unidim.test.csn: Test for Unidimensionality of CSN

In sirt: Supplementary Item Response Theory Models

Test for Unidimensionality of CSN

Description

This function tests whether item covariances given the sum score are non-positive (CSN; see Junker 1993), i.e. for items i and j it holds that

Cov( X_i, X_j | X^+ ) \le 0

Note that this function only works for dichotomous data.

Usage

unidim.test.csn(dat, RR=400, prop.perm=0.75, progress=TRUE)

Arguments

dat	Data frame with dichotomous item responses. All persons with (some) missing responses are removed.
RR	Number of permutations used for statistical testing
prop.perm	A positive value indicating the amount of permutation in an existing permuted data set
progress	An optional logical indicating whether computation progress should be displayed

Details

For each item pair (i,j) and a each sum score group k a conditional covariance r(i,j|k) is calculated. Then, the test statistic for CSN is

h=\sum_{k=1}^{I-1} \frac{n_k}{n} \max_{i,j} r(i,j|k)

where n_k is the number of persons in score group k. "'Large values"' of h are not in agreement with the null hypothesis of non-positivity of conditional covariances.

The distribution of the test statistic h under the null hypothesis is empirically obtained by column wise permutation of items within all score groups. In the population, this procedure corresponds to conditional covariances of zero. See de Gooijer and Yuan (2011) for more details.

Value

A list with following entries

stat	Value of the statistic
stat_perm	Distribution of statistic under H_0 of permuted dataset
p	The corresponding p value of the statistic
H0_quantiles	Quantiles of the statistic under permutation (the null hypothesis H_0)

References

De Gooijer, J. G., & Yuan, A. (2011). Some exact tests for manifest properties of latent trait models. Computational Statistics and Data Analysis, 55, 34-44.

Junker, B.W. (1993). Conditional association, essential independence, and monotone unidimensional item response models. Annals of Statistics, 21, 1359-1378.

Examples

#############################################################################
# EXAMPLE 1: Dataset data.read
#############################################################################

data(data.read)
dat <- data.read
set.seed(778)
res <- sirt::unidim.test.csn( dat )
  ##  CSN Statistic=0.04737, p=0.02

## Not run: 
#############################################################################
# EXAMPLE 2: CSN statistic for two-dimensional simulated data
#############################################################################

set.seed(775)
N <- 2000
I <- 30   # number of items
rho <- .60   # correlation between 2 dimensions
t0 <- stats::rnorm(N)
t1 <- sqrt(rho)*t0 + sqrt(1-rho)*stats::rnorm(N)
t2 <- sqrt(rho)*t0 + sqrt(1-rho)*stats::rnorm(N)
dat1 <- sirt::sim.raschtype(t1, b=seq(-1.5,1.5,length=I/2) )
dat2 <- sirt::sim.raschtype(t2, b=seq(-1.5,1.5,length=I/2) )
dat <- as.matrix(cbind( dat1, dat2) )
res <- sirt::unidim.test.csn( dat )
  ##  CSN Statistic=0.06056, p=0.02

## End(Not run)

sirt documentation built on Aug. 11, 2023, 5:07 p.m.