omega: Congeneric Reliability

In JonasMoss/reliable: Reliability Coefficients and Factor Scores for the Linear Factor Model

Description

The congeneric reliability is a the sum score reliability for the congeneric measurement model. The function takes either a lavaan object or a list containing the matrix of factor loadings and the diagonal matrix of residual variances.

Usage

omega(object)

Arguments

object

Either a lavaan object or a list containing Lambda, the matrix of factor loadings, and Psi, a diagonal matrix of residual variances.

Details

The congeneric measurement model is the linear factor model with one latent variable, potentially different loadings, and a diagonal residual variance matrix. Coefficient H (see coefficient_H) is also a reliability under the congeneric measurement model. The difference between coefficient H and the congeneric reliability lies in the implied factor scores. While the congeneric reliability uses sum scores where each item in the scale is given the same weight, coefficient H uses best possible linear combination of the items in terms of squared error loss.

When all factor loadings are equal the congeneric reliability equals coefficient alpha. If all residual variances are equal as well, the congeneric reliability equals the standardized coefficient alpha.

This function does not find the optimal selection of variables and does not flip the sign of any items. Use reliability with type = "sumscore" to do this.

Value

A numeric containing the value of the congeneric reliability.

References

Cronbach, L.J. (1951) "Coefficient alpha and the internal structure of tests." Psychometrika, 16, 297-334.

See Also

coefficient_H for the linear reliability under the congeneric model. reliability for reliabilities under the linear factor model, which includes optimization of which elements to include in the model when type = "sumscore".

Examples

model <- " g =~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 "
fit <- lavaan::cfa(model = model, data = lavaan::HolzingerSwineford1939)

# The congeneric reliability uses all items supplied.
omega(fit)

# But the reliability function finds the optimal choice of variables.
reliability(fit, type = "sumscore")

JonasMoss/reliable documentation built on Nov. 18, 2019, 5:34 a.m.