mokken (version 3.0.4)

check.bounds: 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).

References

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

Examples

# NOT RUN {
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 
# }