Re: Digest for lavaan@googlegroups.com - 1 update in 1 topic
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Luke Brown
Dec 17, 2025, 1:27:17 AM (2 days ago) Dec 17
to lav...@googlegroups.com
Hi SEM family,
I’m wondering if anyone has experience using SEM with population- or regional-level data that is routinely collected rather than experimentally derived.
Our project aims to explore the relationship between community-related factors and mental health outcomes. We’re currently developing a CFA model with three to four latent constructs (urbanity, community cohesion, community safety, and ethnic diversity).
With some modifications, our goodness-of-fit indices remain below acceptable thresholds, although the model requires numerous correlations that are theoretically supported. We are able to get a better-fitting model, but the observed variables included in our latent construct are less rich and more simplistic.
Has anyone worked with this type of data, and are there examples of published studies where goodness-of-fit measures were somewhat suboptimal but still considered acceptable in context?
Best wishes, Luke
On Tue, 16 Dec 2025 at 18:52, <lav...@googlegroups.com> wrote:
Andres Perez <af.pere...@gmail.com>: Dec 16 03:17AM -0800
Hi everyone,
I have been working with some (simulated) categorical data for a while and
greatly appreciate the developments in the measEq.syntax function, as it
has made my life easier when applying the identification constraints from
Wu & Estabrook (2016).
There is still one thing that I do not understand, though. In the Wu &
Estabrook paper, they mention that it is impossible to test for threshold
and loading invariance simultaneously, as it is “statistically equivalent”
to the baseline (i.e., configural) model (Section 5.3; Proposition 6). A
screenshot of that specific part of the paper is attached to this post. For
brevity, I will write “metric invariance” instead of “threshold and loading
invariance” from now on.
Looking at the documentation from the semTools package, I see that the
measEq.syntax function considers other non-testable non-invariances (e.g.,
Propositions 4 and 5 of Wu & Estabrook) on page 70:
*"For binary data, there is no independent test of threshold, intercept, or
residual-variance equality. Equivalence of thresholds must also be assumed
for three-category indicators."*
However, there is no mention of exactly what happens when testing for
metric invariance with binary data. Following what Wu & Estabrook explain,
I would expect that a configural model and a model with metric invariance
should be “statistically equivalent” (e.g., test statistics; chi-squared).
Is this correct?
I was playing around with a simple (simulated) toy data set with two
groups. It was generated with equal thresholds and loadings across the
groups. I fitted a configural and a metric invariant model and compared
them, but I noticed they are not “statistically equivalent,” at least not
in terms of chi-squared values.
Am I misinterpreting what Wu & Estabrook stated in their paper? Or is
semTools doing something else in the background? I am just trying to
understand precisely what Wu & Estabrook meant by their "Proposition 6".
Attached to this post, you can find the toy dataset and the R script where
I ran the two models. I am also copying & pasting it here if that is easier
to access.
Thank you very much for your help!
Best,
Andres Perez
Code:
# 2025-12-16
# Testing metric invariance with binary data using semTools
# Load libraries
library(lavaan)
library(semTools)
# Load data
load("binary_data.Rdata")
# Define the model
S1 <- '
# factor loadings
F1 =~ x1 + x2 + x3 + x4 + x5
F2 =~ z1 + z2 + z3 + z4 + z5
F3 =~ m1 + m2 + m3 + m4 + m5
F4 =~ y1 + y2 + y3 + y4 + y5
'
######################################
########### CONFIGURAL FIT ###########
######################################
S1.config <- as.character(
semTools::measEq.syntax(configural.model = S1,
dat = binary,
parameterization = "delta",
ordered = T,
ID.fac = "std.lv",
ID.cat = "Wu",
group = "group")
)
fit.config <- cfa(model = S1.config,
data = binary,
group = "group",
ordered = T)
######################################
######## FULLY INVARIANT FIT #########
######################################
S1.inv <- as.character(
semTools::measEq.syntax(configural.model = S1,
dat = binary,
parameterization = "delta",
ordered = T,
ID.fac = "std.lv",
ID.cat = "Wu",
group = "group",
group.equal = c("thresholds", "loadings"))
)
fit.inv <- cfa(model = S1.inv,
data = binary,
group = "group",
ordered = T)
#################################
########### COMPARING ###########
#################################
fit.config
fit.inv
# summary(fit.config)
# summary(fit.inv)
fitmeasures(fit.config , c("chisq")) # chisq 219.339
fitmeasures(fit.inv , c("chisq")) # chisq 255.249
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