Nonparametric Estimation of Conditional Covariances of Item Pairs

This function estimates conditional covariances of itempairs (Stout, Habing, Douglas & Kim, 1996; Zhang & Stout, 1999a). The function is used for the estimation of the DETECT index. The ccov.np function has the (default) option to smooth item response functions (argument smooth) in the computation of conditional covariances (Douglas, Kim, Habing, & Gao, 1998).

Usage

ccov.np(data, score, bwscale=1.1, thetagrid=seq(-3, 3, len=200),
    progress=TRUE, scale_score=TRUE, adjust_thetagrid=TRUE, smooth=TRUE,
    use_sum_score=FALSE, bias_corr=TRUE)

Arguments

data: An \(N \times I\) data frame of dichotomous responses. Missing responses are allowed.
score: An ability estimate, e.g. the WLE
bwscale: Bandwidth factor for calculation of conditional covariance. The bandwidth used in the estimation is bwscale times \(N^{-1/5}\).
thetagrid: A vector which contains theta values where conditional covariances are evaluated.
progress: Display progress?
scale_score: Logical indicating whether score should be z standardized in advance of the calculation of conditional covariances
adjust_thetagrid: Logical indicating whether thetagrid should be adjusted if observed values in score are outside of thetagrid.
smooth: Logical indicating whether smoothing should be applied for conditional covariance estimation
use_sum_score: Logical indicating whether sum score should be used. With this option, the bias corrected conditional covariance of Zhang and Stout (1999) is used.
bias_corr: Logical indicating whether bias correction (Zhang & Stout, 1999) should be utilized if use_sum_score=TRUE.

References

Douglas, J., Kim, H. R., Habing, B., & Gao, F. (1998). Investigating local dependence with conditional covariance functions. Journal of Educational and Behavioral Statistics, 23(2), 129-151. doi:10.3102/10769986023002129

Stout, W., Habing, B., Douglas, J., & Kim, H. R. (1996). Conditional covariance-based nonparametric multidimensionality assessment. Applied Psychological Measurement, 20(4), 331-354. doi:10.1177/014662169602000403

Zhang, J., & Stout, W. (1999). Conditional covariance structure of generalized compensatory multidimensional items. Psychometrika, 64(2), 129-152. doi:10.1007/BF02294532

Note

This function is used in conf.detect and expl.detect.

Examples

if (FALSE) {
#############################################################################
# EXAMPLE 1: data.read | different settings for computing conditional covariance
#############################################################################

data(data.read, package="sirt")
dat <- data.read

#* fit Rasch model
mod <- sirt::rasch.mml2(dat)
score <- sirt::wle.rasch(dat=dat, b=mod$item$b)$theta

#* ccov with smoothing
cmod1 <- sirt::ccov.np(data=dat, score=score, bwscale=1.1)
#* ccov without smoothing
cmod2 <- sirt::ccov.np(data=dat, score=score, smooth=FALSE)

#- compare results
100*cbind( cmod1$ccov.table[1:6, "ccov"], cmod2$ccov.table[1:6, "ccov"])
}