Calculate discriminant validity statistics based on a fitted lavaan object
discriminantValidity(object, cutoff = 0.9, merge = FALSE, level = 0.95)The '>lavaan model object returned by
the cfa function.
A cutoff to be used in the constrained models in likelihood ratio tests.
Whether the constrained models should be constructed by merging
two factors as one. Implies cutoff = 1.
The confidence level required.
A data.frame of latent variable correlation estimates, their
confidence intervals, and a likelihood ratio tests against constrained models.
with the following attributes:
The baseline model after possible rescaling.
A list of the fitted constrained models
used in the likelihood ratio test.
Evaluated on the measurement scale level, discriminant validity is commonly evaluated by checking if each pair of latent correlations is sufficiently below one (in absolute value) that the latent variables can be thought of representing two distinct constructs.
discriminantValidity function calculates two sets of statistics that
are commonly used in discriminant validity evaluation. The first set are
factor correlation estimates and their confidence intervals. The second set
is a series of nested model tests, where the baseline model is compared
against as set of constrained models that are constructed by constraining
each factor correlation to the specified cutoff one at a time.
The function assume that the object is set of confirmatory
factor analysis results where the latent variables are scaled by fixing their
variances to 1s. If the model is not a CFA model, the function will calculate
the statistics for the correlations among exogenous latent variables, but
for the residual variances with endogenous variables. If the
latent variables are scaled in some other way (e.g. fixing the first loadings),
the function issues a warning and re-estimates the model by fixing latent
variances to 1 (and estimating all loadings) so that factor covariances are
already estimated as correlations.
The likelihood ratio tests are done by comparing the original baseline model against more constrained alternatives. By default, these alternatives are constructed by fixing each correlation at a time to a cutoff value. The typical purpose of this test is to demonstrate that the estimated factor correlation is well below the cutoff and a significant \(chi^2\) statistic thus indicates support for discriminant validity. In some cases, the original correlation estimate may already be greater than the cutoff, making it redundant to fit a "restricted" model. When this happens, the likelihood ratio test will be replaced by comparing the baseline model against itself. For correlations that are estimated to be negative, a negation of the cutoff is used in the constrained model.
Another alternative is to do a nested model comparison against a model where
two factors are merged as one by setting the merge argument to
TRUE. In this comparison, the constrained model is constructed by
removing one of the correlated factors from the model and assigning its
indicators to the factor that remains in the model.
# NOT RUN {
library(lavaan)
HS.model <- ' visual =~ x1 + x2 + x3
textual =~ x4 + x5 + x6
speed =~ x7 + x8 + x9 '
fit <- cfa(HS.model, data = HolzingerSwineford1939)
discriminantValidity(fit)
discriminantValidity(fit, merge = TRUE)
# }
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