Package ‘classify’February 19, 2015
Type Package
Title Classification Accuracy and Consistency under IRT models.
Version 1.3
Date 2014-08-16
Author Dr Chris Wheadon and Dr Ian Stockford
Maintainer Dr Chris Wheadon <[email protected]>
Description IRT classification uses the probability that candidates ofa given ability, will answer correctly questions of a specifieddifficulty to calculate the probability of their achievingevery possible score in a test. Due to the IRT assumption ofconditional independence (that is every answer given is assumedto depend only on the latent trait being measured) theprobability of candidates achieving these potential scores canbe expressed by multiplication of probabilities for itemresponses for a given ability. Once the true score and theprobabilities of achieving all other scores have beendetermined for a candidate the probability of their score lyingin the same category as that of their true score(classification accuracy), or the probability of consistentclassification in a category over administrations(classification consistency), can be calculated.
License GPL (>= 2)
Imports Rcpp (>= 0.9.10), plyr, ggplot2, lattice, methods, R2jags,reshape2
Suggests R2WinBUGS
LinkingTo Rcpp
Repository CRAN
Date/Publication 2014-08-17 12:17:00
Collate 'bugs.R' 'classify.R' 'gpcm.rc.R' 'prob_functions.R''scores.R' 'w_lord.R'
NeedsCompilation yes
1
2 classify-package
R topics documented:classify-package . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2across.reps-methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7beta.list . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8biology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8classification-class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9classify . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10classify.bug . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11expected.rc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11gpcm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12gpcm.bug . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13gpcm.rc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14pcm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16plot Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16rasch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17scores-class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17scores.gpcm.bug . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18summary-methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19thpl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19tpl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20wlord . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Index 22
classify-package Classification Accuracy and Consistency under IRT models.
Description
IRT classification uses the probability that candidates of a given ability, will answer correctly ques-tions of a specified difficulty to calculate the probability of their achieving every possible score ina test. Due to the IRT assumption of conditional independence (that is every answer given is as-sumed to depend only on the latent trait being measured) the probability of candidates achievingthese potential scores can be expressed by multiplication of probabilities for item responses for agiven ability. Once the true score and the probabilities of achieving all other scores have been de-termined for a candidate the probability of their score lying in the same category as that of theirtrue score (classification accuracy), or the probability of consistent classification in a category overadministrations (classification consistency), can be calculated.
Details
Package: classifyType: PackageVersion: 1.0Date: 2012-04-30License: GPL (>= 2)
classify-package 3
Depends: Rcpp (>= 0.9.10), plyr, ggplot2, R2WinBUGS, lattice, reshape2, methods, R2jagsLinkingTo: RcppPackaged: 2012-06-08 12:43:25 UTC; cwheadonBuilt: R 2.15.0; i386-pc-mingw32; 2012-06-08 12:43:33 UTC; windows
Index:
beta.list Extracts Beta Values from Bugs Sims Filebiology Polytomous Responses from 200 Candidates to 31
Questionsclassification-class Class '"classification"'classify Calculate Classification Statisticsclassify-package Classification Accuracy and Consistency under
IRT Modelsclassify.bug Classification Accuracy and Consistency from
Bugs Replicate Parametersgpcm Generalised Partial Credit Model Derived
Probabilitiesgpcm.bug Extracts IRT Model Parameters from Bugs Modelsgpcm.rc IRT Derived Predicted Conditional Number
Correct Score Distributionpcm Partial Credit Model Derived Probabilitiesphysics Dichotomous Responses from 200 Candidates to 25
Questionsplot.scores Plot Methods for Classification and Scores
Objectsrasch Rasch Derived Probabilitiesscores-class Class '"scores"'scores.gpcm.bug Expected and Conditional Summed Score
Distributionssummary-methods Summary Stats for Classification Accuracy and
Consistencythpl Three Parameter IRT Model Derived Probabilitiestpl Two Parameter IRT model Derived Probabilitieswlord Lord and Wingersky Recursion Formula
Author(s)
Dr Chris Wheadon and Dr Ian Stockford
Maintainer: Dr Chris Wheadon <[email protected]>
References
Curtis, S.M.(2010) BUGS Code for Item Response Theory, Journal of Statistical Software, CodeSnippets, 36(1),1–34.
Hanson, B.A., Beguin, A.A.(2002) Obtaining a common scale for item response theory item pa-rameters using separate versus concurrent estimation in the common-item equating design. AppliedPsychological Measurement, 26, 3–24.
4 classify-package
Kolen M.J., Brennan, R.L. (2004) Test Equating, Scaling, and Linking. Statistics in Social Scienceand Public Policy.
Lee, W. (2008) Classification consistency and accuracy for complex assessments using item re-sponse theory, (No. 27) CASMA Research Report Iowa City, IA: Center for Advanced Studies inMeasurement and Assessment, University of Iowa.
Lord, F., Wingersky, M. (1984) Comparison of IRT true-score and equipercentile observed-scoreequatings, Applied Psychological Measurement, 8, 452–461.
Lunn, D.J., Thomas, A., Best, N., Spiegelhalter, D. (2000) WinBUGS, A Bayesian modellingframework: concepts, structure, and extensibility. Statistics and Computing, 10, 325–337.
Plummer, M (2012) Just Another Gibbs Sampler, version 3.2.0 http://mcmcjags.sourceforge.net/
Swaminathan, H., Hambleton, R. K., Rogers, H. J. (2007) Assessing the fit of Item Response Theorymodels. In C. R. Rao, S. Sinharay (Eds.), Handbook of statistics, Vol. 26, 683–718.
Wheadon, C., (2014) Classification Accuracy and Consistency under Item Response Theory ModelsUsing the Package classify, Journal of Statistical Software, 56(10) 1–14.
Wheadon, C., Stockford, I., (2011) Classification accuracy and consistency in GCSE and A levelexaminations offered by the Assessment and Qualifications Alliance (AQA) November 2008 to June2009, Ofqual’s Reliability Compendium. Office of Qualification and Examinations Regulation.
Examples
## Not run:
## Rasch or 2pl Model
# Data should be a numeric matrix, with one row per candidate, one column per itemdata(physics)# If reading from csv, the following is recommended:# physics<-read.csv("physics.csv", header=TRUE, sep=",", na.strings = "-")# physics<-physics[complete.cases(physics),]# physics<-physics[sample(1:nrow(physics), 200, replace=FALSE),]# physics<-as.matrix(physics)
n <- nrow(physics)p <- ncol(physics)
# Boundary marks in ascending orderbnds <- c(9,11,13,15,18,21)
# Labels for boundaries (one more boundary than label)lbls <- c("U","E","D","C","B","A","A*")
# Specify bugs file - included in the classify/bugs directory# 2 pl modelmdl <- "tpl.bug"# Rasch model# mdl <- "rasch.bug"
# Item marksY <- physics
classify-package 5
# Mean and standard deviation of deltam.delta <- 0.0s.delta <- 1.0
# Mean and standard deviation of alpha, comment out for Rasch modelm.alpha <- 0.0s.alpha <- 1.0
# Data set for the 2 pl modeldata <- list("Y", "n", "p", "m.delta", "s.delta", "m.alpha", "s.alpha")
# Parameters to monitor for the 2 pl modelmonitor <- c("delta", "theta", "alpha")
# Rasch model# data <- list("Y", "n", "p", "m.delta", "s.delta")# monitor <- c("delta", "theta")
# Set to location of bug filejags.file <- file.path(getwd(), "R/R-2.15.0/library/classify/bugs" ,mdl)
# JAGS# may require set.seed(1234) depending on version of Rsystem.time(jagsout <- jags(data=data, inits=NULL, parameters.to.save=monitor,
model.file=jags.file,n.iter=2000, n.thin=10, n.burnin=1000))
sims <- jagsout$BUGSoutput$sims.matrix
# Bugs# Change this to your bugs directory# bugs.directory = "C:/Program Files/WinBUGS14"# system.time(bugsout <- bugs(data=data, inits=NULL, parameters.to.save=monitor,# model.file=jags.file,# n.iter=2000, n.thin=10, n.burnin=1000))
# sims <- bugsout$sims.matrix
# Estimate conditional score and expected score distributionsscores <- scores.gpcm.bug(Y,sims,mdl)# Plotsplot(scores)# Save plot# ggsave("expected.pdf")plot(scores,type="cond")plot(scores,type="qq",alpha=0.5)
# Estimate accuracy statisticsaccs <- classify.bug(sims,scores,bnds,lbls)summary(accs)plot(accs)plot(accs,type="kappa")
6 classify-package
plot(accs,type="density")
############################################################################################
## PCM or GPCM models# Data should be a numeric matrix, with one row per candidate, one column per itemdata(biology)# If reading from csv, the following is recommended:# biology<-read.csv("biology.csv", header=TRUE, sep=",", na.strings = "-")# biology<-biology[complete.cases(biology),]# biology<-biology[sample(1:nrow(biology), 200, replace=FALSE),]# biology<-as.matrix(biology)
n <- nrow(biology)p <- ncol(biology)
# Boundary marks in ascending orderbnds <- c(26,30,35,40,45)
# Labels for boundaries (one more boundary than label)lbls <- c("U","E","D","C","B","A")
# Specify bugs file - included in the classify/bugs directory# GPCMmdl <- "gpcm.bug"# PCM#mdl <- "pcm.bug"
# Bugs polytomous models require polytomous scores as categoriesY <- biology + 1# Specify response categoriesK <- as.numeric(apply(Y,2,max,na.rm = TRUE))
# Mean and standard deviation of alpha and beta parameters
m.beta <- 0.0s.beta <- 1.0
# Comment out for PCMm.alpha <- 0.0s.alpha <- 1.0
# GPCMdata <- list("Y", "n", "p", "K","m.beta", "s.beta", "m.alpha", "s.alpha")monitor <- c("beta", "theta", "alpha")
# PCM#data <- list("Y", "n", "p", "K",# "m.beta", "s.beta")#monitor <- c("beta", "theta")
across.reps-methods 7
# Initial values for beta set to 0, matrix padded with NAbeta <- t(sapply(1:p, function(j) c(rep(NA, K[j]), rep(0.0, max(K) - K[j]))))data <- c(data, "beta")
# Change this to bugs file directoryjags.file <- file.path(getwd(), "R/R-2.15.0/library/classify/bugs" ,mdl)
# Simulations and samplingiter <- 2000burnin <- 1000thin <- 10
## JAGSestimation <- "jags"# may require set.seed(1234) depending on version of Rsystem.time(jagsout <- jags(data=data, inits=NULL, parameters.to.save=monitor,
model.file=jags.file,n.iter=iter, n.thin=thin, n.burnin=burnin))
sims <- jagsout$BUGSoutput$sims.matrix
## Bugs#estimation <- "bugs"# Change this to your bugs directory#bugs.directory = "C:/Program Files/WinBUGS14"#system.time(bugsout <- jags(data=data, inits=NULL, parameters.to.save=monitor,# model.file=jags.file,# n.iter=iter, n.thin=thin, n.burnin=burnin))#sims <- bugsout$sims.matrix
# Estimate conditional score and expected score distributionsscores <- scores.gpcm.bug(biology,sims,mdl)# Plotsplot(scores)# Save plot#ggsave("expected.pdf")plot(scores,type="cond")plot(scores,type="qq",alpha=0.5)
# Estimate accuracy statisticsaccs <- classify.bug(sims,scores,bnds,lbls)summary(accs)plot(accs)plot(accs,type="kappa")plot(accs,type="density")
## End(Not run)
across.reps-methods Summarises classification values across bugs or jags replications
8 biology
Description
Summarises classification values across bugs or jags replications
Methods
signature(object = "classification")
beta.list Extract Beta Values from Bugs Sims File
Description
Extracts beta values from bugs sims file.
Usage
beta.list(v)
Arguments
v Bugs sims file
Details
Draws heavily on Curtis, S.M.(2010).
Value
Returns list of beta parameters.
References
Curtis, S.M.(2010) BUGS Code for Item Response Theory, Journal of Statistical Software, CodeSnippets, 36(1),1–34
biology Polytomous Responses from 200 Candidates to 31 Questions
Description
Sample data set for polytomous IRT models.
Usage
data(biology)
Format
A matrix containing responses.
classification-class 9
classification-class Class "classification"
Description
S4 object with classification statistics.
Slots
acc: Classification accuracy summary statistic across replications.
fp: False positive summary statistic across replications.
fn: False negative summary statistic across replications.
cand.acc: Candidate level accuracy across replications.
cand.fn: Candidate level false negative across replications.
cand.fp: Candidate level false positive across replications.
consist: Classification consistency summary statistic across replications.
cand.consist: Candidate level classification consistency across replications.
Xij: Summary matrix of classification probability into all grade combinations.
kappa: Kappa value for classification accuracy across replications.
item.scores: Raw item scores used.
bnds: Grade bounaries used.
tru.grades: Candidate grades.
tru.scores: Candidate true scores.
acc.by.grade: Accuracy by grade.
fp.by.grade: False positive by grade.
fn.by.grade: False negative by grade.
consist.by.grade: Consistency by grade.
labels: Grade labels.
m.acc: Mean of Classification accuracy summary statistic across replications.
m.consist: Mean of Candidate level classification consistency across replications.
m.kappa: Mean of Kappa value for classification accuracy across replications.
m.fp: Mean of Candidate level false positive across replications.
m.fn: Mean of Candidate level false negative across replications.
sd.acc: SD of Classification accuracy summary statistic across replications.
sd.consist: SD of Candidate level classification consistency across replications.
sd.kappa: SD of Kappa value for classification accuracy across replications.
sd.fp: SD of Candidate level false positive across replications.
sd.fn: SD of Candidate level false negative across replications.
10 classify
m.acc.by.grade: Mean accuracy by grade.m.fp.by.grade: Mean false positive by grade.m.fn.by.grade: Mean false negative by grade.m.consist.by.grade: Mean consistency by grade.max: Maximum test score.
Methods
plot Plots.across.reps Summarise stats across replications.summary Summary statistics.
classify Calculate Classification Statistics
Description
Internal function to calculate classification statistics.
Usage
classify(cssd, expected, bnds, cats, lbls=NULL)
Arguments
cssd Conditional Summed Score Distributionexpected Numeric vector of Expected Scoresbnds Numeric vector of grade boundaries, specified in ascending order, including the
minimum and maximum mark on the test.cats Numeric vector of item categories.lbls Character vector of grade labels. Optional.
Value
List of classification statistics:Candidate level accuracyCandidate level false negativesCandidate level false positivesSummary of consistencyMatrix of grade probability combinationsKappaCandidate level classification consistencySummary of accuracy by gradeSummary of false positives by gradeSummary of false negatives by gradeSummary of consistency by grade
classify.bug 11
classify.bug Classification Accuracy and Consistency from Bugs Replicate Param-eters
Description
Calculates classification statistics under IRT models in bugs.
Usage
classify.bug(sims, scores, bnds, lbls=NULL)
Arguments
sims bugs sims matrix.
scores scores
bnds Numeric vector of grade boundaries, monotonically increasing.
lbls Character vector of grade labels. Optional.
Details
Calculates classification statistics under IRT models in bugs.
Value
classification
expected.rc Expected scores under the PCM or the GPCM.
Description
Calculates expected scores under the PCM or the GPCM.
Usage
expected.rc(beta=NULL,theta=NULL,cats=NULL,alpha=NULL)
Arguments
beta Matrix of Beta parameters
theta Vector of Theta parameters
cats Vector Item category parameters
alpha Vector of Alpha parameters (optional)
12 gpcm
Details
The beta parameters are the intersection points of adjacent category information functions. Thereshould be one less delta parameter than categories. Assumes that the location parameter is zero. Ifno alpha parameters are supplied it assumes the PCM.
Value
Vector of expected scores
Examples
#One item with three categoriesbeta <- matrix(c(0,-1.586,-3.798),nrow=1,ncol=3)theta <- 0.674cats <- 3alpha <- 1expected.rc(beta,theta,cats,alpha)
gpcm Generalised Partial Credit Model Derived Probabilities
Description
Calculate vector of probabilities of success from person and item parameters under the GeneralisedPartial Credit Model.
Usage
gpcm(theta=NULL,alpha=NULL,delta=NULL,n=NULL)
Arguments
theta Theta parameter
alpha Alpha parameter
delta Vector of delta parameters
n Number of item categories
Details
The delta parameters are the intersection points of adjacent category information functions. Thereshould be one less delta parameter than categories. Assumes that the location parameter is zero
Value
Vector of probabilities of success
gpcm.bug 13
Examples
## Generalized Partial Credit Model## Item parameters from Embretson & Reise (2000, p. 112) item 5theta <- 1alpha <- .683delta <- c(-3.513,-.041,.182)n <- 4gpcm(theta,alpha,delta,n)
gpcm.bug Extract IRT Model Parameters from Bugs Models
Description
Internal function which draws heavily on Curtis, S.M.(2010).
Usage
gpcm.bug(v, cats, mdl, gibbs=c("bugs","jags"))
Arguments
v Bugs sims matrix
cats Numeric vector of item categories
mdl Bugs file: Partial Credit Model - "pcm.bug" or Generalised Partial Credit Model- "gpcm.bug" or Rasch model - "rasch.bug" or 2pl model "tpl.bug"
gibbs Gibbs sampler: "bugs" or "jags"
Details
Extracts IRT Model Parameters from Bugs Models
Value
List with theta and beta parameters
References
Curtis, S.M.(2010) BUGS Code for Item Response Theory, Journal of Statistical Software, CodeSnippets, 36(1),1–34
14 gpcm.rc
gpcm.rc IRT Derived Predicted Conditional Number Correct Score Distribu-tion
Description
Obtains the predicted number-correct score distribution from parameters estimated under the Gen-eralised Partial Credit Model.
Usage
gpcm.rc(beta=NULL,theta=NULL,cats=NULL,alpha=NULL)
Arguments
beta Item threshold parameters. These should be a matrix, with rows for items andcolumns for categories. Following Muraki, the first column should be zero.
theta Theta parameters
cats Vector of item categories. A dichotomous item is specified as two categories.
alpha Discrimination parameters. If none are specified the model will default to thePartial Credit Model.
Details
The beta parameters are defined as the intersection points of adjacent category information func-tions. There should be the same number of beta parameters as categories, with the first column,following Muraki, specified as zero.
Value
Vector of probabilities of achieving any item score
Examples
beta <- matrix(c(0,-1.586,-3.798),nrow=1,ncol=3)theta <- 0.674cats <- 3alpha <- 1gpcm.rc(beta,theta,cats,alpha)
pcm 15
pcm Partial Credit Model Derived Probabilities
Description
Calculate vector of probabilities of success from person and item parameters under the Partial CreditModel.
Usage
pcm(theta=NULL, delta=NULL, n=NULL)
Arguments
theta Theta parameter
delta Vector of delta parameters
n Number of item categories
Details
The delta parameters are the intersection points of adjacent category information functions. Thereshould be one less delta parameter than categories.
Value
Vector of probabilities of success
Examples
# Example from The Theory and Practice of Item Response Theory# By Rafael Jaime De Ayala# p.204theta <- 0n <- 3d <- c(-1,1)
pcm(theta,d,n)
#0.2119416 0.5761169 0.2119416
16 plot Classification
physics Dichotomous Responses from 200 Candidates to 25 Questions
Description
Sample data set for the Rasch and 2PL models.
Usage
data(physics)
Format
A matrix containing responses.
plot Classification Plot Methods for Classification and Scores s4 objects
Description
Produces various plots of score distributions and classification statistics.
Usage
## S3 method for class 'scores'plot(x, type = c("exp","cond","qq"),alpha = 0.05, ...)## S3 method for class 'classification'plot(x, type = c("acc", "kappa", "density"), ...)
Arguments
x an object inheriting either from class scores or class classificationtype the type of plot:
"exp": Expected summed scores compared to observed"cond": Conditional summed scores compared to observed"qq": QQ plot of conditional summed scores compared to observed"acc": Classification accuracy"kappa": Kappa"density" Density
alpha Alpha value for points on qq plot.... extra graphical parameters
Details
Produces various plots of score distributions and classification statistics.
rasch 17
rasch Rasch Derived Probabilities
Description
Calculate vector of probabilities of success from person and item parameters under the Rasch model.
Usage
rasch(theta=NULL, delta=NULL)
Arguments
theta Vector of theta parameters
delta Vector of delta parameters
Details
Calculates vector of probabilities of success from person and item parameters under the Raschmodel.
Value
Vector of probabilities of success, persons in columns, items in rows
Examples
theta <- c(-5:5)delta <- c(-5:5)rasch(theta,delta)
scores-class Class "scores"
Description
S4 object for score distributions.
18 scores.gpcm.bug
Slots
item: Item scores
expected: Expected scores
conditional: Conditional Summed scores
summed: Summed scores
persons: Number of persons
items: Number of items
sims: Number of simulations
max: Maximum test score
cats: Item categories
model: Bugs model
estimation: Bugs estimation software
scores.gpcm.bug Expected and Conditional Summed Score Distributions
Description
Obtains the predicted number-correct score distribution from the IRT models specified in the bugsfiles pcm.bug, gpcm.bug, rasch.bug, tpl.bug.
Usage
scores.gpcm.bug(item.scores,sims,mdl = c("rasch.bug", "pcm.bug", "tpl.bug","gpcm.bug"),gibbs = c("bugs","jags"))
Arguments
item.scores Matrix of item scores, one candidate per row.
sims Winbugs sims matrix
mdl Bugs file: "rasch.bug", "pcm.bug", "tpl.bug", "gpcm.bug"
gibbs Gibbs sampler: "bugs" or "jags"
Value
an object of class scores
summary-methods 19
summary-methods Summary Statistics for S4 Class Classification
Description
Summary Statistics for S4 Class Classification
Methods
signature(object = "classification") Produces summary statistics from the S4 classifica-tion object.
thpl Three Parameter IRT Model Derived Probabilities
Description
Calculate vector of probabilities of success from person and item parameters under the 3pl IRTmodel.
Usage
thpl(theta=NULL,beta=NULL,alpha=NULL,eta=NULL)
Arguments
theta Vector of theta parametersbeta Vector of beta parametersalpha Vector of alpha parameterseta Vector of eta parameters
Details
Three Parameter IRT Model Derived Probabilities
Value
Vector of probabilities of success, persons in columns, items in rows
Examples
theta <- c(-2:2)beta <- rep(0,5)alpha <- rep(1,5)eta <- seq(from=0.2,by=0.2,to=1)thpl(theta,beta,alpha,eta)
20 wlord
tpl Two Parameter IRT Model Derived Probabilities
Description
Calculate vector of probabilities of success from person and item parameters under the 2pl IRTmodel.
Usage
tpl(theta=NULL, beta=NULL, alpha=NULL)
Arguments
theta Vector of theta parameters
beta Vector of beta parameters
alpha Vector of alpha parameters
Details
Calculates vector of probabilities of success from person and item parameters under the 2pl IRTmodel.
Value
Vector of probabilities of success, persons in columns, items in rows
Examples
theta <- c(-2:2)beta <- rep(0,5)alpha <- seq(from=0.2,by=0.2,to=1)tpl(theta,beta,alpha)
wlord Lord and Wingersky Recursion Formula
Description
The Lord and Wingersky Recursion Formula allows for efficient computation of the predictednumber-correct score distribution (also known as the expected score distribution) given probabilitiesof correct responses to items.
wlord 21
Usage
wlord(probs=NULL,cats=NULL)
Arguments
probs Probability matrix specifying the probability of achieving each category. Thereshould be one row per item and one column per category. Where the number ofcategories differs between items, the matrix should be padded with zeros.
cats Numeric vector specifying the number of categories in each item. A dichoto-mous item, for example, has two categories.
Details
The Lord and Wingersky Recursion Formula is a particularly useful short-cut in computations withthe probabilities derived from IRT models. The algorithm simplifies the process of calculating thecompound probabilities involved when the probability of achieving any score on an assessmentinstrument is required. It is essentially an elegant solution to combining the probabilities of re-sponding in any particular category with the multiple ways in which any test score can be achievedthrough responses to different categories on different items.
Value
A vector of probabilities of achieving every test score
References
Kolen MJ, Brennan RL (2004). Test Equating, Scaling, and Linking. Statistics in Social Scienceand Public Policy. Springer, New York.Lord F, Wingersky M (1984). Comparison of IRT true-score and equipercentile observed-scoreequatings. Applied Psychological Measurement, 8, 452-461.
Examples
#This reproduces the example on page 183 of Kolen & Brennan (2004)probs <- matrix(c(.74,.73,.82,.26,.27,.18),nrow=3,ncol=2, byrow = FALSE)cats <- c(2,2,2)wlord(probs,cats)
Index
∗Topic bugsclassify-package, 2
∗Topic classificationclassify-package, 2
∗Topic irtclassify-package, 2
∗Topic jagsclassify-package, 2
∗Topic packageclassify-package, 2
∗Topic reliabilityclassify-package, 2
∗Topic winbugsclassify-package, 2
across-reps (classification-class), 9across.reps (across.reps-methods), 7across.reps,classification-method
(across.reps-methods), 7across.reps-methods, 7
beta.list, 8biology, 8
classification, 11classification (classification-class), 9classification-class, 9classify, 10classify-package, 2classify.bug, 11
expected.rc, 11
gpcm, 12gpcm.bug, 13gpcm.rc, 14
pcm, 15physics, 16plot Classification, 16
plot.classification (plotClassification), 16
plot.scores (plot Classification), 16
rasch, 17
scores, 11, 18scores,missing-method (scores-class), 17scores-class, 17scores.gpcm.bug, 18summary (summary-methods), 19summary,classification-method
(summary-methods), 19summary-methods, 19
thpl, 19tpl, 20
wlord, 20
22