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##' Add regression association to latent variable model
##'
##' Define regression association between variables in a \code{lvm}-object and
##' define linear constraints between model equations.
##'
#
##'
##' The \code{regression} function is used to specify linear associations
##' between variables of a latent variable model, and offers formula syntax
##' resembling the model specification of e.g. \code{lm}.
##'
##' For instance, to add the following linear regression model, to the
##' \code{lvm}-object, \code{m}:
##' \deqn{ E(Y|X_1,X_2) = \beta_1 X_1 + \beta_2 X_2}
##' We can write
##'
##' \code{regression(m) <- y ~ x1 + x2}
##'
##' Multivariate models can be specified by successive calls with
##' \code{regression}, but multivariate formulas are also supported, e.g.
##'
##' \code{regression(m) <- c(y1,y2) ~ x1 + x2}
##'
##' defines
##' \deqn{ E(Y_i|X_1,X_2) = \beta_{1i} X_1 + \beta_{2i} X_2 }
##'
##' The special function, \code{f}, can be used in the model specification to
##' specify linear constraints. E.g. to fix \eqn{\beta_1=\beta_2}
##' , we could write
##'
##' \code{regression(m) <- y ~ f(x1,beta) + f(x2,beta)}
##'
##' The second argument of \code{f} can also be a number (e.g. defining an
##' offset) or be set to \code{NA} in order to clear any previously defined
##' linear constraints.
##'
##' Alternatively, a more straight forward notation can be used:
##'
##' \code{regression(m) <- y ~ beta*x1 + beta*x2}
##'
##' All the parameter values of the linear constraints can be given as the right
##' handside expression of the assigment function \code{regression<-} (or
##' \code{regfix<-}) if the first (and possibly second) argument is defined as
##' well. E.g:
##'
##' \code{regression(m,y1~x1+x2) <- list("a1","b1")}
##'
##' defines \eqn{E(Y_1|X_1,X_2) = a1 X_1 + b1 X_2}. The rhs argument can be a
##' mixture of character and numeric values (and NA's).
##'
##' The function \code{regression} (called without additional arguments) can be
##' used to inspect the linear constraints of a \code{lvm}-object.
##'
##' For backward compatibility the "$"-symbol can be used to fix parameters at
##' a given value. E.g. to add a linear relationship between \code{y} and
##' \code{x} with slope 2 to the model \code{m}, we can write
##' \code{regression(m,"y") <- "x$2"}. Similarily we can use the "@@"-symbol to
##' name parameters. E.g. in a multiple regression we can force the parameters
##' to be equal: \code{regression(m,"y") <- c("x1@@b","x2@@b")}. Fixed parameters
##' can be reset by fixing (with \$) them to \code{NA}.
##'
##' @aliases regression regression<- regression<-.lvm regression.lvm regfix
##' regfix regfix<- regfix.lvm regfix<-.lvm
##' @param object \code{lvm}-object.
##' @param value A formula specifying the linear constraints or if
##' \code{to=NULL} a \code{list} of parameter values.
##' @param to Character vector of outcome(s) or formula object.
##' @param from Character vector of predictor(s).
##' @param fn Real function defining the functional form of predictors (for
##' simulation only).
##' @param silent Logical variable which indicates whether messages are turned
##' on/off.
##' @param additive If FALSE and predictor is categorical a non-additive effect is assumed
##' @param quick Faster implementation without parameter constraints
##' @param \dots Additional arguments to be passed to the low level functions
##' @usage
##' \method{regression}{lvm}(object = lvm(), to, from, fn = NA,
##' silent = lava.options()$silent, additive=TRUE, ...)
##' \method{regression}{lvm}(object, to=NULL, quick=FALSE, ...) <- value
##' @return A \code{lvm}-object
##' @note Variables will be added to the model if not already present.
##' @author Klaus K. Holst
##' @seealso \code{\link{intercept<-}}, \code{\link{covariance<-}},
##' \code{\link{constrain<-}}, \code{\link{parameter<-}},
##' \code{\link{latent<-}}, \code{\link{cancel<-}}, \code{\link{kill<-}}
##' @keywords models regression
##' @examples
##'
##' m <- lvm() ## Initialize empty lvm-object
##' ### E(y1|z,v) = beta1*z + beta2*v
##' regression(m) <- y1 ~ z + v
##' ### E(y2|x,z,v) = beta*x + beta*z + 2*v + beta3*u
##' regression(m) <- y2 ~ f(x,beta) + f(z,beta) + f(v,2) + u
##' ### Clear restriction on association between y and
##' ### fix slope coefficient of u to beta
##' regression(m, y2 ~ v+u) <- list(NA,"beta")
##'
##' regression(m) ## Examine current linear parameter constraints
##'
##' ## ## A multivariate model, E(yi|x1,x2) = beta[1i]*x1 + beta[2i]*x2:
##' m2 <- lvm(c(y1,y2) ~ x1+x2)
##'
##'
##'
##' @export
"regression<-" <- function(object,...,value) UseMethod("regression<-")
##' @export
"regression<-.lvm" <- function(object, to=NULL, quick=FALSE, ..., value) {
dots <- list(...)
if (length(dots$additive)>0 && !dots$additive && !inherits(value,"formula")) {
regression(object,beta=value,...) <- to
return(object)
}
if (!is.null(to)) {
regfix(object, to=to, ...) <- value
return(object)
} else {
if (is.list(value)) {
for (v in value) {
regression(object,...) <- v
}
return(object)
}
if (class(value)[1]=="formula") {
yx <- lapply(strsplit(as.character(value),"~"),function(x) gsub(" ","",x))[-1]
iscovar <- FALSE
if (length(yx)==1) {
lhs <- NULL; xidx <- 1
} else {
lhs <- yx[1]; xidx <- 2
if (yx[[xidx]][1]=="") {
yx[[xidx]] <- yx[[xidx]][-1]
iscovar <- TRUE
}
}
X <- strsplit(yx[[xidx]],"+",fixed=TRUE)[[1]]
if (iscovar) {
## return(covariance(object,var1=decomp.specials(lhs[[1]]),var2=X))
covariance(object) <- toformula(decomp.specials(lhs[[1]]),X)
return(object)
}
if (!is.null(lhs) && nchar(lhs[[1]])>2 && substr(lhs[[1]],1,2)=="v(") {
v <- update(value,paste(decomp.specials(lhs),"~."))
covariance(object,...) <- v
return(object)
}
curvar <- index(object)$var
res <- lapply(X,decomp.specials,pattern2="[*]",reverse=TRUE)
xx <- unlist(lapply(res, function(x) x[1]))
notexo <- c()
if (length(lhs)>0) {
yy <- decomp.specials(lhs)
yyf <- lapply(yy,function(y) decomp.specials(y,NULL,pattern2="[",fixed=TRUE))
ys <- unlist(lapply(yyf,function(x) x[1]))
object <- addvar(object,ys,reindex=FALSE,...)
notexo <- ys
}
exo <- c()
xxf <- lapply(as.list(xx),function(x) decomp.specials(x,NULL,pattern2="[",fixed=TRUE))
xs <- unlist(lapply(xxf,function(x) x[1]))
## Remove intercepts?
rmint <- na.omit(match("-1",xs))
if (length(rmint)>0) intercept(object,ys) <- 0
xs <- setdiff(xs,c("-1","1"))
object <- addvar(object,xs,reindex=FALSE ,...)
for (i in seq_len(length(xs))) {
xf <- unlist(strsplit(xx[[i]],"[\\[\\]]",perl=TRUE))
if (length(xf)>1) {
xpar <- strsplit(xf[2],":")[[1]]
if (length(xpar)>1) {
val <- ifelse(xpar[2]=="NA",NA,xpar[2])
valn <- suppressWarnings(as.numeric(val))
covariance(object,xs[i]) <- ifelse(is.na(valn),val,valn)
}
val <- ifelse(xpar[1]=="NA",NA,xpar[1])
valn <- suppressWarnings(as.numeric(val))
if (val!=".") {
intercept(object,xs[i]) <- ifelse(is.na(valn),val,valn)
notexo <- c(notexo,xs[i])
}
} else { exo <- c(exo,xs[i]) }
}
if (length(lhs)==0) {
index(object) <- reindex(object)
return(object)
}
if (lava.options()$exogenous) {
oldexo <- exogenous(object)
newexo <- setdiff(exo,c(notexo,curvar,ys))
exogenous(object) <- union(newexo,setdiff(oldexo,notexo))
}
for (i in seq_len(length(ys))) {
y <- ys[i]
yf <- unlist(strsplit(yy[i],"[\\[\\]]",perl=TRUE))
if (length(yf)>1) {
ypar <- strsplit(yf[2],":")[[1]]
if (length(ypar)>1) {
val <- ifelse(ypar[2]=="NA",NA,ypar[2])
valn <- suppressWarnings(as.numeric(val))
covariance(object,y) <- ifelse(is.na(valn),val,valn)
}
val <- ifelse(ypar[1]=="NA",NA,ypar[1])
valn <- suppressWarnings(as.numeric(val))
if (val!=".")
intercept(object,y) <- ifelse(is.na(valn),val,valn)
}
for (j in seq_len(length(xs))) {
if (length(res[[j]])>1) {
regfix(object, to=y[1], from=xs[j],...) <- res[[j]][2]
} else {
object <- regression(object,to=y[1],from=xs[j],...)
}
}
}
object$parpos <- NULL
return(object)
}
if (!is.list(value) | length(value)>2) stop("Value should contain names of outcome (to) and predictors (from)")
if (all(c("to","from")%in%names(value))) {
xval <- value$x; yval <- value$y
} else {
yval <- value[[1]]; xval <- value[[2]]
}
regression(object, to=yval, from=xval,...)
}
}
##' @export
`regression` <-
function(object,to,from,...) UseMethod("regression")
##' @export
`regression.lvm` <-
function(object=lvm(),to,from,fn=NA,silent=lava.options()$silent,
additive=TRUE, ...) {
if (!additive) {
if (!inherits(to,"formula")) to <- toformula(to,from)
x <- attributes(getoutcome(to))$x
K <- object$attributes$nordinal[x]
if (is.null(K) || is.na(K)) {
K <- list(...)$K
if (is.null(K)) stop("Supply number of categories, K (or use method 'categorical' before calling 'regression').")
object <- categorical(object,x,...)
}
dots <- list(...);
dots$K <- K
dots$x <- object
dots$formula <- to
dots$regr.only <- TRUE
object <- do.call("categorical",dots)
return(object)
}
if (missing(to)) {
return(regfix(object))
}
if (class(to)[1]=="formula") {
regression(object,silent=silent,...) <- to
object$parpos <- NULL
return(object)
}
if (is.list(to)) {
for (t in to)
regression(object,silent=silent,...) <- t
object$parpos <- NULL
return(object)
}
sx <- strsplit(from,"@")
xx <- sapply(sx, FUN=function(i) i[1])
ps <- sapply(sx, FUN=function(i) i[2])
sx <- strsplit(xx,"$",fixed=TRUE)
xs <- sapply(sx, FUN=function(i) i[1])
fix <- as.numeric(sapply(sx, FUN=function(i) i[2]))
allv <- index(object)$vars
object <- addvar(object, c(to,xs), silent=silent,reindex=FALSE)
for (i in to)
for (j in xs) {
object$M[j,i] <- 1
if (!is.na(fn))
functional(object,j,i) <- fn
}
if (lava.options()$exogenous) {
newexo <- setdiff(xs,c(to,allv))
exo <- exogenous(object)
if (length(newexo)>0)
exo <- unique(c(exo,newexo))
exogenous(object) <- setdiff(exo,to)
}
if (lava.options()$debug) {
print(object$fix)
}
object$fix[xs,to] <- fix
object$par[xs,to] <- ps
object$parpos <- NULL
index(object) <- reindex(object)
return(object)
}
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