# discriminantValidity: Calculate discriminant validity statistics In semTools: Useful Tools for Structural Equation Modeling

## Description

Calculate discriminant validity statistics based on a fitted lavaan object

## Usage

 `1` ```discriminantValidity(object, cutoff = 0.9, merge = FALSE, level = 0.95) ```

## Arguments

 `object` The `lavaan` model object returned by the `cfa` function. `cutoff` A cutoff to be used in the constrained models in likelihood ratio tests. `merge` Whether the constrained models should be constructed by merging two factors as one. Implies `cutoff` = 1. `level` The confidence level required.

## Details

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 a 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.

## Value

A `data.frame` of latent variable correlation estimates, their confidence intervals, and a likelihood ratio tests against constrained models. with the following attributes:

baseline

The baseline model after possible rescaling.

constrained

A `list` of the fitted constrained models used in the likelihood ratio test.

## Author(s)

Mikko Rönkkö (University of Jyväskylä; mikko.ronkko@jyu.fi):

## References

Rönkkö, M., & Cho, E. (2020). An updated guideline for assessing discriminant validity. Organizational Research Methods. doi: 10.1177/1094428120968614

## Examples

 ```1 2 3 4 5 6 7 8 9``` ```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) ```

semTools documentation built on Jan. 13, 2021, 8:09 p.m.