Rasch Model (1PL IRT)

Main
About

Option:

The input data includes variable names (the header) in the first row.

The first column contains person IDs and should not be used for analysis. If unchecked, IDs are automatically assigned as P1, P2, P3, and so on.

Note: Input values must be separated by tabs. Copy and paste from Excel/Numbers. When the person-ID option is checked, the first column is treated as examinee IDs only and is excluded from the analysis.

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:

Show comparison of raw scores and theta

Plot person-item map

Plot pathway map (Bond & Fox, 2001, 2007)

Plot ICC (item characteristic curves)

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 definitely the way to go!

Author

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

library(shiny) library(shinyAce) library(psych) library(ltm) library(CTT) library(eRm) library(beeswarm) shinyServer(function(input, output) { options(warn = -1) prepared_data <- reactive({ raw <- if (input$colname == 0) { read.table( text = input$text1, sep = "\t", header = FALSE, stringsAsFactors = FALSE, check.names = FALSE ) } else { read.delim( text = input$text1, sep = "\t", header = TRUE, stringsAsFactors = FALSE, check.names = FALSE ) } if (isTRUE(input$personid)) { if (ncol(raw) < 2) { stop("The data must contain one ID column and at least one item column.") } ids <- as.character(raw[[1]]) blank_id <- is.na(ids) | trimws(ids) == "" ids[blank_id] <- paste0("P", which(blank_id)) ids <- make.unique(ids) dat <- raw[, -1, drop = FALSE] } else { dat <- raw ids <- paste0("P", seq_len(nrow(dat))) } if (input$colname == 0) { colnames(dat) <- paste0("V", seq_len(ncol(dat))) } dat[] <- lapply(dat, function(z) as.numeric(as.character(z))) dat <- as.data.frame(dat, stringsAsFactors = FALSE, check.names = FALSE) rownames(dat) <- ids list( dat = dat, mat = as.matrix(dat) ) }) bs <- reactive({ dat <- prepared_data()$dat total <- rowSums(dat, na.rm = TRUE) result <- describe(total)[2:13] row.names(result) <- "Total " result }) alpha.result <- reactive({ dat <- prepared_data()$dat brownRpbi <- function(data, missing) { m <- mean(rowSums(data)) sd <- sd(rowSums(data)) totalDat <- cbind(data, rowSums(data)) sortDat <- totalDat[order(-totalDat[, length(totalDat)]), ] r <- c() itemD <- c() rownames(sortDat) <- c(1:nrow(sortDat)) highDat <- head(sortDat, nrow(sortDat) %/% 3) lowDat <- tail(sortDat, nrow(sortDat) %/% 3) for (i in 1:length(data)) { if (is.element(colnames(data)[i], missing) == FALSE) { mhigh <- mean(subset(totalDat[, length(totalDat)], (data[, i] == 1))) mlow <- mean(subset(totalDat[, length(totalDat)], (data[, i] == 0))) imean <- mean(data[, i]) itemD <- c(itemD, round((mean(highDat[, i]) - mean(lowDat[, i])), 3)) rtemp <- round(cor(data[, i], totalDat[, ncol(totalDat)]), 3) r <- c(r, rtemp) } } pbiDF <- data.frame(itemD, r) colnames(pbiDF) <- c("ID", "r") return(pbiDF) } myAlpha <- function(data) { alphaRes <- reliability(data, itemal = TRUE) if (length(alphaRes$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({ dat <- prepared_data()$mat options(digits = 3) resRM <- RM(dat) p.res <- person.parameter(resRM) list(rasch = resRM, pp = p.res) }) item.est <- reactive({ resRM <- data()$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$X) raschTable }) person.est <- reactive({ p.res <- data()$pp theta_tab <- as.data.frame(p.res$theta.table, check.names = FALSE, stringsAsFactors = FALSE) ciVal <- qnorm(0.975) if (ncol(theta_tab) < 2) { stop("Could not extract person estimates from theta.table.") } theta_names <- colnames(theta_tab) est_col <- if ("Person Parameter" %in% theta_names) "Person Parameter" else theta_names[1] se_col <- if ("Std.Error" %in% theta_names) "Std.Error" else theta_names[2] nagroup_col <- if ("NAgroup" %in% theta_names) { "NAgroup" } else if (length(theta_names) >= 3) { theta_names[3] } else { NULL } interpolated_col <- if ("Interpolated" %in% theta_names) { "Interpolated" } else if (length(theta_names) >= 4) { theta_names[4] } else { NULL } person_ids <- rownames(theta_tab) if (is.null(person_ids) || all(person_ids == "")) { person_ids <- paste0("P", seq_len(nrow(theta_tab))) } raw_score <- rowSums(prepared_data()$dat, na.rm = TRUE) if (!is.null(names(raw_score)) && all(person_ids %in% names(raw_score))) { raw_score <- raw_score[person_ids] } else { raw_score <- raw_score[seq_len(nrow(theta_tab))] } out <- data.frame( ID = person_ids, `Raw score` = as.numeric(raw_score), Estimate = round(as.numeric(theta_tab[[est_col]]), 3), `Std. Error` = round(as.numeric(theta_tab[[se_col]]), 3), `CI low` = round(as.numeric(theta_tab[[est_col]]) - ciVal * as.numeric(theta_tab[[se_col]]), 3), `CI high` = round(as.numeric(theta_tab[[est_col]]) + ciVal * as.numeric(theta_tab[[se_col]]), 3), check.names = FALSE, row.names = NULL, stringsAsFactors = FALSE ) if (!is.null(nagroup_col)) { out$NAgroup <- theta_tab[[nagroup_col]] } if (!is.null(interpolated_col)) { out$Interpolated <- theta_tab[[interpolated_col]] } out }) item.fit <- reactive({ p.res <- data()$pp itemfit(p.res) }) person.fit <- reactive({ p.res <- data()$pp personfit(p.res) }) compare <- reactive({ if (input$compare == 1) { p.res <- data()$pp options(digits = 3) list("Comparison of raw scores and theta" = p.res) } }) makecompPlot <- function() { if (input$compare == 1) { p.res <- data()$pp plot(p.res) } } output$compPlot <- renderPlot({ print(makecompPlot()) }) makepiMap <- function() { if (input$map == 1) { resRM <- data()$rasch plotPImap(resRM, sorted = TRUE) } } output$piMap <- renderPlot({ print(makepiMap()) }) makepathMap <- function() { if (input$path == 1) { dat <- prepared_data()$mat options(digits = 3) dat <- dat[rowSums(dat, na.rm = TRUE) != ncol(dat), , drop = FALSE] resRM <- RM(dat) pparm <- person.parameter(resRM) plotPWmap(resRM, pp = pparm, pmap = TRUE) } } output$pathMap <- renderPlot({ print(makepathMap()) }) makeICC <- function() { if (input$icc == 1) { dat <- prepared_data()$mat plot.rasch(rasch(dat)) } } output$ICC <- renderPlot({ print(makeICC()) }) makedistPlot <- function() { x <- rowSums(prepared_data()$dat, na.rm = TRUE) simple.bincount <- function(x, breaks) { nx <- length(x) nbreaks <- length(breaks) counts <- integer(nbreaks - 1) for (i in 1:nx) { lo <- 1 hi <- nbreaks if (breaks[lo] <= x[i] && x[i] <= breaks[hi]) { while (hi - lo >= 2) { new <- (hi + lo) %/% 2 if (x[i] > breaks[new]) { lo <- new } else { hi <- new } } counts[lo] <- counts[lo] + 1 } } return(counts) } nclass <- nclass.FD(x) breaks <- pretty(x, nclass) counts <- simple.bincount(x, breaks) counts.max <- max(counts) h <- hist( x, las = 1, breaks = "FD", xlab = "Red vertical line shows the mean.", ylim = c(0, counts.max * 1.2), main = "", col = "cyan" ) rug(x) abline(v = mean(x), col = "red", lwd = 2) xfit <- seq(min(x), max(x)) yfit <- dnorm(xfit, mean = mean(x), sd = sd(x)) yfit <- yfit * diff(h$mids[1:2]) * length(x) lines(xfit, yfit, col = "blue", lwd = 2) } output$distPlot <- renderPlot({ print(makedistPlot()) }) makeboxPlot <- function() { x <- rowSums(prepared_data()$dat, na.rm = TRUE) 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 = "") info2 <- paste("It was executed on ", date(), ".", sep = "") 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)"), 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") ), mainPanel( tabsetPanel( tabPanel( "Main", strong("Option:"), checkboxInput( "colname", label = "The input data includes variable names (the header) in the first row.", TRUE ), checkboxInput( "personid", label = "The first column contains person IDs and should not be used for analysis. If unchecked, IDs are automatically assigned as P1, P2, P3, and so on.", FALSE ), br(), p( "Note: Input values must be separated by tabs. Copy and paste from Excel/Numbers. ", "When the person-ID option is checked, the first column is treated as examinee IDs only and is excluded from the analysis." ), aceEditor( "text1", value = 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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 definitely the way to go!" ), br(), strong("Author"), p( a("Atsushi MIZUMOTO,", href = "http://mizumot.com", target = "_blank"), " Ph.D.", br(), "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()) ) ) ) ))