R/BIFIE.pathmodel.R

In BIFIEsurvey: Tools for Survey Statistics in Educational Assessment

## File Name: BIFIE.pathmodel.R
## File Version: 1.321


#--- path model
BIFIE.pathmodel <- function( BIFIEobj, lavaan.model, reliability=NULL,
            group=NULL, group_values=NULL, se=TRUE )
{
    requireNamespace("TAM")
    s1 <- Sys.time()
    cl <- match.call()
    bifieobj <- BIFIEobj
    dat <- bifieobj$dat1

    # lavaanify syntax
    lavpartable <- TAM::lavaanify.IRT( lavmodel=lavaan.model, data=dat )$lavpartable
    vars <- colnames(dat)
    lav1 <- lavpartable[ lavpartable$op %in% c("=~", "~"), ]
    lav.vars <- unique( c( lav1$lhs, lav1$rhs ) )
    NV <- length(lav.vars)
    # observed variables
    obs.vars <- intersect( vars, lav.vars )
    # latent variables
    lat.vars <- setdiff( lav.vars, obs.vars )
    # create model matrix for latent variables
    NLV <- length(lat.vars)
    L <- matrix( 0, nrow=NLV, ncol=NV )
    rownames(L) <- lat.vars
    colnames(L) <- lav.vars
    if (NLV>0){
        for (vv in 1:NLV){
            lav.vv <- lav1[ ( lav1$op=="=~" ) & ( lav1$lhs==lat.vars[vv] ), ]
            L[ vv, lav.vv$rhs ] <- ifelse( is.na(lav.vv$ustart), 1, lav.vv$ustart )
        }
    }
    L_row_index <- match( rownames(L), lav.vars )

    # model matrix for regressions
    lav2 <- lav1[ lav1$op=="~", ]
    dep <- unique( lav2$lhs )
    NR <- length(dep)
    R <- matrix( 0, nrow=NR, ncol=NV )
    rownames(R) <- dep
    colnames(R) <- lav.vars
    for (vv in 1:NR){
        lav.vv <- lav1[ ( lav1$op=="~" ) & ( lav1$lhs==dep[vv] ), "rhs"]
        R[ vv, lav.vv ] <- 1
    }
    R_row_index <- match( rownames(R), lav.vars )
    # matrix B with regression coefficients
    B <- matrix(0,nrow=NV, ncol=NV)
    rownames(B) <- colnames(B) <- lav.vars
    for (vv in 1:NR){
        B[ rownames(R)[vv], ] <- R[vv, ]
    }
    # error variances and covariances
    E <- matrix( 0, nrow=NV, ncol=NV )
    rownames(E) <- colnames(E) <- lav.vars
    lav2 <- lavpartable[ lavpartable$op=="~~", ]
    lav2 <- stats::na.omit( lav2 )
    NG <- nrow(lav2)
    if (NG > 0){
        for ( gg in 1:NG){
            E[ lav2$lhs[gg], lav2$rhs[gg] ] <- lav2$ustart[gg]
        }
    }

    # compute matrix power for pathe coefficients
    ind <- 0
    Bpow <- B
    Bpowsum <- Bpow
    for (kk in 1:100){
        Bpow <- Bpow %*% B
        Bpowsum <- Bpowsum + Bpow
        ind <- ind + 1
        if ( sum( Bpow ) < 1E-10 ){ break }
    }
    maxpow <- ind

    ind.vars <- colnames(B)[ which( colSums( B ) > 0 ) ]
    M1 <- matrix( ind.vars, ncol=1 )

    for (oo in 1:maxpow){
        NM1 <- nrow(M1)
        M2 <- NULL
        for (mm in 1:NM1){
            v1 <- rownames(B)[  B[, colnames(B)==paste(M1[ mm, oo ]) ] > 0  ]
            if (oo>1 ){ v1 <- c( "", v1 ) }
            M1mm <-  t(M1[ mm, 1:oo ])
            HV <- length(v1)
            H1 <- matrix( "", nrow=HV, ncol=oo+1 )
            H1[, oo+1 ] <- v1
            H1[, 1:oo ] <- matrix( M1mm, nrow=HV, ncol=oo, byrow=TRUE )
            M2 <- rbind(M2, H1 )
        }
        M1 <- M2
    }
    M1_index <- matrix( 0, nrow(M1), ncol(M1) )
    for (mm in 1:ncol(M1) ){
        M1_index[, mm ] <- match( M1[,mm], lav.vars )
    }

    # compute total effects
    tot_paths <- t( apply( M1, 1, FUN=function(ll){
                    vv <- ll[ ll !="" ]
                    N1 <- length(vv)
                    c( paste0( vv[1], "->", vv[N1] ), N1 )
                        } ) )
    tot_paths <- as.data.frame( tot_paths )
    tot_paths2 <- tot_paths[ as.numeric(paste(tot_paths[,2])) > 2, ]
    paths <- unique( paste(tot_paths2[,1 ] ) )
    tot_paths$pathindex <- match( paste(tot_paths[,1]), paths ) + nrow(M1)
    if ( mean( is.na(tot_paths$pathindex ) ) < 1 ){
        NP0 <- max( tot_paths$pathindex, na.rm=TRUE)
    } else {
        NP0 <- nrow(M1)
    }

    coeff_index <- cbind( tot_paths$pathindex, M1_index )
    NV <- ncol(Bpowsum)
    indices <- which( Bpowsum > 0 )

    if (bifieobj$cdata){
        varnames <- unique( c( obs.vars, group, "one" ) )
        bifieobj <- BIFIE.BIFIEcdata2BIFIEdata( bifieobj, varnames=varnames )
    }

    FF <- Nimp <- bifieobj$Nimp
    N <- bifieobj$N
    dat1 <- bifieobj$dat1
    wgt <- bifieobj$wgt
    wgtrep <- bifieobj$wgtrep
    varnames <- bifieobj$varnames
    RR <- bifieobj$RR
    datalistM <- bifieobj$datalistM
    fayfac <- bifieobj$fayfac
    vars_index <- match( lav.vars, colnames(dat1) )

    # unreliability
    unreliability <- rep(0, NV)
    names(unreliability) <- lav.vars
    unreliability[ match( names(reliability), lav.vars) ] <- 1 - reliability
    NL <- nrow(L)
    if (NL==0 ){
        L <- matrix( 0, nrow=1, ncol=NV)
        colnames(L) <- lav.vars
    }

    tot_paths <- data.frame( tot_paths, "pathindex2"=tot_paths$pathindex )
    tot_paths$pathindex2 <- match( tot_paths$pathindex2,
            stats::na.omit(unique( tot_paths$pathindex2 )) ) + NP0
    tot_paths$pathindex2[ as.numeric(paste(tot_paths[,2])) <=2 ] <- NA
    if ( mean( is.na(tot_paths$pathindex2 ) ) < 1 ){
        NP0 <- max( tot_paths$pathindex2, na.rm=TRUE)
    } else {
        NP0 <- nrow(M1)
    }
    coeff_index1 <- cbind( coeff_index[,1], tot_paths$pathindex2, coeff_index[,-1] )

    wgt_ <- matrix( wgt, ncol=1 )
    if ( is.null( group) ){ nogroup <- TRUE } else { nogroup <- FALSE }
    cat(paste0( "|", paste0( rep("*", FF), collapse=""), "|\n" ))
    if (nogroup){
        group <- "one"
        group_values <- c(1)
    }

    #@@@@***
    group_index <- match( group, varnames )
    #@@@@***

    if ( is.null(group_values ) ){
        t1 <- bifie_table( datalistM[, group_index ] )
        group_values <- sort( as.numeric( paste( names(t1) ) ))
    }

    #@@@@***
    res00 <- BIFIE_create_pseudogroup( datalistM, group, group_index, group_values )
    res00$datalistM -> datalistM
    res00$group_index -> group_index
    res00$GR -> GR
    res00$group_values -> group_values
    res00$group -> group
    #@@@@***

    if (RR==1){ RR <- 0 }
    if ( ! se ){
        wgtrep <- matrix( wgt, ncol=1 )
        RR <- 0
    }

    #**** estimate path model
    res <- bifiesurvey_rcpp_pathmodel( datalist=datalistM, wgt1=wgt_, wgtrep=wgtrep,
                        vars_index=vars_index-1, fayfac=fayfac, NI=Nimp, group_index1=group_index-1,
                        group_values=group_values, L=L, L_row_index=L_row_index-1,
                        NL=NL, E=E, R=R, R_row_index=R_row_index-1,
                        coeff_index=coeff_index1, NP0=NP0, unreliability=unreliability )
    GG <- length(group_values)

    #*** create parameter labels
    p0 <- paste(M1[,1])
    for (vv in seq(2,ncol(M1) ) ){
        p0 <- ifelse( M1[,vv] !="", paste0( p0, "->", M1[,vv] ), p0 )
    }

    p1 <- ifelse( tot_paths[,2]=="2", paste0(M1[,2], "~", M1[,1] ), p0 )
    p2 <- unique( paste(tot_paths[ ! is.na( tot_paths$pathindex ), 1 ]) )
    p2 <- gsub( "->", "-+>", p2 )
    p1 <- c( p1, p2 )
    p2 <- unique( paste(tot_paths[ ! is.na( tot_paths$pathindex2 ), 1 ]) )
    p2 <- gsub( "->", "-~>", p2 )
    p1 <- c( p1, p2 )
    p1 <- c( p1, paste0(p1, "_stand") )
    p1 <- c( p1, paste0( rownames(R), "_R2" ) )
    p1 <- c( p1, paste0( rownames(R), "_ResidVar" ) )

    dfr <- data.frame( "parameter"=rep(p1,GG) )
    dfr$type <- ""
    ZZ <- length(p1)

    if (! nogroup){
        dfr$groupvar <- group
        dfr$groupval <- rep( group_values, each=ZZ )
    }
    dfr$Ncases <- rep( res$ncases[,1], each=ZZ )
    dfr$Nweight <- rep( res$sumwgt[,1], each=ZZ )
    dfr <- create_summary_table( res_pars=res$parsL,
                    parsM=res$parsM, parsrepM=res$parsrepM,
                    dfr=dfr, BIFIEobj=BIFIEobj )
    dfr <- clean_summary_table( dfr=dfr, RR=RR, se=se, Nimp=Nimp )

    dfr[ grep( "_R2", paste(dfr$parameter) ), "type"] <- "RSquared"
    dfr[ grep( "_ResidVar", paste(dfr$parameter) ), "type"] <- "ResidVar"
    dfr[ grep( "~", paste(dfr$parameter) ), "type"] <- "RegrCoeff"

    ind <- grep( "->", paste(dfr$parameter) )
    if ( length(ind) > 0 ){
        dfr[ ind, "type"] <- "PathCoeff"
    }

    ind <- grep( "-+>", paste(dfr$parameter), fixed=TRUE )
    if ( length(ind) > 0 ){
        dfr[ ind, "type"] <- "TotalEff"
    }
    ind <- grep( "-~>", paste(dfr$parameter), fixed=TRUE )
    if ( length(ind) > 0 ){
        dfr[ ind, "type"] <- "IndEff"
    }


    # create vector of parameter names
    nogroupL <- rep( nogroup, nrow(dfr) )
    parnames <- paste0( dfr$parameter, "_",
            ifelse( ! nogroupL, paste0( "_", dfr$groupvar, "_" ), "" ),
            ifelse( ! nogroupL, dfr$groupval, "" ) )

    #@@@@***
    # multiple groupings
    dfr <- BIFIE_table_multiple_groupings( dfr, res00 )
    #@@@@***

    #*************************** OUTPUT ***************************************
    s2 <- Sys.time()
    timediff <- c( s1, s2 )
    res1 <- list( stat=dfr, output=res, timediff=timediff,
            N=N, Nimp=Nimp, RR=RR, fayfac=fayfac,
            NMI=BIFIEobj$NMI, Nimp_NMI=BIFIEobj$Nimp_NMI,
            GG=GG, parnames=parnames, lavaan.model=lavaan.model,
            reliability=reliability, CALL=cl)
    class(res1) <- "BIFIE.pathmodel"
    return(res1)
}


#-- summary for BIFIE.pathmodel function
summary.BIFIE.pathmodel <- function( object, digits=4, ... )
{
    BIFIE.summary(object)
    #- model specification
    BIFIE_pathmodel_summary_print_model_specification(object=object, digits=digits)
    # estimated parameters
    cat("Statistical Inference for Path Model \n\n")
    obji <- object$stat
    print_object_summary( obji, digits=digits )
}