check.bounds {mokken}

Check the relative lower bound for scalability coefficients

Description

Returns the relative bounds for Mokken's scalability coefficients for dichotomous items as described by Ellis (2014).

Usage

check.bounds(X, quant = .90, lower = TRUE, upper = 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

quant

numerical value between 0 and 1 used for the computation of lower bound L2rij. The computation deviates somewhat from the proposal in Ellis (2014) because the stats function quantile is used.

lower

Boolean: If TRUE, the lower bounds are given.

upper

Boolean: If TRUE, the upper bounds are given.

Value

List containing two lists UpperBounds and LowerBounds, each containing a list of two J x J matrices (J = number of items): L1rij (overestimator of the lower bound for the correlation) and L2rij (underestimator of the lower bound for the correlation).

Author(s)

L. A. van der Ark [e-mail]

References

Ellis, J. L. (2014). An inequality for correlations in unidimensional monotone latent variable models for binary variables. Psychometrika, 79, 303-316. doi:10.1007/S11336-013-9341-5

Examples

data(acl)
Communality <- acl[,1:10]
R <- cor(Communality)
res <- check.bounds(Communality, upper = TRUE)
L1rij <- res$LowerBounds$L1rij
L2rij <- res$LowerBounds$L2rij
U1rij <- res$UpperBounds$U1rij
U2rij <- res$UpperBounds$U2rij
# Correlations that meet L1rij (possibly an overestimation of the lower bound). 
R >= L1rij 
# Correlations that meet U1rij (possibly an overestimation of the upper bound). 
R <= U1rij 
# Correlations that meet L2rij (possibly an underestimation of the lower bound). 
R >= L2rij 
# Correlations that meet U2rij (possibly an underestimation of the upper bound). 
R <= U2rij