as.double(exp(p[np])),
delta=double(states),
nn=as.integer(nob),
filter=double(states*nob),
cf=as.logical(0),
a=double(states),
b=double(states*states),
c=double(states),
gmod=double(states*states),
rhs=double(states),
pivot=integer(states),
qraux=double(states),
work=double(2*states),
work2=double(states),
work3=double(states*states),
like=double(1),
#DUP=FALSE,
PACKAGE="repeated")
z$like}
#
# likelihood function returning parameter values
#
like <- function(p){
if(is.function(muf))pmu0 <- muf(p[nm1:nmu])
if(is.function(cmuf))pmu1 <- cmuf(p[nm1:ncmu])
if(is.function(tvmuf))pmu2 <- tvmuf(p[ncmu1:np])
if(np>np1){
if(np3-np1==1)pshape <- rep(p[np3],states)
else pshape <- p[np2:np3]}
z <- .Fortran("cphidden_f",
x=as.double(p),
as.integer(states),
iq=as.integer(nosubj),
nobs=as.integer(nobs(response)),
mobs=as.integer(mobs),
s=as.double(if(mdl==4)y else response$response$y),
n=as.integer(response$response$n),
times=as.double(response$response$times),
l=as.integer(l),
pgamma=as.double(pgamma),
gamma=double(states*states),
gamma2=double(states*states),
val=double(states),
vec=double(states*states),
invec=double(states*states),
model=as.integer(mdl),
lgam=as.double(lgam),
ismu=as.logical(ismu),
pmu=as.double(pmu0),
pcmu=as.double(pmu1),
ptvmu=as.double(pmu2),
pshape=as.double(pshape),
pfam=as.double(p[np5]),
ppar=as.logical(!is.null(par)),
par=as.double(exp(p[np])),
delta=double(states),
nn=as.integer(nob),
filter=double(states*nob),
cf=as.logical(1),
a=double(states),
b=double(states*states),
c=double(states),
gmod=double(states*states),
rhs=double(states),
pivot=integer(states),
qraux=double(states),
work=double(2*states),
work2=double(states),
work3=double(states*states),
like=double(1),
#DUP=FALSE,
PACKAGE="repeated")
z$gamma <- exp(p[1:nm])
z$gamma <- matrix(c(-z$gamma,z$gamma,0,0),byrow=TRUE,nrow=2)
z}
call <- sys.call()
#
# check distribution
#
tmp <- c("Bernoulli","Poisson","multinomial","continuation ratio",
"proportional odds","binomial","exponential","beta binomial",
"negative binomial","normal","inverse Gauss","logistic",
"Cauchy","Laplace","Levy","Pareto","gamma","Weibull",
"gen gamma","gen logistic","Hjorth","Burr","gen Weibull",
"gen extreme value","gen inverse Gauss","power exponential",
"skew Laplace","Student t")
mdl <- match(distribution <- match.arg(distribution,tmp),tmp)
if(mdl>3)mdl <- mdl+1
ord <- distribution=="continuation ratio"||distribution=="proportional odds"
ord2 <- !(!is.null(cmu)&&!is.null(tvmu))
if(!is.null(par)){
if(ord||distribution=="Bernoulli"||distribution=="multinomial")
stop("par not allowed with multinomial and ordinal responses")
else {
if(par<=0)stop("par must be positive")
par <- log(par)}}
states <- 2
#
# check extra parameters in distribution
#
if(mdl>8&&mdl!=30){
if(is.null(pshape))stop("pshape estimate must be supplied")
else if(length(pshape)!=1&&length(pshape)!=states)
stop(paste("pshape must have 1 or",states,"estimates"))}
else pshape <- NULL
if(mdl>19&&mdl!=30){
if(is.null(pfamily))stop("pfamily estimate must be supplied")
else if(length(pshape)!=1)
stop(paste("pshape must have one estimate"))}
else pfamily <- NULL
#
# check if a data object is being supplied
#
type <- "unknown"
respenv <- exists(deparse(substitute(response)),envir=parent.frame())&&
inherits(response,"repeated")&&!inherits(envir,"repeated")
if(respenv){
if(dim(response$response$y)[2]>1){
if(mdl==3)mdl <- 4
else stop("cphidden only handles univariate responses")}
if(!is.null(response$NAs)&&any(response$NAs))
stop("cphidden does not handle data with NAs")
type <- response$response$type}
envname <- if(respenv)deparse(substitute(response))
else if(!is.null(class(envir)))deparse(substitute(envir))
else NULL
#
#if response is not a data object, make one
#
if(!respenv){
if(inherits(envir,"repeated")){
if(!is.null(envir$NAs)&&any(envir$NAs))
stop("cphidden does not handle data with NAs")
cn <- deparse(substitute(response))
if(length(grep("\"",cn))>0)cn <- response
if(length(cn)>1){
if(mdl==3)mdl <- 4
else stop("only one response variable allowed")}
response <- envir
col <- match(cn,colnames(response$response$y))
if(is.na(col))stop(paste("response variable",cn,"not found"))
type <- response$response$type[col]
if(dim(response$response$y)[2]>1){
response$response$y <- response$response$y[,col,drop=FALSE]
if(!is.null(response$response$delta)){
response$response$delta <- response$response$delta[,col,drop=FALSE]
if(all(response$response$delta==1)||all(is.na(response$response$delta)))response$response$delta <- NULL}}}
else {
if(!inherits(response,"response")){
if(is.vector(response,mode="numeric"))
response <- matrix(response,nrow=1)
response <- restovec(response,times=times,totals=totals,delta=delta)}
type <- response$type
response <- rmna(response=response)}}
#
# check if response is appropriate for distribution
#
if(is.null(response$response$times))stop("no times available")
if(distribution=="binomial"||distribution=="beta binomial"){
if(type!="unknown"&&type!="nominal")stop("nominal data required")
if(is.null(response$response$n))stop("totals must be supplied")}
if(mdl<11){
if((distribution=="Poisson"||distribution=="negative binomial")
&&type!="unknown"&&type!="discrete")
stop("discrete data required")
if(distribution=="Bernoulli"){
if(type!="unknown"&&type!="nominal")
stop("nominal data required")
if(any(response$response$y!=0&response$response$y!=1))
stop("responses must be binary for Bernoulli")}
if(distribution=="multinomial"
&&type!="unknown"&&type!="nominal"&&type!="ordinal")
stop("nominal or ordinal data required")
if((distribution=="continuation ratio"||
distribution=="proportional odds")
&&type!="unknown"&&type!="ordinal")
stop("ordinal data required")
if(any(response$response$y<0))stop("all responses must be non-negative")}
else if(mdl!=11&&mdl!=13&&mdl!=14&&mdl!=15&&mdl!=16&&mdl!=21&&mdl!=27
&&mdl!=28&&mdl!=29&&mdl!=30){
if(type!="unknown"&&type!="duration"&&type!="continuous")
stop("duration data required")
if(any(response$response$y<=0))stop("all responses must be positive")}
else if(mdl==30){
if(any(response$response$y!=0&response$response$y!=1))
stop(paste("responses must be binary for",distribution))}
else if(type!="unknown"&&type!="continuous"&&type!="duration")
stop("continuous data required")
lgam <- NULL
if(mdl==3||ord){
l <- length(unique(response$response$y))-1
if(min(response$response$y)!=0||max(response$response$y)!=l)
stop(paste("multinomial and ordinal categories must be numbered from 0 to",l))
if(l<1)stop("multinomial and ordinal responses must have at least 2 categories")}
else if(mdl==4){
l <- dim(response$response$y)[2]-1
lgam <- lgamma(apply(response$response$y,1,sum)+1)-
apply(lgamma(response$response$y+1),1,sum)
y <- as.vector(t(response$response$y))}
else l <- 1
if(ord){
if(length(pintercept)!=l*states)
stop(paste("pintercept should contain",l*states,"estimates"))
for(i in 1:states){
if(!all(diff(pintercept[(i-1)*l+(1:l)])>0))
stop("intercepts must be monotone increasing for each state")}}
else pintercept <- NULL
if(!is.null(response$response$nest)&&!is.null(par))
stop("cphidden does not handle two levels of nesting with an AR")
if(!is.null(response$response$censor))
stop("cphidden does not handle censoring")
nosubj <- length(nobs(response))
mobs <- max(nobs(response))
nob <- dim(response$response$y)[1]
ismu <- !is.null(mu)
if(ismu)cmu <- tvmu <- pcmu <- ptvmu <- NULL
else pmu <- NULL
#
# if a data object was supplied, modify formulae or functions to read from it
#
muf <- mu1 <- mu3 <- cmuf <- cmu1 <- cmu3 <- tvmuf <- tvmu1 <- tvmu3 <- NULL
if(respenv||inherits(envir,"repeated")||inherits(envir,"tccov")||inherits(envir,"tvcov")){
if(!is.null(mu)){
cl <- is.list(mu)
if(!cl)mu <- list(mu)
tmp2 <- mu3 <- list()
for(i in 1:length(mu)){
if(inherits(mu[[i]],"formula")){
mu3 <- c(mu3,list(if(respenv)finterp(mu[[i]],.envir=response,.name=envname,.intercept=!ord)
else finterp(mu[[i]],.envir=envir,.name=envname,.intercept=!ord)))
tmp2 <- c(tmp2,list(mu[[i]]))}
else if(is.function(mu[[i]])){
tmp <- parse(text=deparse(mu[[i]])[-1])
tmp1 <- if(respenv)fnenvir(mu[[i]],.envir=response,.name=envname)
else fnenvir(mu[[i]],.envir=envir,.name=envname)
tmp2 <- c(tmp2,list(tmp1))
attr(tmp1,"model") <- tmp
mu3 <- c(mu3,list(tmp1))}}
mu <- tmp2
rm(tmp2)
if(!cl){
mu <- mu[[1]]
mu3 <- mu3[[1]]}}
if(!is.null(cmu)){
cl <- is.list(cmu)
if(!cl)cmu <- list(cmu)
tmp2 <- cmu3 <- list()
for(i in 1:length(cmu)){
if(inherits(cmu[[i]],"formula")){
cmu3 <- c(cmu3,list(if(respenv)finterp(cmu[[i]],.envir=response,.name=envname,.intercept=!ord)
else finterp(cmu[[i]],.envir=envir,.name=envname,.intercept=!ord)))
tmp2 <- c(tmp2,list(cmu[[i]]))}
else if(is.function(cmu[[i]])){
tmp <- parse(text=deparse(cmu[[i]])[-1])
tmp1 <- if(respenv)fnenvir(cmu[[i]],.envir=response,.name=envname,.expand=FALSE)
else fnenvir(cmu[[i]],.envir=envir,.name=envname,.expand=FALSE)
tmp2 <- c(tmp2,list(tmp1))
attr(tmp1,"model") <- tmp
cmu3 <- c(cmu3,list(tmp1))}}
cmu <- tmp2
rm(tmp2)
if(!cl){
cmu <- cmu[[1]]
cmu3 <- cmu3[[1]]}}
if(!is.null(tvmu)){
cl <- is.list(tvmu)
if(!cl)tvmu <- list(tvmu)
tmp2 <- tvmu3 <- list()
for(i in 1:length(tvmu)){
if(inherits(tvmu[[i]],"formula")){
tvmu3 <- c(tvmu3,list(if(respenv)finterp(tvmu[[i]],.envir=response,.name=envname,.intercept=!ord)
else finterp(tvmu[[i]],.envir=envir,.name=envname,.intercept=!ord)))
tmp2 <- c(tmp2,list(tvmu[[i]]))}
else if(is.function(tvmu[[i]])){
tmp <- parse(text=deparse(tvmu[[i]])[-1])
tmp1 <- if(respenv)fnenvir(tvmu[[i]],.envir=response,.name=envname)
else fnenvir(tvmu[[i]],.envir=envir,.name=envname)
tmp2 <- c(tmp2,list(tmp1))
attr(tmp1,"model") <- tmp
tvmu3 <- c(tvmu3,list(tmp1))}}
tvmu <- tmp2
rm(tmp2)
if(!cl){
tvmu <- tvmu[[1]]
tvmu3 <- tvmu3[[1]]}}}
#
# transform general formulae to functions and check number of parameters
#
npr0 <- if(ord)length(pmu)/states else length(pmu)/states/l
start <- NULL
if(inherits(mu,"formula")){
mu1 <- if(respenv)finterp(mu,.envir=response,.name=envname,.intercept=!ord)
else finterp(mu,.envir=envir,.name=envname,.intercept=!ord)
npt0 <- length(attr(mu1,"parameters"))
if(is.character(attr(mu1,"model"))){
# W&R formula
if(ord&&length(attr(mu1,"model"))==0)mu1 <- NULL}
else {
# formula with unknowns
if(npr0!=npt0){
cat("\nParameters are ")
cat(attr(mu1,"parameters"),"\n")
stop(paste("pmu should have",if(ord) npt0*states else npt0*states*l,"estimates"))}
if(is.list(pmu))pmu <- unlist(pmu)}
if(is.null(mu1))pmu <- NULL}
else if(is.list(mu)){
if(!ord&&length(mu)!=states*l)
stop(paste("list of mu formulae or functions must have length",states*l))
if(ord&&length(mu)!=states)
stop(paste("list of mu formulae or functions must have length",states))
# only count parameters if list of formulae
if(inherits(mu[[1]],"formula"))start <- 1
tmp <- list()
for(i in mu)if(inherits(i,"formula")){
mu1 <- if(respenv)finterp(i,.envir=response,.name=envname,.start=start,.intercept=!ord)
else finterp(i,.envir=envir,.name=envname,.start=start,.intercept=!ord)
npt0 <- length(attr(mu1,"parameters"))
if(ord&&is.null(attr(mu1,"model")))
stop("all formulae must contain covariates")
if(is.list(pmu))pmu <- unlist(pmu)
# make new list and count parameters
tmp <- c(tmp,list(mu1))
start <- start+npt0}
else if(is.function(i)){
if(inherits(i,"formulafn"))start <- c(start,attr(i,"parameters"))
tmp <- c(tmp,list(i))}
if(!is.null(start)){
if(is.numeric(start))start <- start-1
else start <- length(unique(start))}
mu1 <- tmp
rm(tmp)}
else if(!is.null(mu))mu1 <- mu
#
# give appropriate attributes to mu1 for printing
#
if(!is.null(mu1)&&is.null(attr(mu1,"parameters"))){
attributes(mu1) <- if(is.function(mu)){
if(!inherits(mu,"formulafn")){
if(respenv)attributes(fnenvir(mu,.envir=response))
else attributes(fnenvir(mu,.envir=envir))}
else attributes(mu)}
else {
if(respenv)attributes(fnenvir(mu1,.envir=response))
else attributes(fnenvir(mu1,.envir=envir))}}
#
# if possible, check that correct number of estimates was supplied
#
if(!is.list(mu)){
nlp <- if(is.function(mu1))length(attr(mu1,"parameters"))
else if(is.null(mu1))NULL
else npt0
if(!is.null(nlp)&&nlp!=npr0)
stop(paste("pmu should have",if(ord)nlp*states else nlp*states*l,"initial estimates"))}
if(!is.null(start)&&start!=length(pmu))
stop(paste("pmu should have",start,"initial estimates"))
#
# transform time-constant formulae to functions and check number of parameters
#
npr1 <- if(ord)length(pcmu)/states else length(pcmu)/states/l
start <- NULL
if(inherits(cmu,"formula")){
cmu1 <- if(respenv)finterp(cmu,.envir=response,.expand=FALSE,.name=envname,.intercept=!ord)
else finterp(cmu,.envir=envir,.expand=FALSE,.name=envname,.intercept=!ord)
npt1 <- length(attr(cmu1,"parameters"))
if(is.character(attr(cmu1,"model"))){
# W&R formula
if(length(attr(cmu1,"model"))==1&&length(cmu1(pcmu))!=nosubj){
tmp <- function(p) rep(p[1],nosubj)
attributes(tmp) <- attributes(cmu1)
cmu1 <- tmp
rm(tmp)}
if(ord&&length(attr(cmu1,"model"))==0)cmu1 <- NULL}
else {
# formula with unknowns
if(npr1!=npt1){
cat("\nParameters are ")
cat(attr(cmu1,"parameters"),"\n")
stop(paste("pcmu should have",if(ord)npt1*states
else npt1*states*l,"estimates"))}
if(is.list(pcmu))pcmu <- unlist(pcmu)}
if(is.null(cmu1))pcmu <- NULL}
else if(is.list(cmu)){
if(!ord&&length(cmu)!=states*l)
stop(paste("list of cmu formulae or functions must have length",states*l))
if(ord&&length(cmu)!=states)
stop(paste("list of cmu formulae or functions must have length",states))
# only count parameters if list of formulae
if(inherits(cmu[[1]],"formula"))start <- 1
tmp <- list()
for(i in cmu)if(inherits(i,"formula")){
cmu1 <- if(respenv)finterp(i,.envir=response,.expand=FALSE,.name=envname,.start=start,.intercept=!ord)
else finterp(i,.envir=envir,.expand=FALSE,.name=envname,.start=start,.intercept=!ord)
npt1 <- length(attr(cmu1,"parameters"))
if(is.character(attr(cmu1,"model"))){
# W&R formula
if(ord&&length(attr(cmu1,"model"))==1)cm1 <- NULL}
else if(is.list(pcmu))pcmu <- unlist(pcmu)
# make new list and count parameters
tmp <- c(tmp,list(cmu1))
start <- start+length(attr(cmu1,"parameters"))}
else if(is.function(i)){
if(inherits(i,"formulafn"))start <- c(start,attr(i,"parameters"))
tmp <- c(tmp,list(i))}
if(!is.null(start)){
if(is.numeric(start))start <- start-1
else start <- length(unique(start))}
cmu1 <- tmp
rm(tmp)}
else if(!is.null(cmu))cmu1 <- cmu
#
# give appropriate attributes to cmu1 for printing
#
if(!is.null(cmu1)&&is.null(attr(cmu1,"parameters"))){
attributes(cmu1) <- if(is.function(cmu)){
if(!inherits(cmu,"formulafn")){
if(respenv)attributes(fnenvir(cmu,.envir=response))
else attributes(fnenvir(cmu,.envir=envir))}
else attributes(cmu)}
else {
if(respenv)attributes(fnenvir(cmu1,.envir=response))
else attributes(fnenvir(cmu1,.envir=envir))}}
#
# if possible, check that correct number of estimates was supplied
#
if(!is.function(cmu)&&!is.list(cmu)){
nlp <- if(is.function(cmu1))length(attr(cmu1,"parameters"))
else if(is.null(cmu1))NULL
else npt1
if(!is.null(nlp)&&nlp!=npr1)
stop(paste("pcmu should have",if(ord)nlp*states else nlp*states*l,"initial estimates"))}
if(!is.null(start)&&start!=length(pcmu))
stop(paste("pcmu should have",start,"initial estimates"))
#
# transform time-varying formulae to functions and check number of parameters
#
npr2 <- if(ord)length(ptvmu)/states else length(ptvmu)/states/l
start <- NULL
if(inherits(tvmu,"formula")){
tvmu1 <- if(respenv)finterp(tvmu,.envir=response,.name=envname,.intercept=!ord)
else finterp(tvmu,.envir=envir,.name=envname,.intercept=!ord)
npt2 <- length(attr(tvmu1,"parameters"))
if(is.character(attr(tvmu1,"model"))){
# W&R formula
if(length(attr(tvmu1,"model"))==1&&length(tvmu1(ptvmu))!=mobs){
tmp <- function(p) rep(p[1],mobs)
attributes(tmp) <- attributes(tvmu1)
tvmu1 <- tmp
rm(tmp)}
else if(ord&&length(attr(tvmu1,"model"))==0)tvmu1 <- NULL}
else {
# formula with unknowns
if(npr2!=npt2){
cat("\nParameters are ")
cat(attr(tvmu1,"parameters"),"\n")
stop(paste("ptvmu should have",if(ord) npt2*states else npt2*states*l,"estimates"))}
if(is.list(ptvmu))ptvmu <- unlist(ptvmu)}
if(is.null(tvmu1))ptvmu <- NULL}
else if(is.list(tvmu)){
if(!ord&&length(tvmu)!=states*l)
stop(paste("list of tvmu formulae or functions must have length",states*l))
if(ord&&length(tvmu)!=states)
stop(paste("list of tvmu formulae or functions must have length",states))
# only count parameters if list of formulae
if(inherits(tvmu[[1]],"formula"))start <- 1
tmp <- list()
for(i in tvmu)if(inherits(i,"formula")){
tvmu1 <- if(respenv)finterp(i,.envir=response,.expand=FALSE,.name=envname,.start=start,.intercept=!ord)
else finterp(i,.envir=envir,.expand=FALSE,.name=envname,.start=start,.intercept=!ord)
npt2 <- length(attr(tvmu1,"parameters"))
if(is.character(attr(tvmu1,"model"))){
# W&R formula (don't know how to change index of p[i])
if(ord&&length(attr(tvmu1,"model"))==1)tvm1 <- NULL}
else if(is.list(ptvmu))ptvmu <- unlist(ptvmu)
# make new list and count parameters
tmp <- c(tmp,list(tvmu1))
start <- start+length(attr(tvmu1,"parameters"))}
else if(is.function(i)){
if(inherits(i,"formulafn"))start <- c(start,attr(i,"parameters"))
tmp <- c(tmp,list(i))}
if(!is.null(start)){
if(is.numeric(start))start <- start-1
else start <- length(unique(start))}
tvmu1 <- tmp
rm(tmp)}
else if(!is.null(tvmu))tvmu1 <- tvmu
#
# give appropriate attributes to tvmu1 for printing
#
if(!is.null(tvmu1)&&is.null(attr(tvmu1,"parameters"))){
attributes(tvmu1) <- if(is.function(tvmu)){
if(!inherits(tvmu,"formulafn")){
if(respenv)attributes(fnenvir(tvmu,.envir=response))
else attributes(fnenvir(tvmu,.envir=envir))}
else attributes(tvmu)}
else {
if(respenv)attributes(fnenvir(tvmu1,.envir=response))
else attributes(fnenvir(tvmu1,.envir=envir))}}
#
# if possible, check that correct number of estimates was supplied
#
if(!is.function(tvmu)&&!is.list(tvmu)){
nlp <- if(is.function(tvmu1))length(attr(tvmu1,"parameters"))
else if(is.null(tvmu1))NULL
else npt2
if(!is.null(nlp)&&nlp!=npr2)
stop(paste("ptvmu should have",if(ord)nlp*states else nlp*states*l,"initial estimates"))}
if(!is.null(start)&&start!=length(ptvmu))
stop(paste("ptvmu should have",start,"initial estimates"))
#
# set up general regression function for likelihood
# if arg==FALSE, can print out general parameter estimates as matrices
#
arg <- TRUE
if(ord&&is.null(mu1))arg <- FALSE
if(is.function(mu1)){
if(!ord&&is.null(pmu))stop("Initial values of pmu must be supplied")
tmp <- mu1(pmu)
if(length(tmp)!=nob)
stop("mu function or formula must return a vector with one element per observation")
if(any(is.na(tmp))||any(abs(tmp)==Inf))stop("mu returns NAs or Infs")
rm(tmp)
# will be able to print coefficients as matrices
arg <- FALSE
# create regression function by repeatedly calling
# function or formula supplied
if(distribution=="multinomial"){
zm <- array(0,c(nob,states,l))
muf <- function(p){
k <- 0
for(j in 1:l)for(i in 1:states){
k <- k+1
zm[,i,j] <- mu1(p[(1:npr0)+(k-1)*npr0])}
zm}}
else if(ord){
zm <- array(0,c(nob,states,l))
muf <- function(p){
k <- 0
for(i in 1:states){
tmp <- mu1(p[(1:npr0)+(i-1)*npr0])
for(j in 1:l){
k <- k+1
zm[,i,j] <- p[np0+k]+tmp}}
zm}}
else {
muf <- function(p){
z <- NULL
for(i in 1:states)
z <- cbind(z,mu1(p[(1:npr0)+(i-1)*npr0]))
z}}
attributes(muf) <- attributes(mu)}
else if(is.list(mu1)){
if(is.null(pmu))stop("Initial values of pmu must be supplied")
for(i in mu1)if(length(i(pmu))!=nob)stop("each mu function or formula must return a vector with one element per observation")
# create one regression function from list
if(distribution=="multinomial"){
zm <- array(0,c(nob,states,l))
muf <- function(p){
k <- 0
for(j in 1:l)for(i in 1:states){
k <- k+1
zm[,i,j] <- mu1[[k]](p)}
zm}}
else if(ord){
zm <- array(0,c(nob,states,l))
muf <- function(p){
k <- 0
for(i in 1:states){
tmp <- mu1[[i]](p)
for(j in 1:l){
k <- k+1
zm[,i,j] <- p[np0+k]+tmp}}
zm}}
else {
muf <- function(p){
z <- NULL
for(i in mu1)z <- cbind(z,i(p))
z}}}
else pmu0 <- NULL
#
# set up time-constant regression function for likelihood
# if arc==FALSE, can print out time-constant parameter estimates as matrices
#
arc <- TRUE
if(is.function(cmu1)){
if(!ord&&is.null(pcmu))stop("Initial values of pcmu must be supplied")
# check if array returned or one function/formula for all states
tmp <- cmu1(pcmu)
d <- dim(tmp)
if(length(d)==0){
# one formula or function
if(length(tmp)!=nosubj)
stop("cmu function or formula must return a vector with one element per individual")
if(any(is.na(tmp))||any(abs(tmp)==Inf))
stop("cmu returns NAs or Infs")
rm(tmp)
# will be able to print coefficients as matrices
arc <- FALSE
# create regression function by repeatedly calling
# function or formula supplied
if(distribution=="multinomial"){
zmc <- array(0,c(nosubj,states,l))
cmuf <- function(p){
k <- 0
for(j in 1:l)for(i in 1:states){
k <- k+1
zmc[,i,j] <- cmu1(p[(1:npr1)+(k-1)*npr1])}
zmc}}
else if(ord){
zmc <- array(0,c(nosubj,states,l))
cmuf <- function(p){
k <- 0
for(i in 1:states){
tmp <- cmu1(p[(1:npr1)+(i-1)*npr1])
for(j in 1:l){
k <- k+1
zmc[,i,j] <- p[np0+k]+tmp}}
zmc}}
else {
cmuf <- function(p){
z <- NULL
for(i in 1:states)
z <- cbind(z,cmu1(p[(1:npr1)+(i-1)*npr1]))
z}}
attributes(cmuf) <- attributes(cmu)}
else {
# returns an array: check dimensions
if(d[2]!=states)stop(paste("cmu must return a",states,"column array"))
if(d[1]!=nosubj)
stop("cmu must return an array with one row per individual")
if(distribution=="multinomial"){
if(length(d)!=3)
stop("cmu must return a 3 dimensional array")
if(d[3]!=l)
stop(paste("cmu must return an array with",l,"layers"))}
else if(length(d)!=2)
stop("cmu must return a 2 dimensional array")
arc <- FALSE
cmuf <- cmu1}}
else if(is.list(cmu1)){
if(is.null(pcmu))stop("Initial values of pcmu must be supplied")
for(i in cmu1)if(length(i(pcmu))!=nosubj)stop("each cmu function or formula must return a vector with one element per individual")
# create one regression function from list
if(distribution=="multinomial"){
zmc <- array(0,c(nosubj,states,l))
cmuf <- function(p){
k <- 0
for(j in 1:l)for(i in 1:states){
k <- k+1
zmc[,i,j] <- cmu1[[k]](p)}
zmc}}
else if(ord){
zmc <- array(0,c(nosubj,states,l))
cmuf <- function(p){
k <- 0
for(i in 1:states){
tmp <- cmu1[[i]](p)
for(j in 1:l){
k <- k+1
zmc[,i,j] <- p[np0+k]+tmp}}
zmc}}
else {
cmuf <- function(p){
z <- NULL
for(i in cmu1)z <- cbind(z,i(p))
z}}}
else pmu1 <- array(0,c(states,nosubj,l))
#
# set up time-varying regression function for likelihood
# if arv==FALSE, can print out time-varying parameter estimates as matrices
#
arv <- TRUE
if(is.function(tvmu1)){
if(!ord&&is.null(ptvmu))stop("Initial values of ptvmu must be supplied")
# check if array returned or one function/formula for all states
tmp <- tvmu1(ptvmu)
d <- dim(tmp)
if(length(d)==0){
# one formula or function
if(length(tmp)!=mobs)
stop("tvmu function or formula must return a vector with one element per time point")
if(any(is.na(tmp))||any(abs(tmp)==Inf))
stop("tvmu returns NAs or Infs")
rm(tmp)
# will be able to print coefficients as matrices
arv <- FALSE
# create regression function by repeatedly calling
# function or formula supplied
if(distribution=="multinomial"){
zmv <- array(0,c(mobs,states,l))
tvmuf <- function(p){
k <- 0
for(j in 1:l)for(i in 1:states){
k <- k+1
zmv[,i,j] <- tvmu1(p[(1:npr2)+(k-1)*npr2])}
zmv}}
else if(ord){
zmv <- array(0,c(mobs,states,l))
tvmuf <- function(p){
k <- 0
for(i in 1:states){
tmp <- tvmu1(p[(1:npr2)+(i-1)*npr2])
for(j in 1:l){
k <- k+1
zmv[,i,j] <- ord2*p[np0+k]+tmp}}
zmv}}
else {
tvmuf <- function(p){
z <- NULL
for(i in 1:states)
z <- cbind(z,tvmu1(p[(1:npr2)+(i-1)*npr2]))
z}}
attributes(tvmuf) <- attributes(tvmu)}
else {
# returns an array: check dimensions
if(d[2]!=states)stop(paste("tvmu must return a",states,"column array"))
else if(d[1]!=mobs)
stop("tvmu must return an array with one row per time point")
if(distribution=="multinomial"){
if(length(d)!=3)
stop("tvmu must return a 3 dimensional array")
if(d[3]!=l)
stop(paste("tvmu must return an array with",l,"layers"))}
else if(length(d)!=2)
stop("tvmu must return a 2 dimensional array")
arv <- FALSE
tvmuf <- tvmu1}}
else if(is.list(tvmu1)){
if(is.null(ptvmu))stop("Initial values of ptvmu must be supplied")
for(i in tvmu1)if(length(i(ptvmu))!=mobs)stop("each tvmu function or formula must return a vector with one element per time point")
# create one regression function from list
if(distribution=="multinomial"){
zmv <- array(0,c(mobs,states,l))
tvmuf <- function(p){
k <- 0
for(j in 1:l)for(i in 1:states){
k <- k+1
zmv[,i,j] <- tvmu1[[k]](p)}
zmv}}
else if(ord){
zmv <- array(0,c(mobs,states,l))
tvmuf <- function(p){
k <- 0
for(i in 1:states){
tmp <- tvmu1[[i]](p)
for(j in 1:l){
k <- k+1
zmv[,i,j] <- ord2*p[np0+k]+tmp}}
zmv}}
else {
tvmuf <- function(p){
z <- NULL
for(i in tvmu1)z <- cbind(z,i(p))
z}}}
else pmu2 <- array(0,c(states,mobs,l))
if(!is.function(muf)&&!is.function(cmuf)&&!is.function(tvmuf)){
if(ord){
if(is.null(pintercept))
stop(paste("pintercept must contain ",l," initial estimates",sep=""))
else {
ismu <- TRUE
zm <- array(0,c(nob,states,l))
muf <- function(p){
k <- 0
for(i in 1:states){
tmp <- rep(1,nob)
for(j in 1:l){
k <- k+1
zm[,i,j] <- p[np0+k]*tmp}}
zm}}}
else stop("Either mu, cmu or tvmu must be a list, function, or formula")}
#
# prepare to call nlm
#
nm <- length(pgamma)
nm1 <- nm+1
nmu <- nm+length(pmu)+length(pintercept)
ncmu <- nm+length(pcmu)+length(ptvmu)+length(pintercept)
ncmu1 <- nm+length(pcmu)+1
p <- c(log(pgamma),pmu,pcmu,ptvmu,pshape,pfamily,pintercept,par)
np <- length(p)
np0 <- np-nm-length(pintercept)-length(par)
np1 <- np-length(pshape)-length(pfamily)-length(pintercept)-length(par)
np2 <- np1+1
np3 <- np-length(pfamily)-length(pintercept)-length(par)
np4 <- np-length(pintercept)-length(par)
np5 <- np-length(par)
pshape <- rep(0,states)
z <- nlm(likel,p, hessian=TRUE, print.level=print.level,
typsize=typsize, ndigit=ndigit, gradtol=gradtol, stepmax=stepmax,
steptol=steptol, iterlim=iterlim, fscale=fscale)
#
# prepare mle's
#
delta <- if(!is.null(response$response$delta))
sum(log(response$response$delta)) else 0
maxlike <- z$minimum - delta
z0 <- like(z$estimate)
#
# calculate se's
#
a <- if(any(is.na(z$hessian))||any(abs(z$hessian)==Inf))0
else qr(z$hessian)$rank
if(a==np)cov <- solve(z$hessian)
else cov <- matrix(NA,ncol=np,nrow=np)
se <- sqrt(diag(cov))
corr <- cov/(se%o%se)
#
# calculate predicted values
#
if(mdl<3||mdl>6){
rpred <- 0
if(is.function(muf)){
rpred <- rpred+t(muf(z$estimate[nm1:nmu]))
if(dim(rpred)[2]!=nob)rpred <- rpred[,rep(1:nosubj,nobs(response))]}
if(is.function(cmuf))rpred <- rpred+t(cmuf(z$estimate[nm1:ncmu]))[,rep(1:nosubj,nobs(response))]
if(is.function(tvmuf))rpred <- rpred+t(tvmuf(z$estimate[ncmu1:np]))[,sequence(nobs(response))]
if(mdl==1||mdl==7)rpred <- 1/(1+exp(-rpred))
pred <- rep(1,states)%*%(rpred*z0$delta)
rpred <- rep(1,states)%*%(rpred*matrix(z0$filter,nrow=states))}
else pred <- rpred <- NULL
#
# return appropriate attributes on functions
#
if(!is.null(mu3))mu1 <- mu3
if(!is.null(cmu3))cmu1 <- cmu3
if(!is.null(tvmu3))tvmu1 <- tvmu3
z1 <- list(
call=call,
type="continuous",
changepoint=TRUE,
distribution=distribution,
response=response$response,
maxlike=maxlike,
aic=maxlike+np,
df=length(response$response$y)-np,
states=states,
levels=l,
mu=mu1,
arg=arg,
cmu=cmu1,
arc=arc,
arv=arv,
tvmu=tvmu1,
coef=z$estimate[nm1:np1],
pshape=if(np3>np1&&!ord)z$estimate[np2:np3] else NULL,
pfamily=if(np>np3+!is.null(par)&&!ord)z$estimate[np] else NULL,
pintercept=if(is.null(pintercept)) NULL else z$estimate[np2:np],
nmu=length(pmu),
ncmu=length(pcmu),
ntvmu=length(ptvmu),
gamma=matrix(z0$gamma,ncol=states),
delta=z0$delta,
par=if(!is.null(par))z0$par else NULL,
np=np,
cov=cov,
corr=corr,
se=se,
filter=matrix(z0$filter,nrow=states),
pred=pred,
rpred=rpred,
iterations=z$iter,
code=z$code)
class(z1) <- if(is.null(rpred))"hidden" else c("hidden","recursive")
z1}
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Defines functions cphidden
Documented in cphidden
#
# repeated : A Library of Repeated Measurements Models
# Copyright (C) 1998, 1999, 2000, 2001 J.K. Lindsey
#
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public Licence as published by
# the Free Software Foundation; either version 2 of the Licence, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public Licence for more details.
#
# You should have received a copy of the GNU General Public Licence
# along with this program; if not, write to the Free Software
# Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
#
# SYNOPSIS
#
# cphidden(response=NULL, totals=NULL, times=NULL, distribution="Bernoulli",
# mu=NULL, cmu=NULL, tvmu=NULL, pgamma, pmu=NULL, pcmu=NULL, ptvmu=NULL,
# pshape=NULL, pfamily=NULL, par=NULL, pintercept=NULL, delta=NULL,
# envir=parent.frame(), print.level=0, ndigit=10, gradtol=0.00001,
# steptol=0.00001, fscale=1, iterlim=100, typsize=abs(p),
# stepmax=10*sqrt(p%*%p))
#
# DESCRIPTION
#
# A function to find a changepoint using a hidden Markov chain
# model in continuous time
##' Changepoint Location using a Continuous-time Two-state Hidden Markov Chain
##'
##' \code{cphidden} fits a two-state hidden Markov chain model with a variety
##' of distributions in continuous time in order to locate a changepoint in the
##' chosen distribution. All series on different individuals are assumed to
##' start at the same time point.
##'
##' For quantitative responses, specifying \code{par} allows an `observed'
##' autoregression to be fitted as well as the hidden Markov chain.
##'
##' All functions and formulae for the location parameter are on the
##' (generalized) logit scale for the Bernoulli, binomial, and multinomial
##' distributions.
##'
##' If \code{cmu} and \code{tvmu} are used, these two mean functions are
##' additive so that interactions between time-constant and time-varying
##' variables are not possible.
##'
##' The algorithm will run more quickly if the most frequently occurring time
##' step is scaled to be equal to unity.
##'
##' The object returned can be plotted to give the probabilities of being in
##' each hidden state at each time point. See \code{\link[repeated]{hidden}}
##' for details. For distributions other than the multinomial, proportional
##' odds, and continuation ratio, the (recursive) predicted values can be
##' plotted using \code{\link[rmutil]{mprofile}} and
##' \code{\link[rmutil]{iprofile}}.
##'
##'
##' @param response A list of two or three column matrices with counts or
##' category indicators, times, and possibly totals (if the distribution is
##' binomial), for each individual, one matrix or dataframe of counts, or an
##' object of class, \code{response} (created by
##' \code{\link[rmutil]{restovec}}) or \code{repeated} (created by
##' \code{\link[rmutil]{rmna}} or \code{\link[rmutil]{lvna}}). If the
##' \code{repeated} data object contains more than one response variable, give
##' that object in \code{envir} and give the name of the response variable to
##' be used here. If there is only one series, a vector of responses may be
##' supplied instead.
##'
##' Multinomial and ordinal categories must be integers numbered from 0.
##' @param totals If response is a matrix, a corresponding matrix of totals if
##' the distribution is binomial. Ignored if response has class,
##' \code{response} or \code{repeated}.
##' @param times If \code{response} is a matrix, a vector of corresponding
##' times, when they are the same for all individuals. Ignored if response has
##' class, \code{response} or \code{repeated}.
##' @param distribution Bernoulli, Poisson, multinomial, proportional odds,
##' continuation ratio, binomial, exponential, beta binomial, negative
##' binomial, normal, inverse Gauss, logistic, gamma, Weibull, Cauchy, Laplace,
##' Levy, Pareto, gen(eralized) gamma, gen(eralized) logistic, Hjorth, Burr,
##' gen(eralized) Weibull, gen(eralized) extreme value, gen(eralized) inverse
##' Gauss, power exponential, skew Laplace, or Student t. (For definitions of
##' distributions, see the corresponding [dpqr]distribution help.)
##' @param mu A general location function with two possibilities: (1) a list of
##' formulae (with parameters having different names) or functions (with one
##' parameter vector numbering for all of them) each returning one value per
##' observation; or (2) a single formula or function which will be used for all
##' states (and all categories if multinomial) but with different parameter
##' values in each so that pmu must be a vector of length the number of
##' unknowns in the function or formula times the number of states (times the
##' number of categories minus one if multinomial).
##' @param cmu A time-constant location function with three possibilities: (1)
##' a list of formulae (with parameters having different names) or functions
##' (with one parameter vector numbering for all of them) each returning one
##' value per individual; (2) a single formula or function which will be used
##' for all states (and all categories if multinomial) but with different
##' parameter values in each so that pcmu must be a vector of length the number
##' of unknowns in the function or formula times the number of states (times
##' the number of categories minus one if multinomial); or (3) a function
##' returning an array with one row for each individual, one column for each
##' state of the hidden Markov chain, and, if multinomial, one layer for each
##' category but the last. If used, this function or formula should contain the
##' intercept. Ignored if \code{mu} is supplied.
##' @param tvmu A time-varying location function with three possibilities: (1)
##' a list of formulae (with parameters having different names) or functions
##' (with one parameter vector numbering for all of them) each returning one
##' value per time point; (2) a single formula or function which will be used
##' for all states (and all categories if multinomial) but with different
##' parameter values in each so that ptvmu must be a vector of length the
##' number of unknowns in the function or formula times the number of states
##' (times the number of categories minus one if multinomial); or (3) a
##' function returning an array with one row for each time point, one column
##' for each state of the hidden Markov chain, and, if multinomial, one layer
##' for each category but the last. This function or formula is usually a
##' function of time; it is the same for all individuals. It only contains the
##' intercept if \code{cmu} does not. Ignored if \code{mu} is supplied.
##' @param pgamma An initial estimate of the transition intensity between the
##' two states in the continuous-time hidden Markov chain.
##' @param pmu Initial estimates of the unknown parameters in \code{mu}.
##' @param pcmu Initial estimates of the unknown parameters in \code{cmu}.
##' @param ptvmu Initial estimates of the unknown parameters in \code{tvmu}.
##' @param pshape Initial estimate(s) of the dispersion parameter, for those
##' distributions having one. This can be one value or a vector with a
##' different value for each state.
##' @param pfamily Initial estimate of the family parameter, for those
##' distributions having one.
##' @param par Initial estimate of the autoregression parameter.
##' @param pintercept For multinomial, proportional odds, and continuation
##' ratio models, \code{p-2} initial estimates for intercept contrasts from the
##' first intercept, where \code{p} is the number of categories.
##' @param delta Scalar or vector giving the unit of measurement (always one
##' for discrete data) for each response value, set to unity by default. For
##' example, if a response is measured to two decimals, delta=0.01. If the
##' response is transformed, this must be multiplied by the Jacobian. For
##' example, with a log transformation, \code{delta=1/response}. Ignored if
##' response has class, \code{response} or \code{repeated}.
##' @param envir Environment in which model formulae are to be interpreted or a
##' data object of class, \code{repeated}, \code{tccov}, or \code{tvcov}; the
##' name of the response variable should be given in \code{response}. If
##' \code{response} has class \code{repeated}, it is used as the environment.
##' @param print.level Arguments for nlm.
##' @param typsize Arguments for nlm.
##' @param ndigit Arguments for nlm.
##' @param gradtol Arguments for nlm.
##' @param stepmax Arguments for nlm.
##' @param steptol Arguments for nlm.
##' @param iterlim Arguments for nlm.
##' @param fscale Arguments for nlm.
##' @return A list of classes \code{hidden} and \code{recursive} (unless
##' multinomial, proportional odds, or continuation ratio) is returned that
##' contains all of the relevant information calculated, including error codes.
##' @author J.K. Lindsey
### @seealso \code{\link[repeated]{chidden}}, \code{\link[repeated]{gar}},
### \code{\link[repeated]{gnlmm}}, \code{\link[repeated]{hidden}},
### \code{\link[rmutil]{iprofile}}, \code{\link[repeated]{kalcount}},
### \code{\link[rmutil]{mexp}}, \code{\link[rmutil]{mprofile}},
### \code{\link[repeated]{nbkal}}, \code{\link[rmutil]{read.list}},
### \code{\link[rmutil]{restovec}}, \code{\link[rmutil]{rmna}}.
##' @keywords models
##' @examples
##'
##' # model for one randomly-generated binary series
##' y <- c(rbinom(10,1,0.1), rbinom(10,1,0.9))
##' mu <- function(p) array(p, c(1,2))
##' print(z <- cphidden(y, times=1:20, dist="Bernoulli",
##' pgamma=0.1,cmu=mu, pcmu=c(-2,2)))
##' # or equivalently
##' print(z <- cphidden(y, times=1:20, dist="Bernoulli",
##' pgamma=0.2,cmu=~1, pcmu=c(-2,2)))
##' # or
##' print(z <- cphidden(y, times=1:20, dist="Bernoulli",
##' pgamma=0.2,mu=~rep(a,20), pmu=c(-2,2)))
##' mexp(z$gamma)
##' par(mfcol=c(2,2))
##' plot(z)
##' plot(iprofile(z), lty=2)
##' print(z <- cphidden(y, times=(1:20)*2, dist="Bernoulli",
##' pgamma=0.1,cmu=~1, pcmu=c(-2,2)))
##' mexp(z$gamma) %*% mexp(z$gamma)
##' plot(z)
##' plot(iprofile(z), lty=2)
##'
##' @export cphidden
<- function(response=NULL, totals=NULL, times=NULL,
distribution="Bernoulli", mu=NULL, cmu=NULL, tvmu=NULL, pgamma,
pmu=NULL, pcmu=NULL, ptvmu=NULL, pshape=NULL, pfamily=NULL,
par=NULL, pintercept=NULL, delta=NULL, envir=parent.frame(),
print.level=0, ndigit=10, gradtol=0.00001, steptol=0.00001,
fscale=1, iterlim=100, typsize=abs(p),stepmax=10*sqrt(p%*%p)){
#
# likelihood function for nlm
#
likel <- function(p){
if(ord)for(i in 1:states){
if(!all(diff(p[np4+l*(i-1)+(1:l)])>0))
p[np4+l*(i-1)+(1:l)] <- p[np4+l*(i-1)+1]*seq(1,1.1,length=l)}
if(is.function(muf))pmu0 <- muf(p[nm1:nmu])
if(is.function(cmuf))pmu1 <- cmuf(p[nm1:ncmu])
if(is.function(tvmuf))pmu2 <- tvmuf(p[ncmu1:np])
if(np>np1){
if(np3-np1==1)pshape <- rep(p[np3],states)
else pshape <- p[np2:np3]}
z <- .Fortran("cphidden_f",
x=as.double(p),
as.integer(states),
iq=as.integer(nosubj),
nobs=as.integer(nobs(response)),
mobs=as.integer(mobs),
s=as.double(if(mdl==4)y else response$response$y),
n=as.integer(response$response$n),
times=as.double(response$response$times),
l=as.integer(l),
pgamma=as.double(pgamma),
gamma=double(states*states),
gamma2=double(states*states),
val=double(states),
vec=double(states*states),
invec=double(states*states),
model=as.integer(mdl),
lgam=as.double(lgam),
ismu=as.logical(ismu),
pmu=as.double(pmu0),
pcmu=as.double(pmu1),
ptvmu=as.double(pmu2),
pshape=as.double(pshape),
pfam=as.double(p[np5]),
ppar=as.logical(!is.null(par)),
par=as.double(exp(p[np])),
delta=double(states),
nn=as.integer(nob),
filter=double(states*nob),
cf=as.logical(0),
a=double(states),
b=double(states*states),
c=double(states),
gmod=double(states*states),
rhs=double(states),
pivot=integer(states),
qraux=double(states),
work=double(2*states),
work2=double(states),
work3=double(states*states),
like=double(1),
#DUP=FALSE,
PACKAGE="repeated")
z$like}
#
# likelihood function returning parameter values
#
like <- function(p){
if(is.function(muf))pmu0 <- muf(p[nm1:nmu])
if(is.function(cmuf))pmu1 <- cmuf(p[nm1:ncmu])
if(is.function(tvmuf))pmu2 <- tvmuf(p[ncmu1:np])
if(np>np1){
if(np3-np1==1)pshape <- rep(p[np3],states)
else pshape <- p[np2:np3]}
z <- .Fortran("cphidden_f",
x=as.double(p),
as.integer(states),
iq=as.integer(nosubj),
nobs=as.integer(nobs(response)),
mobs=as.integer(mobs),
s=as.double(if(mdl==4)y else response$response$y),
n=as.integer(response$response$n),
times=as.double(response$response$times),
l=as.integer(l),
pgamma=as.double(pgamma),
gamma=double(states*states),
gamma2=double(states*states),
val=double(states),
vec=double(states*states),
invec=double(states*states),
model=as.integer(mdl),
lgam=as.double(lgam),
ismu=as.logical(ismu),
pmu=as.double(pmu0),
pcmu=as.double(pmu1),
ptvmu=as.double(pmu2),
pshape=as.double(pshape),
pfam=as.double(p[np5]),
ppar=as.logical(!is.null(par)),
par=as.double(exp(p[np])),
delta=double(states),
nn=as.integer(nob),
filter=double(states*nob),
cf=as.logical(1),
a=double(states),
b=double(states*states),
c=double(states),
gmod=double(states*states),
rhs=double(states),
pivot=integer(states),
qraux=double(states),
work=double(2*states),
work2=double(states),
work3=double(states*states),
like=double(1),
#DUP=FALSE,
PACKAGE="repeated")
z$gamma <- exp(p[1:nm])
z$gamma <- matrix(c(-z$gamma,z$gamma,0,0),byrow=TRUE,nrow=2)
z}
call <- sys.call()
#
# check distribution
#
tmp <- c("Bernoulli","Poisson","multinomial","continuation ratio",
"proportional odds","binomial","exponential","beta binomial",
"negative binomial","normal","inverse Gauss","logistic",
"Cauchy","Laplace","Levy","Pareto","gamma","Weibull",
"gen gamma","gen logistic","Hjorth","Burr","gen Weibull",
"gen extreme value","gen inverse Gauss","power exponential",
"skew Laplace","Student t")
mdl <- match(distribution <- match.arg(distribution,tmp),tmp)
if(mdl>3)mdl <- mdl+1
ord <- distribution=="continuation ratio"||distribution=="proportional odds"
ord2 <- !(!is.null(cmu)&&!is.null(tvmu))
if(!is.null(par)){
if(ord||distribution=="Bernoulli"||distribution=="multinomial")
stop("par not allowed with multinomial and ordinal responses")
else {
if(par<=0)stop("par must be positive")
par <- log(par)}}
states <- 2
#
# check extra parameters in distribution
#
if(mdl>8&&mdl!=30){
if(is.null(pshape))stop("pshape estimate must be supplied")
else if(length(pshape)!=1&&length(pshape)!=states)
stop(paste("pshape must have 1 or",states,"estimates"))}
else pshape <- NULL
if(mdl>19&&mdl!=30){
if(is.null(pfamily))stop("pfamily estimate must be supplied")
else if(length(pshape)!=1)
stop(paste("pshape must have one estimate"))}
else pfamily <- NULL
#
# check if a data object is being supplied
#
type <- "unknown"
respenv <- exists(deparse(substitute(response)),envir=parent.frame())&&
inherits(response,"repeated")&&!inherits(envir,"repeated")
if(respenv){
if(dim(response$response$y)[2]>1){
if(mdl==3)mdl <- 4
else stop("cphidden only handles univariate responses")}
if(!is.null(response$NAs)&&any(response$NAs))
stop("cphidden does not handle data with NAs")
type <- response$response$type}
envname <- if(respenv)deparse(substitute(response))
else if(!is.null(class(envir)))deparse(substitute(envir))
else NULL
#
#if response is not a data object, make one
#
if(!respenv){
if(inherits(envir,"repeated")){
if(!is.null(envir$NAs)&&any(envir$NAs))
stop("cphidden does not handle data with NAs")
cn <- deparse(substitute(response))
if(length(grep("\"",cn))>0)cn <- response
if(length(cn)>1){
if(mdl==3)mdl <- 4
else stop("only one response variable allowed")}
response <- envir
col <- match(cn,colnames(response$response$y))
if(is.na(col))stop(paste("response variable",cn,"not found"))
type <- response$response$type[col]
if(dim(response$response$y)[2]>1){
response$response$y <- response$response$y[,col,drop=FALSE]
if(!is.null(response$response$delta)){
response$response$delta <- response$response$delta[,col,drop=FALSE]
if(all(response$response$delta==1)||all(is.na(response$response$delta)))response$response$delta <- NULL}}}
else {
if(!inherits(response,"response")){
if(is.vector(response,mode="numeric"))
response <- matrix(response,nrow=1)
response <- restovec(response,times=times,totals=totals,delta=delta)}
type <- response$type
response <- rmna(response=response)}}
#
# check if response is appropriate for distribution
#
if(is.null(response$response$times))stop("no times available")
if(distribution=="binomial"||distribution=="beta binomial"){
if(type!="unknown"&&type!="nominal")stop("nominal data required")
if(is.null(response$response$n))stop("totals must be supplied")}
if(mdl<11){
if((distribution=="Poisson"||distribution=="negative binomial")
&&type!="unknown"&&type!="discrete")
stop("discrete data required")
if(distribution=="Bernoulli"){
if(type!="unknown"&&type!="nominal")
stop("nominal data required")
if(any(response$response$y!=0&response$response$y!=1))
stop("responses must be binary for Bernoulli")}
if(distribution=="multinomial"
&&type!="unknown"&&type!="nominal"&&type!="ordinal")
stop("nominal or ordinal data required")
if((distribution=="continuation ratio"||
distribution=="proportional odds")
&&type!="unknown"&&type!="ordinal")
stop("ordinal data required")
if(any(response$response$y<0))stop("all responses must be non-negative")}
else if(mdl!=11&&mdl!=13&&mdl!=14&&mdl!=15&&mdl!=16&&mdl!=21&&mdl!=27
&&mdl!=28&&mdl!=29&&mdl!=30){
if(type!="unknown"&&type!="duration"&&type!="continuous")
stop("duration data required")
if(any(response$response$y<=0))stop("all responses must be positive")}
else if(mdl==30){
if(any(response$response$y!=0&response$response$y!=1))
stop(paste("responses must be binary for",distribution))}
else if(type!="unknown"&&type!="continuous"&&type!="duration")
stop("continuous data required")
lgam <- NULL
if(mdl==3||ord){
l <- length(unique(response$response$y))-1
if(min(response$response$y)!=0||max(response$response$y)!=l)
stop(paste("multinomial and ordinal categories must be numbered from 0 to",l))
if(l<1)stop("multinomial and ordinal responses must have at least 2 categories")}
else if(mdl==4){
l <- dim(response$response$y)[2]-1
lgam <- lgamma(apply(response$response$y,1,sum)+1)-
apply(lgamma(response$response$y+1),1,sum)
y <- as.vector(t(response$response$y))}
else l <- 1
if(ord){
if(length(pintercept)!=l*states)
stop(paste("pintercept should contain",l*states,"estimates"))
for(i in 1:states){
if(!all(diff(pintercept[(i-1)*l+(1:l)])>0))
stop("intercepts must be monotone increasing for each state")}}
else pintercept <- NULL
if(!is.null(response$response$nest)&&!is.null(par))
stop("cphidden does not handle two levels of nesting with an AR")
if(!is.null(response$response$censor))
stop("cphidden does not handle censoring")
nosubj <- length(nobs(response))
mobs <- max(nobs(response))
nob <- dim(response$response$y)[1]
ismu <- !is.null(mu)
if(ismu)cmu <- tvmu <- pcmu <- ptvmu <- NULL
else pmu <- NULL
#
# if a data object was supplied, modify formulae or functions to read from it
#
muf <- mu1 <- mu3 <- cmuf <- cmu1 <- cmu3 <- tvmuf <- tvmu1 <- tvmu3 <- NULL
if(respenv||inherits(envir,"repeated")||inherits(envir,"tccov")||inherits(envir,"tvcov")){
if(!is.null(mu)){
cl <- is.list(mu)
if(!cl)mu <- list(mu)
tmp2 <- mu3 <- list()
for(i in 1:length(mu)){
if(inherits(mu[[i]],"formula")){
mu3 <- c(mu3,list(if(respenv)finterp(mu[[i]],.envir=response,.name=envname,.intercept=!ord)
else finterp(mu[[i]],.envir=envir,.name=envname,.intercept=!ord)))
tmp2 <- c(tmp2,list(mu[[i]]))}
else if(is.function(mu[[i]])){
tmp <- parse(text=deparse(mu[[i]])[-1])
tmp1 <- if(respenv)fnenvir(mu[[i]],.envir=response,.name=envname)
else fnenvir(mu[[i]],.envir=envir,.name=envname)
tmp2 <- c(tmp2,list(tmp1))
attr(tmp1,"model") <- tmp
mu3 <- c(mu3,list(tmp1))}}
mu <- tmp2
rm(tmp2)
if(!cl){
mu <- mu[[1]]
mu3 <- mu3[[1]]}}
if(!is.null(cmu)){
cl <- is.list(cmu)
if(!cl)cmu <- list(cmu)
tmp2 <- cmu3 <- list()
for(i in 1:length(cmu)){
if(inherits(cmu[[i]],"formula")){
cmu3 <- c(cmu3,list(if(respenv)finterp(cmu[[i]],.envir=response,.name=envname,.intercept=!ord)
else finterp(cmu[[i]],.envir=envir,.name=envname,.intercept=!ord)))
tmp2 <- c(tmp2,list(cmu[[i]]))}
else if(is.function(cmu[[i]])){
tmp <- parse(text=deparse(cmu[[i]])[-1])
tmp1 <- if(respenv)fnenvir(cmu[[i]],.envir=response,.name=envname,.expand=FALSE)
else fnenvir(cmu[[i]],.envir=envir,.name=envname,.expand=FALSE)
tmp2 <- c(tmp2,list(tmp1))
attr(tmp1,"model") <- tmp
cmu3 <- c(cmu3,list(tmp1))}}
cmu <- tmp2
rm(tmp2)
if(!cl){
cmu <- cmu[[1]]
cmu3 <- cmu3[[1]]}}
if(!is.null(tvmu)){
cl <- is.list(tvmu)
if(!cl)tvmu <- list(tvmu)
tmp2 <- tvmu3 <- list()
for(i in 1:length(tvmu)){
if(inherits(tvmu[[i]],"formula")){
tvmu3 <- c(tvmu3,list(if(respenv)finterp(tvmu[[i]],.envir=response,.name=envname,.intercept=!ord)
else finterp(tvmu[[i]],.envir=envir,.name=envname,.intercept=!ord)))
tmp2 <- c(tmp2,list(tvmu[[i]]))}
else if(is.function(tvmu[[i]])){
tmp <- parse(text=deparse(tvmu[[i]])[-1])
tmp1 <- if(respenv)fnenvir(tvmu[[i]],.envir=response,.name=envname)
else fnenvir(tvmu[[i]],.envir=envir,.name=envname)
tmp2 <- c(tmp2,list(tmp1))
attr(tmp1,"model") <- tmp
tvmu3 <- c(tvmu3,list(tmp1))}}
tvmu <- tmp2
rm(tmp2)
if(!cl){
tvmu <- tvmu[[1]]
tvmu3 <- tvmu3[[1]]}}}
#
# transform general formulae to functions and check number of parameters
#
npr0 <- if(ord)length(pmu)/states else length(pmu)/states/l
start <- NULL
if(inherits(mu,"formula")){
mu1 <- if(respenv)finterp(mu,.envir=response,.name=envname,.intercept=!ord)
else finterp(mu,.envir=envir,.name=envname,.intercept=!ord)
npt0 <- length(attr(mu1,"parameters"))
if(is.character(attr(mu1,"model"))){
# W&R formula
if(ord&&length(attr(mu1,"model"))==0)mu1 <- NULL}
else {
# formula with unknowns
if(npr0!=npt0){
cat("\nParameters are ")
cat(attr(mu1,"parameters"),"\n")
stop(paste("pmu should have",if(ord) npt0*states else npt0*states*l,"estimates"))}
if(is.list(pmu))pmu <- unlist(pmu)}
if(is.null(mu1))pmu <- NULL}
else if(is.list(mu)){
if(!ord&&length(mu)!=states*l)
stop(paste("list of mu formulae or functions must have length",states*l))
if(ord&&length(mu)!=states)
stop(paste("list of mu formulae or functions must have length",states))
# only count parameters if list of formulae
if(inherits(mu[[1]],"formula"))start <- 1
tmp <- list()
for(i in mu)if(inherits(i,"formula")){
mu1 <- if(respenv)finterp(i,.envir=response,.name=envname,.start=start,.intercept=!ord)
else finterp(i,.envir=envir,.name=envname,.start=start,.intercept=!ord)
npt0 <- length(attr(mu1,"parameters"))
if(ord&&is.null(attr(mu1,"model")))
stop("all formulae must contain covariates")
if(is.list(pmu))pmu <- unlist(pmu)
# make new list and count parameters
tmp <- c(tmp,list(mu1))
start <- start+npt0}
else if(is.function(i)){
if(inherits(i,"formulafn"))start <- c(start,attr(i,"parameters"))
tmp <- c(tmp,list(i))}
if(!is.null(start)){
if(is.numeric(start))start <- start-1
else start <- length(unique(start))}
mu1 <- tmp
rm(tmp)}
else if(!is.null(mu))mu1 <- mu
#
# give appropriate attributes to mu1 for printing
#
if(!is.null(mu1)&&is.null(attr(mu1,"parameters"))){
attributes(mu1) <- if(is.function(mu)){
if(!inherits(mu,"formulafn")){
if(respenv)attributes(fnenvir(mu,.envir=response))
else attributes(fnenvir(mu,.envir=envir))}
else attributes(mu)}
else {
if(respenv)attributes(fnenvir(mu1,.envir=response))
else attributes(fnenvir(mu1,.envir=envir))}}
#
# if possible, check that correct number of estimates was supplied
#
if(!is.list(mu)){
nlp <- if(is.function(mu1))length(attr(mu1,"parameters"))
else if(is.null(mu1))NULL
else npt0
if(!is.null(nlp)&&nlp!=npr0)
stop(paste("pmu should have",if(ord)nlp*states else nlp*states*l,"initial estimates"))}
if(!is.null(start)&&start!=length(pmu))
stop(paste("pmu should have",start,"initial estimates"))
#
# transform time-constant formulae to functions and check number of parameters
#
npr1 <- if(ord)length(pcmu)/states else length(pcmu)/states/l
start <- NULL
if(inherits(cmu,"formula")){
cmu1 <- if(respenv)finterp(cmu,.envir=response,.expand=FALSE,.name=envname,.intercept=!ord)
else finterp(cmu,.envir=envir,.expand=FALSE,.name=envname,.intercept=!ord)
npt1 <- length(attr(cmu1,"parameters"))
if(is.character(attr(cmu1,"model"))){
# W&R formula
if(length(attr(cmu1,"model"))==1&&length(cmu1(pcmu))!=nosubj){
tmp <- function(p) rep(p[1],nosubj)
attributes(tmp) <- attributes(cmu1)
cmu1 <- tmp
rm(tmp)}
if(ord&&length(attr(cmu1,"model"))==0)cmu1 <- NULL}
else {
# formula with unknowns
if(npr1!=npt1){
cat("\nParameters are ")
cat(attr(cmu1,"parameters"),"\n")
stop(paste("pcmu should have",if(ord)npt1*states
else npt1*states*l,"estimates"))}
if(is.list(pcmu))pcmu <- unlist(pcmu)}
if(is.null(cmu1))pcmu <- NULL}
else if(is.list(cmu)){
if(!ord&&length(cmu)!=states*l)
stop(paste("list of cmu formulae or functions must have length",states*l))
if(ord&&length(cmu)!=states)
stop(paste("list of cmu formulae or functions must have length",states))
# only count parameters if list of formulae
if(inherits(cmu[[1]],"formula"))start <- 1
tmp <- list()
for(i in cmu)if(inherits(i,"formula")){
cmu1 <- if(respenv)finterp(i,.envir=response,.expand=FALSE,.name=envname,.start=start,.intercept=!ord)
else finterp(i,.envir=envir,.expand=FALSE,.name=envname,.start=start,.intercept=!ord)
npt1 <- length(attr(cmu1,"parameters"))
if(is.character(attr(cmu1,"model"))){
# W&R formula
if(ord&&length(attr(cmu1,"model"))==1)cm1 <- NULL}
else if(is.list(pcmu))pcmu <- unlist(pcmu)
# make new list and count parameters
tmp <- c(tmp,list(cmu1))
start <- start+length(attr(cmu1,"parameters"))}
else if(is.function(i)){
if(inherits(i,"formulafn"))start <- c(start,attr(i,"parameters"))
tmp <- c(tmp,list(i))}
if(!is.null(start)){
if(is.numeric(start))start <- start-1
else start <- length(unique(start))}
cmu1 <- tmp
rm(tmp)}
else if(!is.null(cmu))cmu1 <- cmu
#
# give appropriate attributes to cmu1 for printing
#
if(!is.null(cmu1)&&is.null(attr(cmu1,"parameters"))){
attributes(cmu1) <- if(is.function(cmu)){
if(!inherits(cmu,"formulafn")){
if(respenv)attributes(fnenvir(cmu,.envir=response))
else attributes(fnenvir(cmu,.envir=envir))}
else attributes(cmu)}
else {
if(respenv)attributes(fnenvir(cmu1,.envir=response))
else attributes(fnenvir(cmu1,.envir=envir))}}
#
# if possible, check that correct number of estimates was supplied
#
if(!is.function(cmu)&&!is.list(cmu)){
nlp <- if(is.function(cmu1))length(attr(cmu1,"parameters"))
else if(is.null(cmu1))NULL
else npt1
if(!is.null(nlp)&&nlp!=npr1)
stop(paste("pcmu should have",if(ord)nlp*states else nlp*states*l,"initial estimates"))}
if(!is.null(start)&&start!=length(pcmu))
stop(paste("pcmu should have",start,"initial estimates"))
#
# transform time-varying formulae to functions and check number of parameters
#
npr2 <- if(ord)length(ptvmu)/states else length(ptvmu)/states/l
start <- NULL
if(inherits(tvmu,"formula")){
tvmu1 <- if(respenv)finterp(tvmu,.envir=response,.name=envname,.intercept=!ord)
else finterp(tvmu,.envir=envir,.name=envname,.intercept=!ord)
npt2 <- length(attr(tvmu1,"parameters"))
if(is.character(attr(tvmu1,"model"))){
# W&R formula
if(length(attr(tvmu1,"model"))==1&&length(tvmu1(ptvmu))!=mobs){
tmp <- function(p) rep(p[1],mobs)
attributes(tmp) <- attributes(tvmu1)
tvmu1 <- tmp
rm(tmp)}
else if(ord&&length(attr(tvmu1,"model"))==0)tvmu1 <- NULL}
else {
# formula with unknowns
if(npr2!=npt2){
cat("\nParameters are ")
cat(attr(tvmu1,"parameters"),"\n")
stop(paste("ptvmu should have",if(ord) npt2*states else npt2*states*l,"estimates"))}
if(is.list(ptvmu))ptvmu <- unlist(ptvmu)}
if(is.null(tvmu1))ptvmu <- NULL}
else if(is.list(tvmu)){
if(!ord&&length(tvmu)!=states*l)
stop(paste("list of tvmu formulae or functions must have length",states*l))
if(ord&&length(tvmu)!=states)
stop(paste("list of tvmu formulae or functions must have length",states))
# only count parameters if list of formulae
if(inherits(tvmu[[1]],"formula"))start <- 1
tmp <- list()
for(i in tvmu)if(inherits(i,"formula")){
tvmu1 <- if(respenv)finterp(i,.envir=response,.expand=FALSE,.name=envname,.start=start,.intercept=!ord)
else finterp(i,.envir=envir,.expand=FALSE,.name=envname,.start=start,.intercept=!ord)
npt2 <- length(attr(tvmu1,"parameters"))
if(is.character(attr(tvmu1,"model"))){
# W&R formula (don't know how to change index of p[i])
if(ord&&length(attr(tvmu1,"model"))==1)tvm1 <- NULL}
else if(is.list(ptvmu))ptvmu <- unlist(ptvmu)
# make new list and count parameters
tmp <- c(tmp,list(tvmu1))
start <- start+length(attr(tvmu1,"parameters"))}
else if(is.function(i)){
if(inherits(i,"formulafn"))start <- c(start,attr(i,"parameters"))
tmp <- c(tmp,list(i))}
if(!is.null(start)){
if(is.numeric(start))start <- start-1
else start <- length(unique(start))}
tvmu1 <- tmp
rm(tmp)}
else if(!is.null(tvmu))tvmu1 <- tvmu
#
# give appropriate attributes to tvmu1 for printing
#
if(!is.null(tvmu1)&&is.null(attr(tvmu1,"parameters"))){
attributes(tvmu1) <- if(is.function(tvmu)){
if(!inherits(tvmu,"formulafn")){
if(respenv)attributes(fnenvir(tvmu,.envir=response))
else attributes(fnenvir(tvmu,.envir=envir))}
else attributes(tvmu)}
else {
if(respenv)attributes(fnenvir(tvmu1,.envir=response))
else attributes(fnenvir(tvmu1,.envir=envir))}}
#
# if possible, check that correct number of estimates was supplied
#
if(!is.function(tvmu)&&!is.list(tvmu)){
nlp <- if(is.function(tvmu1))length(attr(tvmu1,"parameters"))
else if(is.null(tvmu1))NULL
else npt2
if(!is.null(nlp)&&nlp!=npr2)
stop(paste("ptvmu should have",if(ord)nlp*states else nlp*states*l,"initial estimates"))}
if(!is.null(start)&&start!=length(ptvmu))
stop(paste("ptvmu should have",start,"initial estimates"))
#
# set up general regression function for likelihood
# if arg==FALSE, can print out general parameter estimates as matrices
#
arg <- TRUE
if(ord&&is.null(mu1))arg <- FALSE
if(is.function(mu1)){
if(!ord&&is.null(pmu))stop("Initial values of pmu must be supplied")
tmp <- mu1(pmu)
if(length(tmp)!=nob)
stop("mu function or formula must return a vector with one element per observation")
if(any(is.na(tmp))||any(abs(tmp)==Inf))stop("mu returns NAs or Infs")
rm(tmp)
# will be able to print coefficients as matrices
arg <- FALSE
# create regression function by repeatedly calling
# function or formula supplied
if(distribution=="multinomial"){
zm <- array(0,c(nob,states,l))
muf <- function(p){
k <- 0
for(j in 1:l)for(i in 1:states){
k <- k+1
zm[,i,j] <- mu1(p[(1:npr0)+(k-1)*npr0])}
zm}}
else if(ord){
zm <- array(0,c(nob,states,l))
muf <- function(p){
k <- 0
for(i in 1:states){
tmp <- mu1(p[(1:npr0)+(i-1)*npr0])
for(j in 1:l){
k <- k+1
zm[,i,j] <- p[np0+k]+tmp}}
zm}}
else {
muf <- function(p){
z <- NULL
for(i in 1:states)
z <- cbind(z,mu1(p[(1:npr0)+(i-1)*npr0]))
z}}
attributes(muf) <- attributes(mu)}
else if(is.list(mu1)){
if(is.null(pmu))stop("Initial values of pmu must be supplied")
for(i in mu1)if(length(i(pmu))!=nob)stop("each mu function or formula must return a vector with one element per observation")
# create one regression function from list
if(distribution=="multinomial"){
zm <- array(0,c(nob,states,l))
muf <- function(p){
k <- 0
for(j in 1:l)for(i in 1:states){
k <- k+1
zm[,i,j] <- mu1[[k]](p)}
zm}}
else if(ord){
zm <- array(0,c(nob,states,l))
muf <- function(p){
k <- 0
for(i in 1:states){
tmp <- mu1[[i]](p)
for(j in 1:l){
k <- k+1
zm[,i,j] <- p[np0+k]+tmp}}
zm}}
else {
muf <- function(p){
z <- NULL
for(i in mu1)z <- cbind(z,i(p))
z}}}
else pmu0 <- NULL
#
# set up time-constant regression function for likelihood
# if arc==FALSE, can print out time-constant parameter estimates as matrices
#
arc <- TRUE
if(is.function(cmu1)){
if(!ord&&is.null(pcmu))stop("Initial values of pcmu must be supplied")
# check if array returned or one function/formula for all states
tmp <- cmu1(pcmu)
d <- dim(tmp)
if(length(d)==0){
# one formula or function
if(length(tmp)!=nosubj)
stop("cmu function or formula must return a vector with one element per individual")
if(any(is.na(tmp))||any(abs(tmp)==Inf))
stop("cmu returns NAs or Infs")
rm(tmp)
# will be able to print coefficients as matrices
arc <- FALSE
# create regression function by repeatedly calling
# function or formula supplied
if(distribution=="multinomial"){
zmc <- array(0,c(nosubj,states,l))
cmuf <- function(p){
k <- 0
for(j in 1:l)for(i in 1:states){
k <- k+1
zmc[,i,j] <- cmu1(p[(1:npr1)+(k-1)*npr1])}
zmc}}
else if(ord){
zmc <- array(0,c(nosubj,states,l))
cmuf <- function(p){
k <- 0
for(i in 1:states){
tmp <- cmu1(p[(1:npr1)+(i-1)*npr1])
for(j in 1:l){
k <- k+1
zmc[,i,j] <- p[np0+k]+tmp}}
zmc}}
else {
cmuf <- function(p){
z <- NULL
for(i in 1:states)
z <- cbind(z,cmu1(p[(1:npr1)+(i-1)*npr1]))
z}}
attributes(cmuf) <- attributes(cmu)}
else {
# returns an array: check dimensions
if(d[2]!=states)stop(paste("cmu must return a",states,"column array"))
if(d[1]!=nosubj)
stop("cmu must return an array with one row per individual")
if(distribution=="multinomial"){
if(length(d)!=3)
stop("cmu must return a 3 dimensional array")
if(d[3]!=l)
stop(paste("cmu must return an array with",l,"layers"))}
else if(length(d)!=2)
stop("cmu must return a 2 dimensional array")
arc <- FALSE
cmuf <- cmu1}}
else if(is.list(cmu1)){
if(is.null(pcmu))stop("Initial values of pcmu must be supplied")
for(i in cmu1)if(length(i(pcmu))!=nosubj)stop("each cmu function or formula must return a vector with one element per individual")
# create one regression function from list
if(distribution=="multinomial"){
zmc <- array(0,c(nosubj,states,l))
cmuf <- function(p){
k <- 0
for(j in 1:l)for(i in 1:states){
k <- k+1
zmc[,i,j] <- cmu1[[k]](p)}
zmc}}
else if(ord){
zmc <- array(0,c(nosubj,states,l))
cmuf <- function(p){
k <- 0
for(i in 1:states){
tmp <- cmu1[[i]](p)
for(j in 1:l){
k <- k+1
zmc[,i,j] <- p[np0+k]+tmp}}
zmc}}
else {
cmuf <- function(p){
z <- NULL
for(i in cmu1)z <- cbind(z,i(p))
z}}}
else pmu1 <- array(0,c(states,nosubj,l))
#
# set up time-varying regression function for likelihood
# if arv==FALSE, can print out time-varying parameter estimates as matrices
#
arv <- TRUE
if(is.function(tvmu1)){
if(!ord&&is.null(ptvmu))stop("Initial values of ptvmu must be supplied")
# check if array returned or one function/formula for all states
tmp <- tvmu1(ptvmu)
d <- dim(tmp)
if(length(d)==0){
# one formula or function
if(length(tmp)!=mobs)
stop("tvmu function or formula must return a vector with one element per time point")
if(any(is.na(tmp))||any(abs(tmp)==Inf))
stop("tvmu returns NAs or Infs")
rm(tmp)
# will be able to print coefficients as matrices
arv <- FALSE
# create regression function by repeatedly calling
# function or formula supplied
if(distribution=="multinomial"){
zmv <- array(0,c(mobs,states,l))
tvmuf <- function(p){
k <- 0
for(j in 1:l)for(i in 1:states){
k <- k+1
zmv[,i,j] <- tvmu1(p[(1:npr2)+(k-1)*npr2])}
zmv}}
else if(ord){
zmv <- array(0,c(mobs,states,l))
tvmuf <- function(p){
k <- 0
for(i in 1:states){
tmp <- tvmu1(p[(1:npr2)+(i-1)*npr2])
for(j in 1:l){
k <- k+1
zmv[,i,j] <- ord2*p[np0+k]+tmp}}
zmv}}
else {
tvmuf <- function(p){
z <- NULL
for(i in 1:states)
z <- cbind(z,tvmu1(p[(1:npr2)+(i-1)*npr2]))
z}}
attributes(tvmuf) <- attributes(tvmu)}
else {
# returns an array: check dimensions
if(d[2]!=states)stop(paste("tvmu must return a",states,"column array"))
else if(d[1]!=mobs)
stop("tvmu must return an array with one row per time point")
if(distribution=="multinomial"){
if(length(d)!=3)
stop("tvmu must return a 3 dimensional array")
if(d[3]!=l)
stop(paste("tvmu must return an array with",l,"layers"))}
else if(length(d)!=2)
stop("tvmu must return a 2 dimensional array")
arv <- FALSE
tvmuf <- tvmu1}}
else if(is.list(tvmu1)){
if(is.null(ptvmu))stop("Initial values of ptvmu must be supplied")
for(i in tvmu1)if(length(i(ptvmu))!=mobs)stop("each tvmu function or formula must return a vector with one element per time point")
# create one regression function from list
if(distribution=="multinomial"){
zmv <- array(0,c(mobs,states,l))
tvmuf <- function(p){
k <- 0
for(j in 1:l)for(i in 1:states){
k <- k+1
zmv[,i,j] <- tvmu1[[k]](p)}
zmv}}
else if(ord){
zmv <- array(0,c(mobs,states,l))
tvmuf <- function(p){
k <- 0
for(i in 1:states){
tmp <- tvmu1[[i]](p)
for(j in 1:l){
k <- k+1
zmv[,i,j] <- ord2*p[np0+k]+tmp}}
zmv}}
else {
tvmuf <- function(p){
z <- NULL
for(i in tvmu1)z <- cbind(z,i(p))
z}}}
else pmu2 <- array(0,c(states,mobs,l))
if(!is.function(muf)&&!is.function(cmuf)&&!is.function(tvmuf)){
if(ord){
if(is.null(pintercept))
stop(paste("pintercept must contain ",l," initial estimates",sep=""))
else {
ismu <- TRUE
zm <- array(0,c(nob,states,l))
muf <- function(p){
k <- 0
for(i in 1:states){
tmp <- rep(1,nob)
for(j in 1:l){
k <- k+1
zm[,i,j] <- p[np0+k]*tmp}}
zm}}}
else stop("Either mu, cmu or tvmu must be a list, function, or formula")}
#
# prepare to call nlm
#
nm <- length(pgamma)
nm1 <- nm+1
nmu <- nm+length(pmu)+length(pintercept)
ncmu <- nm+length(pcmu)+length(ptvmu)+length(pintercept)
ncmu1 <- nm+length(pcmu)+1
p <- c(log(pgamma),pmu,pcmu,ptvmu,pshape,pfamily,pintercept,par)
np <- length(p)
np0 <- np-nm-length(pintercept)-length(par)
np1 <- np-length(pshape)-length(pfamily)-length(pintercept)-length(par)
np2 <- np1+1
np3 <- np-length(pfamily)-length(pintercept)-length(par)
np4 <- np-length(pintercept)-length(par)
np5 <- np-length(par)
pshape <- rep(0,states)
z <- nlm(likel,p, hessian=TRUE, print.level=print.level,
typsize=typsize, ndigit=ndigit, gradtol=gradtol, stepmax=stepmax,
steptol=steptol, iterlim=iterlim, fscale=fscale)
#
# prepare mle's
#
delta <- if(!is.null(response$response$delta))
sum(log(response$response$delta)) else 0
maxlike <- z$minimum - delta
z0 <- like(z$estimate)
#
# calculate se's
#
a <- if(any(is.na(z$hessian))||any(abs(z$hessian)==Inf))0
else qr(z$hessian)$rank
if(a==np)cov <- solve(z$hessian)
else cov <- matrix(NA,ncol=np,nrow=np)
se <- sqrt(diag(cov))
corr <- cov/(se%o%se)
#
# calculate predicted values
#
if(mdl<3||mdl>6){
rpred <- 0
if(is.function(muf)){
rpred <- rpred+t(muf(z$estimate[nm1:nmu]))
if(dim(rpred)[2]!=nob)rpred <- rpred[,rep(1:nosubj,nobs(response))]}
if(is.function(cmuf))rpred <- rpred+t(cmuf(z$estimate[nm1:ncmu]))[,rep(1:nosubj,nobs(response))]
if(is.function(tvmuf))rpred <- rpred+t(tvmuf(z$estimate[ncmu1:np]))[,sequence(nobs(response))]
if(mdl==1||mdl==7)rpred <- 1/(1+exp(-rpred))
pred <- rep(1,states)%*%(rpred*z0$delta)
rpred <- rep(1,states)%*%(rpred*matrix(z0$filter,nrow=states))}
else pred <- rpred <- NULL
#
# return appropriate attributes on functions
#
if(!is.null(mu3))mu1 <- mu3
if(!is.null(cmu3))cmu1 <- cmu3
if(!is.null(tvmu3))tvmu1 <- tvmu3
z1 <- list(
call=call,
type="continuous",
changepoint=TRUE,
distribution=distribution,
response=response$response,
maxlike=maxlike,
aic=maxlike+np,
df=length(response$response$y)-np,
states=states,
levels=l,
mu=mu1,
arg=arg,
cmu=cmu1,
arc=arc,
arv=arv,
tvmu=tvmu1,
coef=z$estimate[nm1:np1],
pshape=if(np3>np1&&!ord)z$estimate[np2:np3] else NULL,
pfamily=if(np>np3+!is.null(par)&&!ord)z$estimate[np] else NULL,
pintercept=if(is.null(pintercept)) NULL else z$estimate[np2:np],
nmu=length(pmu),
ncmu=length(pcmu),
ntvmu=length(ptvmu),
gamma=matrix(z0$gamma,ncol=states),
delta=z0$delta,
par=if(!is.null(par))z0$par else NULL,
np=np,
cov=cov,
corr=corr,
se=se,
filter=matrix(z0$filter,nrow=states),
pred=pred,
rpred=rpred,
iterations=z$iter,
code=z$code)
class(z1) <- if(is.null(rpred))"hidden" else c("hidden","recursive")
z1}
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