wb {fungible}

Wu & Browne model error method

Description

Generate a population correlation matrix using the model described in Wu and Browne (2015).

Usage

wb(mod, target_rmsea, wb_mod = NULL, adjust_target = TRUE)

Arguments

mod

A 'fungible::simFA()' model object.

target_rmsea

(scalar) Target RMSEA value.

wb_mod

('lm' object) An optional 'lm' object used to find a target RMSEA value that results in solutions with RMSEA values close to the desired value. Note that if no 'wb_mod' is provided, a model will be estimated at run time. If many population correlation matrices are going to be simulated using the same model, it will be considerably faster to estimate 'wb_mod' ahead of time. See also 'get_wb_mod()'.

adjust_target

(TRUE; logical) Should the target_rmsea value be adjusted to ensure that solutions have RMSEA values that are close to the provided target RMSEA value? Defaults to TRUE and should stay there unless you have a compelling reason to change it.

Details

The Wu and Browne method generates a correlation matrix with model error (\Sigma) using

(\Sigma | \Omega) ~ IW(m, m \Omega),

where m ~= 1/\epsilon^2 is a precision parameter related to RMSEA (\epsilon) and IW(m, m \Omega) denotes an inverse Wishart distribution. Note that *there is no guarantee that the RMSEA will be very close to the target RMSEA*, particularly when the target RMSEA value is large. Based on experience, the method tends to give solutions with RMSEA values that are larger than the target RMSEA values. Therefore, it might be worth using a target RMSEA value that is somewhat lower than what is actually needed. Alternatively, the get_wb_mod function can be used to estimate a coefficient to shrink the target RMSEA value by an appropriate amount so that the solution RMSEA values are close to the (nominal) target values.

Author(s)

Justin Kracht <[e-mail]>

References

Wu, H., & Browne, M. W. (2015). Quantifying adventitious error in a covariance structure as a random effect. *Psychometrika*, *80*(3), 571–600. <https://doi.org/10/gjrkc4>

Examples

# Specify a default model using simFA()
mod <- fungible::simFA(Seed = 42)

set.seed(42)
wb(mod, target_rmsea = 0.05)