ChenThissen1997: Computes local dependence indices for all pairs of items

Description

Item Factor Analysis makes two assumptions: (1) that the latent distribution is reasonably approximated by the multivariate Normal and (2) that items are conditionally independent. This test examines the second assumption. The presence of locally dependent items can inflate the precision of estimates causing a test to seem more accurate than it really is.

Usage

ChenThissen1997(grp, ..., data = NULL, inames = NULL, qwidth = 6,
  qpoints = 49, method = "pearson", .twotier = TRUE, .parallel = TRUE)

Arguments

grp

a list with the spec, param, mean, and cov describing the group

...

Not used. Forces remaining arguments to be specified by name.

data

inames

a subset of items to examine

qwidth

quadrature width

qpoints

number of equally spaced quadrature points

method

method to use to calculate P values. The default is the Pearson X^2 statistic. Use "lr" for the similar likelihood ratio statistic.

.twotier

whether to enable the two-tier optimization

.parallel

whether to take advantage of multiple CPUs (default TRUE)

Value

a list with raw, pval and detail. The pval matrix is a lower triangular matrix of log P values with the sign determined by relative association between the observed and expected tables (see ordinal.gamma)

Details

Statically significant entries suggest that the item pair has local dependence. Since log(.01)=-4.6, an absolute magitude of 5 is a reasonable cut-off. Positive entries indicate that the two item residuals are more correlated than expected. These items may share an unaccounted for latent dimension. Consider a redesign of the items or the use of testlets for scoring. Negative entries indicate that the two item residuals are less correlated than expected.

References

Chen, W.-H. & Thissen, D. (1997). Local dependence indexes for item pairs using Item Response Theory. Journal of Educational and Behavioral Statistics, 22(3), 265-289.

Thissen, D., Steinberg, L., & Mooney, J. A. (1989). Trace lines for testlets: A use of multiple-categorical-response models. Journal of Educational Measurement, 26 (3), 247--260.