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| Package: sirt | ||
| Type: Package | ||
| Title: Supplementary Item Response Theory Models | ||
| Version: 3.10-79 | ||
| Date: 2021-03-09 13:01:29 | ||
| Version: 3.10-91 | ||
| Date: 2021-04-02 14:53:21 | ||
| Author: Alexander Robitzsch [aut,cre] (<https://orcid.org/0000-0002-8226-3132>) | ||
| Maintainer: Alexander Robitzsch <[email protected]> | ||
| Description: | ||
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| ## File Name: dif.strata.variance.R | ||
| ## File Version: 0.14 | ||
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| #* stratified DIF variance | ||
| dif.strata.variance <- function( dif, se.dif, itemcluster ) | ||
| { | ||
| # stratified DIF variance | ||
| # means in differential item functioning | ||
| # itemcluster is a vector of strata corresponding to items | ||
| stratadif <- stats::aggregate( 1+0*dif, list(itemcluster), sum, na.rm=TRUE ) | ||
| colnames(stratadif) <- c("strata", "N.Items" ) | ||
| stratadif <- data.frame(stratadif) | ||
| stratadif$M.DIF <- stats::aggregate( dif, list(itemcluster), mean, na.rm=TRUE )[,2] | ||
| # DIF in strata | ||
| SS <- nrow(stratadif) | ||
| for (ss in 1:SS){ | ||
| items.ss <- which( itemcluster==stratadif[ss,"strata"] ) | ||
| dif.ss <- dif[ items.ss ] | ||
| difv.ss <- dif.variance( dif=dif.ss, se.dif=se.dif[ items.ss ] ) | ||
| stratadif$weighted.tau[ss] <- difv.ss$weighted.DIFSD | ||
| stratadif$unweighted.tau[ss] <- difv.ss$unweighted.DIFSD | ||
| } | ||
| stratadif[ is.na(stratadif ) ] <- 0 | ||
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| sd_ni1 <- stratadif$N.Items-1 | ||
| weighted.DIFSD <- sum(stratadif$N.Items/sum(stratadif$N.Items)*stratadif$weighted.tau) | ||
| unweighted.DIFSD <- sum( sd_ni1/ (sum(stratadif$N.Items)-1)*stratadif$unweighted.tau) | ||
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| #-- output | ||
| res <- list( stratadif=stratadif, weighted.DIFSD=weighted.DIFSD, | ||
| unweighted.DIFSD=unweighted.DIFSD) | ||
| return(res) | ||
| } | ||
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| ## File Name: dif.variance.R | ||
| ## File Version: 0.18 | ||
| ## File Version: 0.193 | ||
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| #-------------------------------------------------------------------------# | ||
| # Routine for calculating DIF variance (Camilli & Penfield, 1997) # | ||
| dif.variance <- function( dif, se.dif, items=paste("item",1:length(dif),sep="") ){ | ||
| # calculating the weights | ||
| wi <- 1/se.dif^2 | ||
| # mean DIF | ||
| md <- mean(dif) | ||
| # weighted tau2 estimator | ||
| # formula (5) of PENFIELD & ALGINA (2006) | ||
| weighted.tauq <- sum( wi^2 * ( dif - md )^2 - wi ) / sum( wi^2 ) | ||
| # unweighted tau2 estimator | ||
| # formula (5) of PENFIELD & ALGINA (2006) | ||
| unweighted.tauq <- sum( ( dif - md )^2 - se.dif^2 ) / ( length(items) - 1 ) | ||
| # calculation of variances v_i | ||
| vi <- weighted.tauq + se.dif^2 | ||
| weighted.tauq[ weighted.tauq < 0 ] <- 0 | ||
| unweighted.tauq[ unweighted.tauq < 0 ] <- 0 | ||
| # Empirical Bayes DIF estimate | ||
| lambda.i <- weighted.tauq / vi | ||
| eb.dif <- lambda.i * ( dif - md ) + ( 1 - lambda.i) *md | ||
| list( weighted.DIFSD=sqrt(weighted.tauq), | ||
| unweighted.DIFSD=sqrt(unweighted.tauq), | ||
| mean.se.dif=sqrt( mean( se.dif^2 ) ), eb.dif=eb.dif ) | ||
| } | ||
| #-------------------------------------------------------------------------# | ||
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| #*** Routine for calculating DIF variance (Camilli & Penfield, 1997) # | ||
| dif.variance <- function( dif, se.dif, items=paste("item",1:length(dif),sep="") ) | ||
| { | ||
| # calculating the weights | ||
| wi <- 1/se.dif^2 | ||
| # mean DIF | ||
| md <- mean(dif) | ||
| # weighted tau2 estimator | ||
| # formula (5) of PENFIELD & ALGINA (2006) | ||
| weighted.tauq <- sum( wi^2 * ( dif - md )^2 - wi ) / sum( wi^2 ) | ||
| # unweighted tau2 estimator | ||
| # formula (5) of PENFIELD & ALGINA (2006) | ||
| unweighted.tauq <- sum( ( dif - md )^2 - se.dif^2 ) / ( length(items) - 1 ) | ||
| # calculation of variances v_i | ||
| vi <- weighted.tauq + se.dif^2 | ||
| weighted.tauq[ weighted.tauq < 0 ] <- 0 | ||
| unweighted.tauq[ unweighted.tauq < 0 ] <- 0 | ||
| # Empirical Bayes DIF estimate | ||
| lambda.i <- weighted.tauq / vi | ||
| eb.dif <- lambda.i * ( dif - md ) + ( 1 - lambda.i) *md | ||
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| ################################################################################# | ||
| dif.strata.variance <- function( dif, se.dif, itemcluster ){ | ||
| # stratified DIF variance | ||
| # means in differential item functioning | ||
| # itemcluster is a vector of strata corresponding to items | ||
| stratadif <- stats::aggregate( 1+0*dif, list( itemcluster ), sum, na.rm=T ) | ||
| colnames(stratadif) <- c("strata", "N.Items" ) | ||
| stratadif <- data.frame(stratadif) | ||
| stratadif$M.DIF <- stats::aggregate( dif, list( itemcluster ), mean, na.rm=T )[,2] | ||
| # DIF in strata | ||
| SS <- nrow(stratadif) | ||
| for (ss in 1:SS){ | ||
| # ss <- 1 | ||
| items.ss <- which( itemcluster==stratadif[ss,"strata"] ) | ||
| dif.ss <- dif[ items.ss ] | ||
| difv.ss <- dif.variance( dif=dif.ss, se.dif=se.dif[ items.ss ] ) | ||
| stratadif$weighted.tau[ss] <- difv.ss$weighted.DIFSD | ||
| stratadif$unweighted.tau[ss] <- difv.ss$unweighted.DIFSD | ||
| } | ||
| stratadif[ is.na(stratadif ) ] <- 0 | ||
| res <- list( "stratadif"=stratadif, | ||
| "weighted.DIFSD"=sum( stratadif$N.Items / sum( stratadif$N.Items ) * | ||
| stratadif$weighted.tau ), | ||
| "unweighted.DIFSD"=sum( | ||
| ( stratadif$N.Items -1 )/ ( sum( stratadif$N.Items ) - 1) * stratadif$unweighted.tau ) | ||
| ) | ||
| #* output | ||
| res <- list( weighted.DIFSD=sqrt(weighted.tauq), | ||
| unweighted.DIFSD=sqrt(unweighted.tauq), | ||
| mean.se.dif=sqrt( mean( se.dif^2 ) ), eb.dif=eb.dif ) | ||
| return(res) | ||
| } | ||
| ################################################################################# | ||
| } | ||
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| ## File Name: fuzcluster.R | ||
| ## File Version: 0.15 | ||
| ## File Version: 0.163 | ||
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| #********************************************* | ||
| # Clustering for continuous fuzzy data | ||
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| #*** Clustering for continuous fuzzy data | ||
| fuzcluster <- function(dat_m, dat_s, K=2, nstarts=7, | ||
| seed=NULL, maxiter=100, parmconv=.001, | ||
| fac.oldxsi=0.75, progress=TRUE ){ | ||
| seed=NULL, maxiter=100, parmconv=.001, fac.oldxsi=0.75, progress=TRUE ) | ||
| { | ||
| s1 <- Sys.time() | ||
| dev0 <- 10^(200) | ||
| dev0 <- 1e200 | ||
| dat_resp <- 1 - is.na(dat_m) | ||
| if ( ! is.null(seed) ){ nstarts <- 1 } | ||
| if ( ! is.null(seed) ){ | ||
| nstarts <- 1 | ||
| } | ||
| for ( rr in 1:nstarts ){ | ||
| res1 <- fuzcluster_estimate(K, dat_m, dat_s, dat_resp, | ||
| maxiter=maxiter, parmconv=parmconv, progress=progress, | ||
| seed=seed, fac.oldxsi=fac.oldxsi) | ||
| maxiter=maxiter, parmconv=parmconv, progress=progress, | ||
| seed=seed, fac.oldxsi=fac.oldxsi) | ||
| if ( res1$deviance < dev0 ){ | ||
| res <- res1 | ||
| dev0 <- res1$deviance | ||
| } | ||
| } | ||
| } | ||
| } | ||
| s2 <- Sys.time() | ||
| ### end random starts | ||
| ### computation of information criteria | ||
| dev <- res$deviance | ||
| ic <- list( "deviance"=dev, "n"=nrow(dat_m) ) | ||
| ic <- list( deviance=dev, n=nrow(dat_m) ) | ||
| I <- ncol(dat_m) | ||
| ic$np <- (K-1) + 2*K*I | ||
| # AIC | ||
| ic$AIC <- dev + 2*ic$np | ||
| # BIC | ||
| ic$BIC <- dev + ( log(ic$n) )*ic$np | ||
| # CAIC (conistent AIC) | ||
| ic$CAIC <- dev + ( log(ic$n) + 1 )*ic$np | ||
| # corrected AIC | ||
| ic$AICc <- ic$AIC + 2*ic$np * ( ic$np + 1 ) / ( ic$n - ic$np - 1 ) | ||
| ic$AIC <- dev + 2*ic$np | ||
| ic$BIC <- dev + ( log(ic$n) )*ic$np | ||
| ic$CAIC <- dev + ( log(ic$n) + 1 )*ic$np | ||
| ic$AICc <- ic$AIC + 2*ic$np * ( ic$np + 1 ) / ( ic$n - ic$np - 1 ) | ||
| res$ic <- ic | ||
| res$K <- K | ||
| res$s1 <- s1 | ||
| res$s2 <- s2 | ||
| res$nstarts <- nstarts | ||
| class(res) <- "fuzcluster" | ||
| ### | ||
| return(res) | ||
| } | ||
| } |
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