Some Example Datasets for the sirt Package
Some example datasets for the sirt package.
data(data.si01) data(data.si02) data(data.si03) data(data.si04) data(data.si05) data(data.si06) data(data.si07) data(data.si08) data(data.si09) data(data.si10)
The format of the dataset data.si01 is:
'data.frame': 1857 obs. of 3 variables: $ idgroup: int 1 1 1 1 1 1 1 1 1 1 ... $ item1 : int NA NA NA NA NA NA NA NA NA NA ... $ item2 : int 4 4 4 4 4 4 4 2 4 4 ...
The dataset data.si02 is the Stouffer-Toby-dataset published
in Lindsay, Clogg and Grego (1991; Table 1, p.97, Cross-classification A):
List of 2 $ data : num [1:16, 1:4] 1 0 1 0 1 0 1 0 1 0 ... ..- attr(*, "dimnames")=List of 2 .. ..$ : NULL .. ..$ : chr [1:4] "I1" "I2" "I3" "I4" $ weights: num [1:16] 42 1 6 2 6 1 7 2 23 4 ...
The format of the dataset data.si03 (containing item
parameters of two studies) is:
'data.frame': 27 obs. of 3 variables: $ item : Factor w/ 27 levels "M1","M10","M11",..: 1 12 21 22 ... $ b_study1: num 0.297 1.163 0.151 -0.855 -1.653 ... $ b_study2: num 0.72 1.118 0.351 -0.861 -1.593 ...
The dataset data.si04 is adapted from Bartolucci, Montanari
and Pandolfi (2012; Table 4, Table 7). The data contains 4999 persons,
79 items on 5 dimensions. See rasch.mirtlc for using the
data in an analysis.
List of 3 $ data : num [1:4999, 1:79] 0 1 1 0 1 1 0 0 1 1 ... ..- attr(*, "dimnames")=List of 2 .. ..$ : NULL .. ..$ : chr [1:79] "A01" "A02" "A03" "A04" ... $ itempars :'data.frame': 79 obs. of 4 variables: ..$ item : Factor w/ 79 levels "A01","A02","A03",..: 1 2 3 4 5 6 7 8 9 10 ... ..$ dim : num [1:79] 1 1 1 1 1 1 1 1 1 1 ... ..$ gamma : num [1:79] 1 1 1 1 1 1 1 1 1 1 ... ..$ gamma.beta: num [1:79] -0.189 0.25 0.758 1.695 1.022 ... $ distribution: num [1:9, 1:7] 1 2 3 4 5 ... ..- attr(*, "dimnames")=List of 2 .. ..$ : NULL .. ..$ : chr [1:7] "class" "A" "B" "C" ...
The dataset data.si05 contains double ratings of two
exchangeable raters for three items which are in Ex1, Ex2
and Ex3, respectively.
List of 3 $ Ex1:'data.frame': 199 obs. of 2 variables: ..$ C7040: num [1:199] NA 1 0 1 1 0 0 0 1 0 ... ..$ C7041: num [1:199] 1 1 0 0 0 0 0 0 1 0 ... $ Ex2:'data.frame': 2000 obs. of 2 variables: ..$ rater1: num [1:2000] 2 0 3 1 2 2 0 0 0 0 ... ..$ rater2: num [1:2000] 4 1 3 2 1 0 0 0 0 2 ... $ Ex3:'data.frame': 2000 obs. of 2 variables: ..$ rater1: num [1:2000] 5 1 6 2 3 3 0 0 0 0 ... ..$ rater2: num [1:2000] 7 2 6 3 2 1 0 1 0 3 ...
The dataset data.si06 contains multiple choice item
responses. The correct alternative is denoted as 0, distractors
are indicated by the codes 1, 2 or 3.
'data.frame': 4441 obs. of 14 variables: $ WV01: num 0 0 0 0 0 0 0 0 0 3 ... $ WV02: num 0 0 0 3 0 0 0 0 0 1 ... $ WV03: num 0 1 0 0 0 0 0 0 0 0 ... $ WV04: num 0 0 0 0 0 0 0 0 0 1 ... $ WV05: num 3 1 1 1 0 0 1 1 0 2 ... $ WV06: num 0 1 3 0 0 0 2 0 0 1 ... $ WV07: num 0 0 0 0 0 0 0 0 0 0 ... $ WV08: num 0 1 1 0 0 0 0 0 0 0 ... $ WV09: num 0 0 0 0 0 0 0 0 0 2 ... $ WV10: num 1 1 3 0 0 2 0 0 0 0 ... $ WV11: num 0 0 0 0 0 0 0 0 0 0 ... $ WV12: num 0 0 0 2 0 0 2 0 0 0 ... $ WV13: num 3 1 1 3 0 0 3 0 0 0 ... $ WV14: num 3 1 2 3 0 3 1 3 3 0 ...
The dataset data.si07 contains parameters of the empirical illustration
of DeCarlo (XXXX). The simulation function sim_fun can be used for
simulating data from the IRSDT model (see DeCarlo, XXXX)
List of 3 $ pars :'data.frame': 16 obs. of 3 variables: ..$ item: Factor w/ 16 levels "I01","I02","I03",..: 1 2 3 4 5 6 7 8 9 10 ... ..$ b : num [1:16] -1.1 -0.18 1.44 1.78 -1.19 0.45 -1.12 0.33 0.82 -0.43 ... ..$ d : num [1:16] 2.69 4.6 6.1 3.11 3.2 ... $ trait :'data.frame': 20 obs. of 2 variables: ..$ x : num [1:20] 0.025 0.075 0.125 0.175 0.225 0.275 0.325 0.375 0.425 0.475 ... ..$ prob: num [1:20] 0.0238 0.1267 0.105 0.0594 0.0548 ... $ sim_fun:function (lambda, b, d, items)
The dataset data.si08 contains 5 items with respect to knowledge
about lung cancer and the kind of information acquisition (Goodman, 1970;
see also Rasch, Kubinger & Yanagida, 2011).
L1: reading newspapers, L2: listening radio,
L3: reading books and magazines,
L4: attending talks, L5: knowledge about lung cancer
'data.frame': 32 obs. of 6 variables: $ L1 : num 1 1 1 1 1 1 1 1 1 1 ... $ L2 : num 1 1 1 1 1 1 1 1 0 0 ... $ L3 : num 1 1 1 1 0 0 0 0 1 1 ... $ L4 : num 1 1 0 0 1 1 0 0 1 1 ... $ L5 : num 1 0 1 0 1 0 1 0 1 0 ... $ wgt: num 23 8 102 67 8 4 35 59 27 18 ...
The dataset data.si09 was used in Fischer and Karl (2019) and they
asked employees in a eight countries, to report whether they typically help
other employees (helping behavior, seven items, help) and whether
they make suggestions to improve work conditions and products
(voice behavior, five items, voice). Individuals responded to these items
on a 1-7 Likert-type scale. The dataset was downloaded from https://osf.io/wkx8c/.
'data.frame': 5201 obs. of 13 variables: $ country: Factor w/ 8 levels "BRA","CAN","KEN",..: 5 5 5 5 5 5 5 5 5 5 ... $ help1 : int 6 6 5 5 5 6 6 6 4 6 ... $ help2 : int 3 6 5 6 6 6 6 6 6 7 ... $ help3 : int 5 6 6 7 7 6 5 6 6 7 ... $ help4 : int 7 6 5 6 6 7 7 6 6 7 ... $ help5 : int 5 5 5 6 6 6 6 6 6 7 ... $ help6 : int 3 4 5 6 6 7 7 6 6 5 ... $ help7 : int 5 4 4 5 5 7 7 6 6 6 ... $ voice1 : int 3 6 5 6 4 7 6 6 5 7 ... $ voice2 : int 3 6 4 7 6 5 6 6 4 7 ... $ voice3 : int 6 6 5 7 6 5 6 6 6 5 ... $ voice4 : int 6 6 6 5 5 7 5 6 6 6 ... $ voice5 : int 6 7 4 7 6 6 6 6 5 7 ...
The dataset data.si10 contains votes of 435 members of the U.S. House of
Representatives, 267 Democrates and 168 Republicans. The dataset was
used by Fop and Murphy (2017).
'data.frame': 435 obs. of 17 variables: $ party : Factor w/ 2 levels "democrat","republican": 2 2 1 1 1 1 1 2 2 1 ... $ vote01: num 0 0 NA 0 1 0 0 0 0 1 ... $ vote02: num 1 1 1 1 1 1 1 1 1 1 ... $ vote03: num 0 0 1 1 1 1 0 0 0 1 ... $ vote04: num 1 1 NA 0 0 0 1 1 1 0 ... $ vote05: num 1 1 1 NA 1 1 1 1 1 0 ... $ vote06: num 1 1 1 1 1 1 1 1 1 0 ... $ vote07: num 0 0 0 0 0 0 0 0 0 1 ... $ vote08: num 0 0 0 0 0 0 0 0 0 1 ... $ vote09: num 0 0 0 0 0 0 0 0 0 1 ... $ vote10: num 1 0 0 0 0 0 0 0 0 0 ... $ vote11: num NA 0 1 1 1 0 0 0 0 0 ... $ vote12: num 1 1 0 0 NA 0 0 0 1 0 ... $ vote13: num 1 1 1 1 1 1 NA 1 1 0 ... $ vote14: num 1 1 1 0 1 1 1 1 1 0 ... $ vote15: num 0 0 0 0 1 1 1 NA 0 NA ... $ vote16: num 1 NA 0 1 1 1 1 1 1 NA ...
Bartolucci, F., Montanari, G. E., & Pandolfi, S. (2012). Dimensionality of the latent structure and item selection via latent class multidimensional IRT models. Psychometrika, 77(4), 782-802. doi: 10.1007/s11336-012-9278-0
DeCarlo, L. T. (XXXX). An item response model for true-false exams based on signal detection theory. Applied Psychological Measurement, xx(xx). xxx-xxx. doi: 10.1177/0146621619843823
Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology | Cultural Psychology, 10:1507. doi: 10.3389/fpsyg.2019.01507
Fop, M., & Murphy, T. B. (2018). Variable selection methods for model-based clustering. Statistics Surveys, 12, 18-65. doi: 10/gktwch
Goodman, L. A. (1970). The multivariate analysis of qualitative data: Interactions among multiple classifications. Journal of the American Statistical Association, 65(329), 226-256. doi: 10.1080/01621459.1970.10481076
Lindsay, B., Clogg, C. C., & Grego, J. (1991). Semiparametric estimation in the Rasch model and related exponential response models, including a simple latent class model for item analysis. Journal of the American Statistical Association, 86(413), 96-107. doi: 10.1080/01621459.1991.10475008
Rasch, D., Kubinger, K. D., & Yanagida, T. (2011). Statistics in psychology using R and SPSS. New York: Wiley. doi: 10.1002/9781119979630
Some free datasets can be obtained from
Psychological questionnaires: http://personality-testing.info/_rawdata/
PISA 2012: http://pisa2012.acer.edu.au/downloads.php
PIAAC: http://www.oecd.org/site/piaac/publicdataandanalysis.htm
TIMSS 2011: http://timssandpirls.bc.edu/timss2011/international-database.html
ALLBUS: http://www.gesis.org/allbus/allbus-home/
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# EXAMPLE 1: Nested logit model multiple choice dataset data.si06
#############################################################################
data(data.si06, package="sirt")
dat <- data.si06
#** estimate 2PL nested logit model
library(mirt)
mod1 <- mirt::mirt( dat, model=1, itemtype="2PLNRM", key=rep(0,ncol(dat) ),
verbose=TRUE )
summary(mod1)
cmod1 <- sirt::mirt.wrapper.coef(mod1)$coef
cmod1[,-1] <- round( cmod1[,-1], 3)
#** normalize item parameters according Suh and Bolt (2010)
cmod2 <- cmod1
# slope parameters
ind <- grep("ak",colnames(cmod2))
h1 <- cmod2[,ind ]
cmod2[,ind] <- t( apply( h1, 1, FUN=function(ll){ ll - mean(ll) } ) )
# item intercepts
ind <- paste0( "d", 0:9 )
ind <- which( colnames(cmod2) %in% ind )
h1 <- cmod2[,ind ]
cmod2[,ind] <- t( apply( h1, 1, FUN=function(ll){ ll - mean(ll) } ) )
cmod2[,-1] <- round( cmod2[,-1], 3)
#############################################################################
# EXAMPLE 2: Item response modle based on signal detection theory (IRSDT model)
#############################################################################
data(data.si07, package="sirt")
data <- data.si07
#-- simulate data
set.seed(98)
N <- 2000 # define sample size
# generate membership scores
lambda <- sample(size=N, x=data$trait$x, prob=data$trait$prob, replace=TRUE)
b <- data$pars$b
d <- data$pars$d
items <- data$pars$item
dat <- data$sim_fun(lambda=lambda, b=b, d=d, items=items)
#- estimate IRSDT model as a grade of membership model with two classes
problevels <- seq( 0.025, 0.975, length=20 )
mod1 <- sirt::gom.em( dat, K=2, problevels=problevels )
summary(mod1)
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