Evaluates model fit from an equivalence-testing perspective by aggregating local EPC-based diagnostics into a global, fit-style assessment. The procedure combines modification indices (MI), expected parameter changes (EPC), statistical power, and confidence intervals relative to a smallest effect size of interest (SESOI).
epcEquivFit(lavaanObj, stdLoad = 0.4, cor = 0.1, corLatent = NULL,
corResidual = NULL, stdBeta = 0.1, stdIntcept = 0.2, stdSesoi = NULL,
sesoi = NULL, cilevel = 0.9, ...)# S3 method for epcequivfit.data.frame
summary(object, ..., top = 5, ssv = FALSE)
A data frame with one row per fixed parameter, containing:
Parameter identifiers: lhs, op, rhs, and group.
Modification index (mi) and expected parameter change estimates
(epc).
Unstandardized and standardized smallest effect size of interest values
(sesoi, std.sesoi).
Power-based decision (decision.pow) and related diagnostics, including
whether the modification index is statistically significant
(significant.mi) and whether the misfit at the SESOI has power greater
than 0.80 (high.power). Decision labels are:
M = Substantially Misspecified,
I = Inconclusive,
NM = Trivially Misspecified,
EPC:M = Substantially Misspecified based on EPC information,
EPC:NM = Trivially Misspecified based on EPC information.
EPC-related statistics, including the standard error of the EPC
(se.epc), confidence interval bounds for the EPC
(lower.epc, upper.epc), and confidence interval bounds for the
standardized EPC (lower.std.epc, upper.std.epc).
Confidence-interval–based equivalence decision (decision.ci), with
labels:
M = Substantially Misspecified (EPC exceeds the SESOI),
I = Inconclusive,
NM = Trivially Misspecified,
U = Underpowered (CI too wide to evaluate equivalence relative to the SESOI).
A fitted lavaan object used to evaluate model fit.
Standardized factor loading defining the SESOI for loading misspecifications. Default is 0.4.
Default standardized correlation defining the SESOI for covariance misspecifications. Used for both latent and residual covariances unless overridden.
Standardized latent factor correlation defining the
SESOI for latent covariance misspecifications. If NULL,
defaults to cor.
Standardized residual correlation defining the
SESOI for residual covariance misspecifications. If NULL,
defaults to cor.
Standardized regression coefficient defining the SESOI for structural misspecifications. Default is 0.1.
Standardized intercept (Cohen's d) defining the SESOI for intercept misspecifications. Default is 0.2.
Optional vector of standardized SESOI values. If provided, overrides operator-specific SESOI definitions.
Optional vector of unstandardized SESOI values. If
provided, overrides stdSesoi and all operator-specific SESOI
arguments.
Confidence level for EPC confidence intervals used in CI-based equivalence testing.
Additional arguments passed to
modificationIndices.
An object returned by epcEquivFit.
Number of top-ranked EPCs to display.
Logical; whether to include power-based diagnostics.
Two complementary local decision rules are implemented:
Method 1 (Power-based; Saris, Satorra, & van der Veld, 2009). Modification indices, statistical power, and EPC magnitude are jointly evaluated (the J-rule) to classify fixed parameters as misspecified, not misspecified, or inconclusive.
Method 2 (CI-based equivalence testing). Confidence intervals of EPCs are compared against a trivial misspecification region defined by the SESOI to determine whether fixed parameters are substantially misspecified, trivially misspecified, underpowered, or inconclusive.
The resulting local classifications are returned in a single data frame and can be summarized to yield a global equivalence-style fit evaluation.
This function provides a local-to-global equivalence-based alternative to traditional exact-fit evaluation. It is designed to assess whether fixed parameters are substantively misspecified relative to a SESOI, rather than whether a model fits exactly.
Models with categorical indicators or unsupported constraints may not be fully supported.
Saris, W. E., Satorra, A., & van der Veld, W. M. (2009). Testing structural equation models or detection of misspecifications? Structural Equation Modeling, 16(4), 561--582.
epcEquivCheck
library(lavaan)
one.model <- ' onefactor =~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 '
fit <- cfa(one.model, data = HolzingerSwineford1939)
out <- epcEquivFit(fit)
out
summary(out)
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