mokken (version 2.4)

check.iio: Check of Invariant Item Ordering

Description

Returns a list 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) (2) Method MS-CPM (manifest scale - cumulative probability model: investigates the manifest item step response functions for all pairs of items) (3) Method IT (increasingness in transposition: investigates all bivariate joint probabilities for all pairs of items) 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 (2009).

Usage

check.iio(X, method="MIIO", minvi = default.minvi, minsize = default.minsize, alpha = .05, item.selection=TRUE, verbose=FALSE)

Arguments

X

matrix or data frame of numeric data containing the responses of nrow(X) respondents to ncol(X) items. Missing values are not allowed

method

Either "MIIO" (default), "MSCPM", or "IT". Partial matching is allowed (e.g. method="ms" is equivalent to method="MSCPM")

minvi

minimum size of a violation that is reported. By default minvi = .03 times the number of item step response functions (m) for Method MIIO; minvi = .03 for Method IT and Method MSCPM

minsize

minimum size of a rest score group. By default minsize = $N/10$ if $N \geq 500$; minsize = $N/5 if$ $250 \leq N < 500$; and minsize = $\max(N/3,50)$ if $N < 250$

alpha

Nominal Type I error for t test (Method MIIO), z test (Method MSCPM), or McNemar test (Method IT). Default alpha = .05

item.selection

Conduct backward item selection procedure (see Ligtvoet et al., 2010). Default item.selection=TRUE

verbose

Show the results of the backward item selection algorithm on screen. Default verbose=FALSE

Value

• 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: Summarizes of the backward item selection (Corresponds to Table 4 in Ligtvoet et al., in press, and Table 1 in Ligtvoet et al., 2009). The first column gives the number of violations of IIO according the method restscore. 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. (in press)
• method
  The argument method
• item.mean
  The mean item scores

References

Ligtvoet, R., van der Ark, L. A., The Marvelde, J. M., and Sijtsma (in press) Investigating an invariant item ordering for polytomously scored items. Educational and Psychological Measurement. Ligtvoet, R., van der Ark, L. A., Bergsma, W. P., and Sijtsma (2009) Polytomous latent scales for the investigation of the ordering of items. Manuscript submitted for publication. Sijtsma, K, and Molenaar, I. W. (2002) Introduction to nonparametric item response theory. Thousand Oaks, CA: Sage. Van der Ark, L. A. (2007). Mokken scale analysis in R. Journal of Statistical Software. http://www.jstatsoft.org

See Also

check.monotonicity, check.pmatrix, check.reliability check.restscore, coefH, summary.iio.class

Examples

# Examples from Ligtvoet et al. (2010).

data(acl)            

Order <- acl[,41:50]               
check.iio(Order)                     

Autonomy <- acl[,91:100]
check.iio(Autonomy)

# Examples from Ligtvoet et al. (2009).
 
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)