LOCALDEP {EFA.dimensions}

Local dependence

Description

Provides the residual correlations after partialling latent trait scores out of an inter-item correlation matrix, along with local dependence statistics.

Usage

LOCALDEP(data, corkind, item_type, thetas, theta_type, verbose)

Arguments

data

An all-numeric dataframe where the rows are cases & the columns are the variables.

corkind

The kind of correlation matrix to be used for the analyses. The options are 'pearson', 'kendall', 'spearman', 'gamma', and 'polychoric'. Required only if the entered data is not a correlation matrix.

item_type

(optional) The type of items for the IRT analyses. If item_type is not specified, then it is assumed that the items follow a graded or 2PL model. The options for item_type are those that can be used in the mirt function from the mirt package, which include 'Rasch', '2PL', '3PL', '3PLu', '4PL', 'graded', 'grsm', 'grsmIRT', 'gpcm', 'gpcmIRT', 'rsm', 'nominal', 'ideal', item_type 'ggum', among other possibilities.

thetas

(optional) A vector of the latent trait scores that will be partialled out of the item correlations and used in computing other local dependence statistics. If thetas are not supplied, then they will be estimated internally using the fscores function from the mirt package.

theta_type

(optional) If thetas are not supplied, then they will be estimated internally using the fscores function from the mirt package with the following options: "EAP" (default), "MAP", "ML", "WLE", "EAPsum", "plausible", and "classify".

verbose

Should detailed results be displayed in console? TRUE (default) or FALSE

Details

Item response theory models are based on the assumption that the items display local independence. The latent trait is presumed to be responsible for the associations between the items. Once the latent trait is partialled out, the residual correlations between pairs of items should be negligible. Local dependence exists when there is additional systematic covariance among the items. It can occur when pairs of items have highly similar content or between sequentially presented items in a test. Local dependence distorts IRT parameter estimates, it can artificially increase scale information, and it distorts the latent trait, which becomes too heavily defined by the locally dependent items. Examining the residual (partial) correlations is a preliminary, exploratory method of determining whether local dependence exists. The function also displays the local dependence Q3 statistic values described by Yen (1984), the X2 statistic values described by Chen and Thissen (1997), the G2 statistic values described by Chen and Thissen (1997), and the jack-knife statistic values described by Edwards et al. (2018). The Q3, X2, G2, and jack-knife statistic values are obtained using the mirt function from the mirt package (Chalmers, 2012).

Value

A list with the following elements:

correlations

The correlation matrix

residcor

The residualized (partial) correlation matrix

eigenvalues

The eigenvalues

resid_Q3

A matrix with the Q3 statistic values described by Yen (1984)

resid_LD

A matrix with the X2 statistic values described by Chen and Thissen (1997)

resid_LDG2

A matrix with the G2 statistic values described by Chen and Thissen (1997)

resid_JSI

A matrix with the jack-knife statistic values described by Edwards et al. (2018)

localdep_stats

All of the above local dependence statistics in long format

Author(s)

Brian P. O'Connor

References

Chalmers, R., P. (2012). mirt: A multidimensional item response theory package for the R environment. Journal of Statistical Software, 48(6), 1-29.

Chen, W. H. & Thissen, D. (1997). Local dependence indices for item pairs using item response theory. Journal of Educational and Behavioral Statistics, 22, 265-289.

Edwards, M. C., Houts, C. R. & Cai, L. (2018). A diagnostic procedure to detect departures from local independence in item response theory models. Psychological Methods, 23, 138-149.

Yen, W. (1984). Effects of local item dependence on the fit and equating performance of the three parameter logistic model. Applied Psychological Measurement, 8, 125-145.

Examples

# Rosenberg Self-Esteem scale items
LOCALDEP(data_RSE)