Rasch Model (1PL IRT)

Loading...
Option:

Note: Input values (either numeric or character) must be separated by tabs. Copy and paste from Excel/Numbers.


                
                

If you need to create 1-0 data first, use Binary (1-0) Data Converter .


Basic statistics (Using the raw score)


                

Histogram of the total score (Using the raw score)


Boxplot (Using the raw score)


Cronbach's coefficient alpha (Using the raw score)


                

Drop if: Cronbach alpha when the item is removed
r dropped: item-total correlation without the item
r: item-total (point-biserial) correlation
IF: item facility or item mean (proportion correct answers)
ID: item discrimination (upper 1/3 - lower 1/3)


Item estimate


                

Person estimate (Theta)


                

Item fit


                

Person fit


                

Plot Options:



                





R session info

              
Note

This web application is developed with Shiny.


List of Packages Used
library(shiny)
library(shinyAce)
library(psych)
library(ltm)
library(CTT)
library(eRm)
library(beeswarm)


Code

Source code for this application is based on "The handbook of Research in Foreign Language Learning and Teaching" (Takeuchi & Mizumoto, 2012). I also referred to the code used in MacR.

The code for this web application is available at GitHub.

If you want to run this code on your computer (in a local R session), run the code below:
library(shiny)
runGitHub("rasch","mizumot")


Citation in Publications

Mizumoto, A. (2015). Langtest (Version 1.0) [Web application]. Retrieved from http://langtest.jp


Article

Mizumoto, A., & Plonsky, L. (2015). R as a lingua franca: Advantages of using R for quantitative research in applied linguistics. Applied Linguistics, Advance online publication. doi:10.1093/applin/amv025


Recommended

To learn more about R, I suggest this excellent and free e-book (pdf), A Guide to Doing Statistics in Second Language Research Using R, written by Dr. Jenifer Larson-Hall.

Also, if you are a cool Mac user and want to use R with GUI, MacR is defenitely the way to go!


Author

Atsushi MIZUMOTO, Ph.D.
Associate Professor of Applied Linguistics
Faculty of Foreign Language Studies /
Graduate School of Foreign Language Education and Research,
Kansai University, Osaka, Japan



Code for "Rasch Model (1PL IRT)"
by Atsushi Mizumoto

show with app
library(shiny)
library(shinyAce)
library(psych)
library(ltm)
library(CTT)
library(eRm)
library(beeswarm)



shinyServer(function(input, output) {


    options(warn=-1)
    
    
    check <- reactive({
        if (input$colname2 == 0) {
            x <- read.table(text=input$text2, sep="\t")
            x <- as.matrix(x)
            
            ans <- read.delim(text=input$text3, sep="\t", fill=TRUE, header=FALSE, stringsAsFactors=FALSE)
            ans <- as.character(ans)
            dat <- score(x, ans, output.scored=TRUE)$scored
            
        } else {
            
            x <- read.csv(text=input$text2, sep="\t")
            
            ans <- read.delim(text=input$text3, sep="\t", fill=TRUE, header=FALSE, stringsAsFactors=FALSE)
            ans <- as.character(ans)
            
            dat <- score(x, ans, output.scored=TRUE)$scored
        }
    })
    
    
    
    bs <- reactive({
        if (input$colname == 0) {
            x <- read.table(text=input$text1, sep="\t")
            dat <- as.matrix(x)
            
            total <- rowSums(dat, na.rm=T)
            result <- describe(total)[2:13]
            row.names(result) <- "Total   "
            result
        
        } else {
            
            dat <- read.csv(text=input$text1, sep="\t")
            
            total <- rowSums(dat, na.rm=T)
            result <- describe(total)[2:13]
            row.names(result) <- "Total   "
            result
        }
    })
    
    
    
    alpha.result <- reactive({
        if (input$colname == 0) {
            x <- read.table(text=input$text1, sep="\t")
            dat <- as.matrix(x)
            
        } else {
            dat <- read.csv(text=input$text1, sep="\t")
            
        }
        
        brownRpbi <- function(data,missing) {
            m <- mean(rowSums(data))
            sd <- sd(rowSums(data))
            totalDat <- cbind(data,rowSums(data))
            sortDat <- totalDat[order(-totalDat[,length(totalDat)]),]
            r <- c()
            itemD <- c()
            rownames(sortDat) <- c(1:nrow(sortDat))
            highDat <- head(sortDat,nrow(sortDat) %/% 3)
            lowDat <- tail(sortDat,nrow(sortDat) %/% 3)
            for (i in 1:length(data)) {
                if (is.element(colnames(data)[i], missing) == F ) {
                    mhigh <- mean(subset(totalDat[,length(totalDat)],(data[,i] == 1)))
                    mlow <- mean(subset(totalDat[,length(totalDat)],(data[,i] == 0)))
                    imean <- mean(data[,i])
                    itemD <- c(itemD,round((mean(highDat[,i]) - mean(lowDat[,i])),3))
                    rtemp <- round(cor(data[,i],totalDat[,ncol(totalDat)]),3)
                    r <- c(r,rtemp)
                }
            }
            pbiDF <- data.frame(itemD, r)
            colnames(pbiDF) <- c("ID", "r")
            return(pbiDF)
        }
        
        myAlpha <- function(data) {
            alphaRes <- reliability(data, itemal = T)
            if (length(alphaRes$N_person) == 0) {
                n <- sprintf("%d",alphaRes$nPerson)
                items <- sprintf("%d",alphaRes$nItem)
                mean <- sprintf("%.2f",round(alphaRes$scaleMean,2))
                sd <- sprintf("%.2f",round(alphaRes$scaleSD,2))
                alpha <- substring(sprintf("%.3f",round(alphaRes$alpha,3)),2,5)
            } else {
                n <- sprintf("%d",alphaRes$N_person)
                items <- sprintf("%d",alphaRes$N_item)
                mean <- sprintf("%.2f",round(alphaRes$scale.mean,2))
                sd <- sprintf("%.2f",round(alphaRes$scale.sd,2))
                alpha <- substring(sprintf("%.3f",round(alphaRes$alpha,3)),2,5)
            }
            
            sumStats <- data.frame(Total=c(n,items,alpha))
            rownames(sumStats) <- c("N","Number of items","Cronbach's alpha")
            if (length(alphaRes$N_person) == 0) {
                dropif <- round(ifelse(is.na(alphaRes$alphaIfDeleted),0,alphaRes$alphaIfDeleted),3)
                r.drop <- round(ifelse(is.na(alphaRes$pBis), 0, alphaRes$pBis),3)
                item.mean <- round(alphaRes$itemMean,3)
                itemStats <- data.frame(dropif,r.drop,item.mean)
                rownames(itemStats) <- colnames(data)
            } else {
                dropif <- round(ifelse(is.na(alphaRes$alpha.if.deleted),0,alphaRes$alpha.if.deleted),3)
                r.drop <- round(ifelse(is.na(alphaRes$pbis), 0, alphaRes$pbis),3)
                item.mean <- round(alphaRes$item.mean,3)
                itemStats <- data.frame(dropif,r.drop,item.mean)
                rownames(itemStats) <- attr(alphaRes$item.mean,"names")
            }
            colnames(itemStats) <- c("Drop if","r dropped","IF")
            itemStats2 <- cbind(itemStats,brownRpbi(data,c()))
            itemStats <- itemStats2[,c(1, 2, 5, 3, 4)]
            
            return(list(sumStats,itemStats))
        }
        
        myAlpha(dat)
        
    })
    
    
    
    
    
    data <- reactive({
         if (input$colname == 0) {
             x <- read.table(text=input$text1, sep="\t")
             dat <- as.matrix(x)
             options(digits=3)
             resRM <- RM(dat)
             p.res <- person.parameter(resRM)
             list(rasch = resRM, pp = p.res)
             
         } else {
             dat <- read.csv(text=input$text1, sep="\t")
             options(digits=3)
             resRM <- RM(dat)
             p.res <- person.parameter(resRM)
             list(rasch = resRM, pp = p.res)
         }
    })
    
    
    
    item.est <- reactive({
        if (input$colname == 0) {
            x <- read.table(text=input$text1, sep="\t")
            dat <- as.matrix(x)
            
            resRM <- data()$rasch
            ciVal <- qnorm(0.975)
            raschTable <- round(data.frame((resRM$betapar * -1), resRM$se.beta,((resRM$betapar*-1)-ciVal*resRM$se.beta),((resRM$betapar*-1)+ciVal*resRM$se.beta)),3)
            colnames(raschTable) <- c("Estimate", "Std. Error", "CI low", "CI high")
            rownames(raschTable) <- colnames(resRM$X)
            print(raschTable)
            
        } else {
            dat <- read.csv(text=input$text1, sep="\t")
            
            resRM <- data()$rasch
            ciVal <- qnorm(0.975)
            raschTable <- round(data.frame((resRM$betapar * -1), resRM$se.beta,((resRM$betapar*-1)-ciVal*resRM$se.beta),((resRM$betapar*-1)+ciVal*resRM$se.beta)),3)
            colnames(raschTable) <- c("Estimate", "Std. Error", "CI low", "CI high")
            rownames(raschTable) <- colnames(resRM$X)
            print(raschTable)
        }
    })
    
    
    
    person.est <- reactive({
        if (input$colname == 0) {
            x <- read.table(text=input$text1, sep="\t")
            dat <- as.matrix(x)
            
            p.res <- data()$pp
            summary(p.res)
            
        } else {
            dat <- read.csv(text=input$text1, sep="\t")
            
            p.res <- data()$pp
            summary(p.res)
            
        }
    })
    
    
    
    item.fit <- reactive({
        if (input$colname == 0) {
            x <- read.table(text=input$text1, sep="\t")
            dat <- as.matrix(x)
            
            p.res <- data()$pp
            itemfit(p.res)
            
        } else {
            dat <- read.csv(text=input$text1, sep="\t")
            
            p.res <- data()$pp
            itemfit(p.res)
            
        }
    })
    
    
    
    person.fit <- reactive({
        if (input$colname == 0) {
            x <- read.table(text=input$text1, sep="\t")
            dat <- as.matrix(x)
            
            p.res <- data()$pp
            personfit(p.res)
            
        } else {
            dat <- read.csv(text=input$text1, sep="\t")
            
            p.res <- data()$pp
            personfit(p.res)
            
        }
    })
    
    
    
    compare <- reactive({
     if (input$compare == 1) {

        if (input$colname == 0) {
            p.res <- data()$pp
            options(digits=3)
            list("Comparison of raw scores and theta" = p.res)

        } else {
            p.res <- data()$pp
            options(digits=3)
            list("Comparison of raw scores and theta" = p.res)
        }
     }
    })
    
    
    
    
    
    makecompPlot <- function(){
        if (input$compare == 1) {
            if (input$colname == 0) {
                p.res <- data()$pp
                plot(p.res)
                
            } else {
                
                dat <- read.csv(text=input$text1, sep="\t")
                p.res <- data()$pp
                plot(p.res)
            }
        }
    }
    
    output$compPlot <- renderPlot({
        print(makecompPlot())
    })





    # Person-Item Map
    
    makepiMap <- function(){
        if (input$map == 1) {
            if (input$colname == 0) {
                resRM <- data()$rasch
                plotPImap(resRM, sorted=TRUE)
                
            } else {
                resRM <- data()$rasch
                plotPImap(resRM, sorted=TRUE)
            }
        }
    }
    
    output$piMap <- renderPlot({
        print(makepiMap())
    })





    # Pathway Map (Bond & Fox, 2001, 2007 参照)
    makepathMap <- function(){
        if (input$path == 1) {
            
            if (input$colname == 0) {
                
                dat <- read.csv(text=input$text1, sep="\t", header=FALSE)
                options(digits=3)
                
                dat <- dat[rowSums(dat) != length(dat),]
                
                resRM <- RM(dat)
                pparm <- person.parameter(resRM)
                plotPWmap(resRM, pp=pparm, pmap=TRUE)
                
            } else {
                
                dat <- read.csv(text=input$text1, sep="\t")
                options(digits=3)
                
                dat <- dat[rowSums(dat) != length(dat),]

                resRM <- RM(dat)
                pparm <- person.parameter(resRM)
                plotPWmap(resRM, pp=pparm, pmap=TRUE)

            }
        }
    }
    
    output$pathMap <- renderPlot({
        print(makepathMap())
    })



    # Item characteristic curves (ICC) Plot
    makeICC <- function(){
        if (input$icc == 1) {
            
            if (input$colname == 0) {
                x <- read.table(text=input$text1, sep="\t")
                dat <- as.matrix(x)
                
                plot.rasch(rasch(dat))
                
            } else {
                
                dat <- read.csv(text=input$text1, sep="\t")
                
                plot.rasch(rasch(dat))
                
            }
        }
    }
    
    output$ICC <- renderPlot({
        print(makeICC())
    })
    
    
    
    
    
    makedistPlot <- function(){
        if (input$colname == 0) {
            x <- read.table(text=input$text1, sep="\t")
            x <- as.matrix(x)
            x <- rowSums(x, na.rm=T)
            
            
        } else {
            x <- read.csv(text=input$text1, sep="\t")
            x <- rowSums(x, na.rm=T)
        }
        
        simple.bincount <- function(x, breaks) {
            nx <- length(x)
            nbreaks <- length(breaks)
            counts <- integer(nbreaks - 1)
            for (i in 1:nx) {
                lo <- 1
                hi <- nbreaks
                if (breaks[lo] <= x[i] && x[i] <= breaks[hi]) {
                    while (hi - lo >= 2) {
                        new <- (hi + lo) %/% 2
                        if(x[i] > breaks[new])
                        lo <- new
                        else
                        hi <- new
                    }
                    counts[lo] <- counts[lo] + 1
                }
            }
            return(counts)
        }
        
        nclass <- nclass.FD(x)
        breaks <- pretty(x, nclass)
        counts <- simple.bincount(x, breaks)
        counts.max <- max(counts)
        
        h <- hist(x, las=1, breaks="FD", xlab= "Red vertical line shows the mean.",
        ylim=c(0, counts.max*1.2), main="", col = "cyan")
        rug(x)
        abline(v = mean(x), col = "red", lwd = 2)
        xfit <- seq(min(x), max(x))
        yfit <- dnorm(xfit, mean = mean(x), sd = sd(x))
        yfit <- yfit * diff(h$mids[1:2]) * length(x)
        lines(xfit, yfit, col = "blue", lwd = 2)
        

    }

    output$distPlot <- renderPlot({
        print(makedistPlot())
    })
    
    
    
    
    makeboxPlot <- function(){
        if (input$colname == 0) {
            x <- read.table(text=input$text1, sep="\t")
            x <- as.matrix(x)
            x <- rowSums(x, na.rm=T)
            
        } else {
            x <- read.csv(text=input$text1, sep="\t")
            x <- rowSums(x, na.rm=T)
        }
        
        boxplot(x, horizontal=TRUE, xlab= "Mean and +/-1 SD are displayed in red.")
        beeswarm(x, horizontal=TRUE, col = 4, pch = 16, add = TRUE)
        points(mean(x), 0.9, pch = 18, col = "red", cex = 2)
        arrows(mean(x), 0.9, mean(x) + sd(x), length = 0.1, angle = 45, col = "red")
        arrows(mean(x), 0.9, mean(x) - sd(x), length = 0.1, angle = 45, col = "red")
    }
    
    output$boxPlot <- renderPlot({
        print(makeboxPlot())
    })
    
    
    
    
    info <- reactive({
        info1 <- paste("This analysis was conducted with ", strsplit(R.version$version.string, " \\(")[[1]][1], ".", sep = "")# バージョン情報
        info2 <- paste("It was executed on ", date(), ".", sep = "")# 実行日時
        cat(sprintf(info1), "\n")
        cat(sprintf(info2), "\n")
    })
    
    output$info.out <- renderPrint({
        info()
    })





    output$textarea.out <- renderPrint({
        bs()
    })
    
    output$item.est.out <- renderPrint({
       item.est()
    })
    
    output$person.est.out <- renderPrint({
        person.est()
    })
    
    output$item.fit.out <- renderPrint({
        item.fit()
    })
    
    output$person.fit.out <- renderPrint({
        person.fit()
    })
    
    output$alpha.result.out <- renderPrint({
        alpha.result()
    })
    
    output$compare.out <- renderPrint({
       compare()
    })
    
})
library(shiny)
library(shinyAce)


shinyUI(bootstrapPage(

    headerPanel("Rasch Model (1PL IRT)"),


########## Adding loading message #########

tags$head(tags$style(type="text/css", "
#loadmessage {
position: fixed;
top: 0px;
left: 0px;
width: 100%;
padding: 10px 0px 10px 0px;
text-align: center;
font-weight: bold;
font-size: 100%;
color: #000000;
background-color: #CCFF66;
z-index: 105;
}
")),

conditionalPanel(condition="$('html').hasClass('shiny-busy')",
tags$div("Loading...",id="loadmessage")),

########## Added up untill here ##########


    mainPanel(
        tabsetPanel(


        tabPanel("Main",

        strong('Option:'),

        checkboxInput("colname", label = "The input data includes variable names (the header) in the first row.", TRUE),

        br(),

        p('Note: Input values (either numeric or character) must be separated by tabs. Copy and paste from Excel/Numbers.'),

        aceEditor("text1", 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            mode="r", theme="cobalt", height="400px"),

            br(),

            p('If you need to create 1-0 data first, use',
            a('Binary (1-0) Data Converter', href='https://langtest4.shinyapps.io/biconv', target="_blank"), '.'),

            br(),

            h3("Basic statistics (Using the raw score)"),
            verbatimTextOutput("textarea.out"),

            br(),

            h3("Histogram of the total score (Using the raw score)"),

            plotOutput("distPlot"),

            br(),

            h3("Boxplot (Using the raw score)"),


            plotOutput("boxPlot"),

            br(),

            h3("Cronbach's coefficient alpha (Using the raw score)"),
            verbatimTextOutput("alpha.result.out"),

            p('Drop if: Cronbach alpha when the item is removed', br(),
            'r dropped: item-total correlation without the item', br(),
            'r: item-total (point-biserial) correlation', br(),
            'IF: item facility or item mean (proportion correct answers)', br(),
            'ID: item discrimination (upper 1/3 - lower 1/3)', br()
            ),

            br(),

            h3("Item estimate"),
            verbatimTextOutput("item.est.out"),

            br(),

            h3("Person estimate (Theta)"),
            verbatimTextOutput("person.est.out"),

            br(),

            h3("Item fit"),
            verbatimTextOutput("item.fit.out"),

            br(),

            h3("Person fit"),
            verbatimTextOutput("person.fit.out"),

            br(),


            p(strong("Plot Options:")),

            checkboxInput("compare", label = "Show comparison of raw scores and theta", FALSE),
            checkboxInput("map", label = "Plot person-item map", FALSE),
            checkboxInput("path", label = "Plot pathway map (Bond & Fox, 2001, 2007)", FALSE),
            checkboxInput("icc", label = "Plot ICC (item characteristic curves)", FALSE),

            br(),

            verbatimTextOutput("compare.out"),

            plotOutput("compPlot", width="70%"),

            br(),

            plotOutput("piMap"),

            br(),

            plotOutput("pathMap"),

            br(),

            plotOutput("ICC"),

            br(),
            br(),

            strong('R session info'),
            verbatimTextOutput("info.out")

            ),





        tabPanel("About",

            strong('Note'),
            p('This web application is developed with',
            a("Shiny.", href="http://www.rstudio.com/shiny/", target="_blank"),
            ''),

            br(),

            strong('List of Packages Used'), br(),
            code('library(shiny)'),br(),
            code('library(shinyAce)'),br(),
            code('library(psych)'),br(),
            code('library(ltm)'),br(),
            code('library(CTT)'),br(),
            code('library(eRm)'),br(),
            code('library(beeswarm)'),br(),

            br(),
            br(),

            strong('Code'),
            p('Source code for this application is based on',
            a('"The handbook of Research in Foreign Language Learning and Teaching" (Takeuchi & Mizumoto, 2012).', href='http://mizumot.com/handbook/', target="_blank"),'I also referred to the code used in', a("MacR.", href="https://sites.google.com/site/casualmacr/", target="_blank")),

            p('The code for this web application is available at',
            a('GitHub.', href='https://github.com/mizumot/rasch', target="_blank")),

            p('If you want to run this code on your computer (in a local R session), run the code below:',br(),

            code('library(shiny)'),br(),
            code('runGitHub("rasch","mizumot")')
            ),

            br(),

            strong('Citation in Publications'),
            p('Mizumoto, A. (2015). Langtest (Version 1.0) [Web application]. Retrieved from http://langtest.jp'),

            br(),

            strong('Article'),
            p('Mizumoto, A., & Plonsky, L. (2015).', a("R as a lingua franca: Advantages of using R for quantitative research in applied linguistics.", href='http://applij.oxfordjournals.org/content/early/2015/06/24/applin.amv025.abstract', target="_blank"), em('Applied Linguistics,'), 'Advance online publication. doi:10.1093/applin/amv025'),

            br(),

            strong('Recommended'),
            p('To learn more about R, I suggest this excellent and free e-book (pdf),',
            a("A Guide to Doing Statistics in Second Language Research Using R,", href="http://cw.routledge.com/textbooks/9780805861853/guide-to-R.asp", target="_blank"),
            'written by Dr. Jenifer Larson-Hall.'),

            p('Also, if you are a cool Mac user and want to use R with GUI,',
            a("MacR", href="https://sites.google.com/site/casualmacr/", target="_blank"),
            'is defenitely the way to go!'),

            br(),

            strong('Author'),
            p(a("Atsushi MIZUMOTO,", href="http://mizumot.com", target="_blank"),' Ph.D.',br(),
            'Associate Professor of Applied Linguistics',br(),
            'Faculty of Foreign Language Studies /',br(),
            'Graduate School of Foreign Language Education and Research,',br(),
            'Kansai University, Osaka, Japan'),

            br(),

            a(img(src="http://i.creativecommons.org/p/mark/1.0/80x15.png"), target="_blank", href="http://creativecommons.org/publicdomain/mark/1.0/"),


            p(br())

            )

))
))
Code license: GPL-3