MBESS: The MBESS R Package

Documented in ss.aipe.rmsea.sensitivity

ss.aipe.rmsea.sensitivity <- function(width, model, Sigma, N=NULL, conf.level=0.95, G=200, save.file="sim.results.txt", ...)
{
options(warn=-1)
  
if(!requireNamespace("MASS", quietly = TRUE)) stop("The package 'MASS' is needed; please install the package and try again.")
if(!requireNamespace("sem", quietly = TRUE)) stop("The package 'sem' is needed; please install the package and try again.")
  
result.file<- save.file

print("Simulation results will be saved to a text file after each replication") 
suppressWarnings(file.exist<-try(read.table(result.file), silent=TRUE))
if(!is.null(dim(file.exist))) cat("A file in the local directory has the same name as the file where simulation","\n", "results will be saved to. Simulation results will be appended to this file.","\n", sep="")
M.fit <- sem(model, Sigma, 1000000)
rmsea <- summary(M.fit)$RMSEA[1]
df <- summary(M.fit)$df

if (is.null(N)) N <- ss.aipe.rmsea(RMSEA=rmsea, df=df, width=width, conf.level =conf.level) 
p<- dim(Sigma)[1]
Data <- matrix(NA, N, p)
rmsea.hat <- rep(NA, G)
CI.upper <- rep(NA, G)
CI.lower <- rep(NA, G)

res.col.names<- cbind("iteration","RMSEA.hat","CI.low","CI.up","width")
write.table(res.col.names, result.file,append=TRUE, sep="      ", row.names=FALSE, col.names=FALSE,...)
for (g in 1:G){
	gc()
	cat("replication = ", g, "\n")
   Data <- MASS::mvrnorm(n = N, mu=rep(0,p), Sigma=Sigma)  
   S <- var(Data)
   colnames(S) <- rownames(S)<- rownames(Sigma)
   
   m.fit <- suppressWarnings(try(sem::sem(model, S, N, gradtol=0.0001), TRUE))
    if(!is.list(m.fit)) {
    	 rmsea.hat[g]<- NA
        CI.upper[g] <- NA
        CI.lower[g] <- NA
    	}else 
    		if (any(is.nan(m.fit$cov))||any(is.na(m.fit$cov)) || inherits(m.fit, "try-error")){
        rmsea.hat[g]<- NA
        CI.upper[g] <- NA
        CI.lower[g] <- NA
        }
    else {
        rmsea.hat[g] <- summary(m.fit)$RMSEA[1]
        CI <- ci.rmsea(rmsea.hat[g], df=df, N=N)
        CI.lower[g] <- CI$Lower.Conf.Limit
        CI.upper[g] <- CI$Upper.Conf.Limit
        sim.result<- cbind(g,rmsea.hat[g], CI.lower[g], CI.upper[g], CI.upper[g]-CI.lower[g])
        write.table(sim.result, result.file, append=TRUE, sep="  ", row.names=FALSE, col.names=FALSE,...)
        }

   #m.fit <- try(sem(model, S, N), FALSE)
   #if(inherits(m.fit, "try-error")|| m.fit$convergence>2) g<- g
   #else{
   #		g<- g+1
   	#	rmsea.hat[g] <- summary(m.fit)$RMSEA[1]
   #   CI <- ci.rmsea(rmsea.hat[g], df=df, N=N)
   #   CI.lower[g] <- CI$Lower.Conf.Limit
   #   CI.upper[g] <- CI$Upper.Conf.Limit
   #		}
	
	
	}#end of while(g<G)

rmsea.hat<- rmsea.hat
CI.upper <- CI.upper
CI.lower <- CI.lower
w <- CI.upper - CI.lower
suc.rep<-sum(!is.na(w))

result <- list()
result$w <- w
result$RMSEA.hat <- rmsea.hat
result$successful.replication<- suc.rep
result$sample.size <- N
result$df <- df
result$RMSEA.pop <- rmsea
result$desired.width <- width
result$mean.width <- mean(w, na.rm=TRUE)
result$median.width <- median(w, na.rm=TRUE)
result$assurance <- sum(w< width, na.rm=TRUE)/suc.rep
result$quantile.width <- quantile(w, c(.99, .97, .95, .90, .80, .70, .60), na.rm=TRUE)
result$alpha.upper <- sum(CI.upper< rmsea, na.rm=TRUE)/suc.rep
result$alpha.lower <- sum(CI.lower> rmsea, na.rm=TRUE)/suc.rep
result$alpha <- result$alpha.upper+result$alpha.lower 
result$conf.level <- conf.level

############################################################
############################################################

sem <- function(ram, ...)
    {
    if (is.character(ram)) class(ram) <- 'mod'
    UseMethod('sem', ram)
    }

sem.mod <- function (ram, S, N, obs.variables=rownames(S), fixed.x=NULL, debug=FALSE, ...){
    parse.path <- function(path) {                                           
        path.1 <- gsub('-', '', gsub(' ','', path))
        direction <- if (regexpr('<>', path.1) > 0) 2 
            else if (regexpr('<', path.1) > 0) -1
            else if (regexpr('>', path.1) > 0) 1
            else stop(paste('ill-formed path:', path))
        path.1 <- strsplit(path.1, '[<>]')[[1]]
        list(first=path.1[1], second=path.1[length(path.1)], direction=direction)
        }
    if ((!is.matrix(ram)) | ncol(ram) != 3) stop ('ram argument must be a 3-column matrix')
    startvalues <- as.numeric(ram[,3])
    par.names <- ram[,2]
    n.paths <- length(par.names)
    heads <- from <- to <- rep(0, n.paths)
    for (p in 1:n.paths){
        path <- parse.path(ram[p,1])
        heads[p] <- abs(path$direction)
        to[p] <- path$second
        from[p] <- path$first
        if (path$direction == -1) {
            to[p] <- path$first
            from[p] <- path$second
            }
        }
    ram <- matrix(0, p, 5)
    all.vars <- unique(c(to, from))
    latent.vars <- setdiff(all.vars, obs.variables)
    not.used <- setdiff(obs.variables, all.vars)
    if (length(not.used) > 0){
        rownames(S) <- colnames(S) <- obs.variables
        obs.variables <- setdiff(obs.variables, not.used)
        S <- S[obs.variables, obs.variables]
        warning("The following observed variables are in the input covariance or raw-moment matrix ",
            "but do not appear in the model:\n",
            paste(not.used, collapse=", "), "\n")
        }
    vars <- c(obs.variables, latent.vars)
    pars <- na.omit(unique(par.names))
    ram[,1] <- heads
    ram[,2] <- apply(outer(vars, to, '=='), 2, which)
    ram[,3] <- apply(outer(vars, from, '=='), 2, which)   
    par.nos <- apply(outer(pars, par.names, '=='), 2, which)
    if (length(par.nos) > 0)
        ram[,4] <- unlist(lapply(par.nos, function(x) if (length(x) == 0) 0 else x))
    ram[,5]<- startvalues
    colnames(ram) <- c('heads', 'to', 'from', 'parameter', 'start')
    if (!is.null(fixed.x)) fixed.x <- apply(outer(vars, fixed.x, '=='), 2, which)
    n <- length(obs.variables)
    m <- length(all.vars)
    t <- length(pars)
    if (debug) {
        cat('\n observed variables:\n') 
        print(paste(paste(1:n,':', sep=''), obs.variables, sep=''))
        cat('\n')
        if (m > n){ 
            cat('\n latent variables:\n')
            print(paste(paste((n+1):m,':', sep=''), latent.vars, sep=''))
            cat('\n')
            }
        cat('\n parameters:\n') 
        print(paste(paste(1:t,':', sep=''), pars, sep=''))
        cat('\n\n RAM:\n')
        print(ram)
        }
    sem(ram=ram, S=S, N=N, param.names=pars, var.names=vars, fixed.x=fixed.x,
        debug=debug, ...)
    }
     

sem.default <- function(ram, S, N, param.names=paste('Param', 1:t, sep=''), 
    var.names=paste('V', 1:m, sep=''), fixed.x=NULL, raw=FALSE, debug=FALSE,
    analytic.gradient=TRUE, warn=FALSE, maxiter=500, par.size=c('ones', 'startvalues'), 
    refit=FALSE, start.tol=1E-6, ...){
    ord <- function(x) 1 + apply(outer(unique(x), x, "<"), 2, sum)
    is.triangular <- function(X) {
        is.matrix(X) && (nrow(X) == ncol(X)) && 
            (all(0 == X[upper.tri(X)])) || (all(0 == X[lower.tri(X)]))
        }    
    S <- unclass(S) # in case S is a rawmoment object
    if (is.triangular(S)) S <- S + t(S) - diag(diag(S))
    if (!isSymmetric(S)) stop('S must be a square triangular or symmetric matrix')
    if (qr(S)$rank < ncol(S)) warning("S is numerically singular: expect problems")
    if (any(eigen(S, symmetric=TRUE, only.values=TRUE)$values <= 0)) 
        warning("S is not positive-definite: expect problems")
    if ((!is.matrix(ram)) | ncol(ram) != 5 | (!is.numeric(ram)))
        stop ('ram argument must be a 5-column numeric matrix')
    par.size <- if (missing(par.size)) {
        range <- range(diag(S))
        if (range[2]/range[1] > 100) 'startvalues' else 'ones'
        }
        else match.arg(par.size)
    n <- nrow(S)
    observed <- 1:n
    n.fix <- length(fixed.x)
    if (!is.null(fixed.x)){
        for (i in 1:n.fix){
            for (j in 1:i){
                ram <- rbind(ram, c(2, fixed.x[i], fixed.x[j], 
                    0, S[fixed.x[i], fixed.x[j]]))
                }
            }
        }
    m <- max(ram[,c(2,3)])
    missing.variances <- setdiff(1:m, ram[,2][ram[,2] == ram[,3]])
    if (length(missing.variances) > 0) warning(paste("The following variables have no variance or error-variance parameter (double-headed arrow):\n",
        paste(var.names[missing.variances], collapse=", "), 
        "\nThe model is almost surely misspecified; check also for missing covariances.\n"))
    t <- max(ram[,4])
    df <- n*(n + 1)/2 - t - n.fix*(n.fix + 1)/2
    if (df < 0) stop(paste("The model has negative degrees of freedom =", df))
    J <- matrix(0, n, m)
    correct <- matrix(2, m, m)
    diag(correct) <- 1
    J[cbind(1:n, observed)]<-1
    par.posn <-  sapply(1:t, function(i) which(ram[,4] == i)[1])
    colnames(ram)<-c("heads", "to", "from", "parameter", "start value")
    rownames(ram)<-rep("",nrow(ram))
    if (length(param.names) > 0) rownames(ram)[par.posn]<-param.names
    fixed <- ram[,4] == 0
    sel.free <- ram[,4]
    sel.free[fixed] <- 1
    one.head <- ram[,1] == 1
    one.free <- which( (!fixed) & one.head )
    two.free <- which( (!fixed) & (!one.head) )
    arrows.1 <- ram[one.head, c(2,3), drop=FALSE]
    arrows.2 <- ram[!one.head, c(2,3), drop=FALSE]
    arrows.2t <- ram[!one.head, c(3,2), drop=FALSE]
    arrows.1.free <- ram[one.free,c(2,3), drop=FALSE]
    arrows.2.free <- ram[two.free,c(2,3), drop=FALSE]
    sel.free.1 <- sel.free[one.free]
    sel.free.2 <- sel.free[two.free]
    unique.free.1 <- unique(sel.free.1)
    unique.free.2 <- unique(sel.free.2)
    objective.1 <- function(par){
        A <- P <- matrix(0, m, m)
        val <- ifelse (fixed, ram[,5], par[sel.free])
        A[arrows.1] <- val[one.head]
        P[arrows.2t] <- P[arrows.2] <- val[!one.head]
        I.Ainv <- solve(diag(m) - A)
        C <- J %*% I.Ainv %*% P %*% t(I.Ainv) %*% t(J)
        Cinv <- solve(C)
        f <- sum(diag(S %*% Cinv)) + log(det(C))
        attributes(f) <- list(C=C, A=A, P=P)
        f
        }
    objective.2 <- function(par){
        A <- P <- matrix(0, m, m)
        val <- ifelse (fixed, ram[,5], par[sel.free])
        A[arrows.1] <- val[one.head]
        P[arrows.2t] <- P[arrows.2] <- val[!one.head]
        I.Ainv <- solve(diag(m) - A)
        C <- J %*% I.Ainv %*% P %*% t(I.Ainv) %*% t(J)
        Cinv <- solve(C) 
        f <- sum(diag(S %*% Cinv)) + log(det(C))
        grad.P <- correct * t(I.Ainv) %*% t(J) %*% Cinv %*% (C - S) %*% Cinv %*% J %*% I.Ainv
        grad.A <- grad.P %*% P %*% t(I.Ainv)        
        gradient <- rep(0, t)
        gradient[unique.free.1] <- tapply(grad.A[arrows.1.free],ram[ram[,1]==1 & ram[,4]!=0, 4], sum)
        gradient[unique.free.2] <- tapply(grad.P[arrows.2.free],ram[ram[,1]==2 & ram[,4]!=0, 4], sum)
        attributes(f) <- list(C=C, A=A, P=P, gradient=gradient)
        f
        }
    result <- list()
    result$var.names <- var.names
    result$ram <- ram
    rownames(S) <- colnames(S) <- var.names[observed]
    result$S <- S
    result$J <- J
    result$n.fix <- n.fix
    result$n <- n
    result$N <- N
    result$m <- m
    result$t <- t
    result$raw <- raw
    if (length(param.names)== 0){
        warning("there are no free parameters in the model")
        obj <- objective.1(NULL)
        }
    else {
        start <- if (any(is.na(ram[,5][par.posn])))
            sem::startvalues(S, ram, debug=debug, tol=start.tol)
            else ram[,5][par.posn]
        if (!warn){
            save.warn <- options(warn=-1)
            on.exit(options(save.warn))
            }
        typsize <- if (par.size == 'startvalues') abs(start) else rep(1,t)
        res <- try(nlm(if (analytic.gradient) objective.2 else objective.1,
            start, hessian=TRUE, iterlim=maxiter, print.level=if(debug) 2 else 0,
            typsize=typsize, ...), silent=TRUE)
        #convergence <- res$code
        if (!warn) options(save.warn)
        
        if (inherits(res, what="try-error")|| res$convergence>2){
            result$coeff <- rep(NA, t)
            result$par.posn <- NA
            result$iterations <- NA
            result$raw <- NA
            cov <- matrix(NA, t, t)
            colnames(cov) <- rownames(cov) <- param.names
            result$cov <- cov
            result$aliased <- NA
            }
        
        else{ 
            par <- res$estimate
            names(par) <- param.names
            obj <- objective.2(par)
            ram[par.posn, 5] <- start
            par.code <- paste(var.names[ram[,2]], c('<---', '<-->')[ram[,1]],
            var.names[ram[,3]])
            result$coeff <- par
            result$par.posn <- par.posn
            #result$convergence <- convergence
            result$iterations <- res$iterations
            result$raw <- raw
            #if (convergence > 2)
            #    warning(paste('Optimization may not have converged; nlm return code = ',
            #        res$code, '. Consult ?nlm.\n', sep=""))
                      
            qr.hess <- try(qr(res$hessian), silent=TRUE)
            if (inherits(qr.hess, what="try-error")){
                #warning("Could not compute QR decomposition of Hessian.\nOptimization probably did not converge.\n")
                cov <- matrix(NA, t, t)
                colnames(cov) <- rownames(cov) <- param.names
                result$cov <- cov
                }
            else if (qr.hess$rank < t){
                #warning(' singular Hessian: model is probably underidentified.\n')
                cov <- matrix(NA, t, t)
                colnames(cov) <- rownames(cov) <- param.names
                result$cov <- cov
                which.aliased <- qr.hess$pivot[-(1:qr.hess$rank)]
                aliased <- param.names[which.aliased]
                position.aliased <- is.element(ram[,4], which.aliased)
                if (refit){
                    warning(' refitting without aliased parameters.\n')
                    ram.refit <- ram[!position.aliased,]
                    par.refit <- ram.refit[,4]
                    par.refit[par.refit != 0] <- ord(par.refit[par.refit != 0])
                    ram.refit[,4] <- par.refit
                    iterations <- result$iterations
                    result <- Recall(ram.refit, S, N,
                        param.names=param.names[-which.aliased], var.names=var.names,
                        debug=debug, analytic.gradient=analytic.gradient,
                        warn=warn, maxiter=maxiter, par.size=par.size, refit=TRUE, ...)
                    result$iterations <- iterations + result$iterations
                    aliased <- c(aliased, result$aliased)
                    }
                result$aliased <- aliased
                }
            else {
                cov <- (2/(N - (!raw))) * solve(res$hessian)
                colnames(cov) <- rownames(cov) <- param.names
                result$cov <- cov
                if (any(diag(cov) < 0)) {
                    result$aliased <- c(param.names[diag(cov) < 0], result$aliased)
                    #warning("Negative parameter variances.\nModel is probably underidentified.\n")
                    }
                }
            
            }#end of if(class(res)!="try-error") else
        }
                    
if (!inherits(res, what="try-error")){
    result$criterion <-  c(obj) - n - log(det(S))
    C <- attr(obj, "C")
    rownames(C) <- colnames(C) <- var.names[observed]
    result$C <- C
    A <- attr(obj, "A")
    rownames(A) <- colnames(A) <- var.names
    result$A <- A
    P <- attr(obj, "P")
    rownames(P) <- colnames(P) <- var.names
    result$P <- P
    if (!raw) {
        CC <- diag(diag(S))
        result$chisqNull <- (N - 1) * 
            (sum(diag(S %*% solve(CC))) + log(det(CC)) -log(det(S)) - n)
        }
    class(result) <- "sem"
    }# end of if (class(res)!="try-error")
else {
    result$criterion <- NA
    result$C <- NA
    result$A <- NA
    result$P <- NA
    result$chisqNull<- NA
    }
class(result) <- "sem"    
result
}    

vcov.sem <- function(object, ...) {
    object$cov
}

coef.sem <- function(object, ...){
    object$coeff
}
############################################################
############################################################

return(result)
}# end of ss.aipe.rmsea.sensitiviti <- function()