check.iio | R Documentation |
Returns a list (of class iio.class
) with results from the investigation of invariant item ordering.
Three methods may be used for the investigation of invariant item ordering.
(1) Method MIIO (manifest invariant item ordering: investigates the manifest item response functions for all pairs of items). For polytomous items, t-tests are used to test violations, for dichotomous items z-tests are used to test are used to test violations.
(2) Method MS-CPM (manifest scale - cumulative probability model: investigates the manifest item step response functions for all pairs of items). Z-tests are used to test violations.
(3) Method IT (increasingness in transposition: investigates all bivariate joint probabilities for all pairs of items). Chi-square tests are used to test violations.
For a complete description of Method MIIO, see Ligtvoet, Van der Ark, Te Marvelde, and Sijtsma (2010); for a complete description of the Method MS-CPM and Method IT with reference to Method MIIO, see Ligtvoet, Van der Ark, Bergsma, and Sijtsma (2011).
For two-level test data (clustered respondents) argument level.two.var exist, such that two lists are returned, containing the results for level 1 (person level) and level 2 (cluster level), respectively. Only method MIIO is implemented for two-level test data.
check.iio(X, method="MIIO", minvi = default.minvi, minsize = default.minsize,
alpha = .05, item.selection=TRUE, verbose=FALSE, level.two.var = NULL)
X |
matrix or data frame of numeric data
containing the responses of |
method |
Either |
minvi |
minimum size of a violation that is reported. By default
|
minsize |
minimum size of a rest score group. By default
|
alpha |
Nominal Type I error for t test (Method MIIO), z test (Method MSCPM), or McNemar test (Method IT).
Default |
item.selection |
Conduct backward item selection procedure (see Ligtvoet et al., 2010).
Default |
verbose |
Show the results of the backward item selection algorithm on screen.
Default |
level.two.var |
Add respondent-clustering variable to get results for Level 1 (person level) and Level 2 (cluster level; see Koopman et al., 2023a,b) |
.
The output is of class iio.class
, and is often numerous.
Functions plot
and summary
can be used to summarize the output.
See Van der Ark (2014) for an example.
results |
A list with as many components as there are item pairs. Each component itself is also a list containing the results of the investigation of IIO. |
violations |
A matrix: Summary of the backward item selection (Corresponds to Table 4 in Ligtvoet et al., 2010, and Table 1 in Ligtvoet et al., 2011). The first column gives, for each item, the number of violations of IIO. If the number of violations is nonzero, then the item with the largest number of violations is removed. If two or more items have the maximum number of violations, then from those items the item producing the lowest value of Loevinger's H is removed. The second column shows the number of violations with one item removed, the third column shows the number of violations with two items removed, etc. |
items.removed |
List of the items removed in chronological order |
HT |
Coefficient HT for the remaining items. For the use of coefficient HT see Ligtvoet et al. (2010). If the sample size is extremely large coefficient HT is estimated using a random subsample. |
method |
The argument |
item.mean |
The mean item scores |
L. A. van der Ark L.A.vanderArk@uva.nl
Koopman, L., Zijlstra, B. J. H., & Van der Ark, L. A. (2023a). Assumptions and Properties of Two-Level Nonparametric Item Response Theory Models. Manuscript submitted for publication.
Koopman, L., Zijlstra, B. J. H., & Van der Ark, L. A. (2023b). Evaluating Model Fit in Two-Level Mokken Scale Analysis. Manuscript submitted for publication.
Ligtvoet, R., L. A. van der Ark, J. M. te Marvelde, & K. Sijtsma (2010). Investigating an invariant item ordering for polytomously scored items. Educational and Psychological Measurement, 70, 578-595. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1177/0013164409355697")}
Ligtvoet, R., L. A. van der Ark, W. P. Bergsma, & K. Sijtsma (2011). Polytomous latent scales for the investigation of the ordering of items. Psychometrika, 76, 200-216. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s11336-010-9199-8")}
Sijtsma, K., R. R. Meijer, & Van der Ark, L. A. (2011). Mokken scale analysis as time goes by: An update for scaling practitioners. Personality and Individual Differences, 50, 31-37. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.paid.2010.08.016")}
Sijtsma, K., & Molenaar, I. W. (2002) Introduction to nonparametric item response theory. Sage.
Van der Ark, L. A. (2007). Mokken scale analysis in R. Journal of Statistical Software, 20 (11), 1-19. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.18637/jss.v020.i11")}
Van der Ark, L. A. (2012). New developments in Mokken scale analysis in R. Journal of Statistical Software, 48(5), 1-27. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.18637/jss.v048.i05")}
check.errors
,
check.monotonicity
,
check.pmatrix
,
check.reliability
check.restscore
,
coefH
,
plot.iio.class
,
summary.iio.class
,
# Examples from Ligtvoet et al. (2010).
data(acl)
Order <- acl[,41:50]
summary(check.iio(Order))
plot(check.iio(Order))
Autonomy <- acl[,91:100]
summary(check.iio(Autonomy))
plot(check.iio(Autonomy))
# Examples from Ligtvoet et al. (2011).
data(cavalini)
X1 <- cavalini[,c(3,5,6,7,9,11,13,14)]
# Use Method MIIO and remove items violating MIIO
iio.list1 <- check.iio(X1)
summary(iio.list1)
X2 <- X1[,is.na(charmatch(dimnames(X1)[[2]],names(iio.list1$items.removed)))]
# Use Method MSCPM and remove items violating MSCPM
iio.list2 <- check.iio(X2,method="MSCPM")
summary(iio.list2)
X3 <- X2[,is.na(charmatch(dimnames(X2)[[2]],names(iio.list2$items.removed)))]
# Use Method IT
iio.list3 <- check.iio(X3,method="IT")
summary(iio.list3)
# Compute two-level fit statistics (Koopman et al., 2023a, 2023b)
data("autonomySupport")
dat <- autonomySupport[, -1]
groups <- autonomySupport[, 1]
autonomyMIIO <- check.iio(dat, item.selection = FALSE, level.two.var = groups)
summary(autonomyMIIO)
plot(autonomyMIIO)
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