With loadings equal across groups (weak invariance and above in
esem_invariance(); esem(),
besem() and esem_ordered() with
group and group_equal = "loadings") the common
loading matrix is now rotated without row scaling, as Mplus does.
lavaan’s default scales the rows by the residual variances averaged over
the groups, which gives the same fit but a different rotation of it.
From the weak level on, standardized loadings and their standard errors
now match Mplus 9 without any alignment, for ESEM and B-ESEM, MLR and
WLSMV (loadings already matched at the configural level). See
test-mg_rotation.R and “Rotation across groups” in
?esem_invariance.
group.partial on a factor loading
("F=~x") now stops with an error in ESEM and B-ESEM models.
lavaan rotates one common loading matrix and reports it in every group,
so a freed loading would be shown as equal.
ESEM with oblique target rotation (esem(),
esem_ordered(),
esem_invariance(model = "esem")) now computes rotation
standard errors with lavaan’s delta method
(rotation.se = "delta") and a tighter rotation convergence
criterion (gpa.tol = 1e-6). Standardized loading standard
errors at the configural level and in single-group models agree more
closely with Mplus 9 (largest difference on the test data 0.014 before,
0.0024 after; see test-mg_rotation.R). B-ESEM keeps
lavaan’s default, which is the closer of the two for orthogonal
rotation. A rotation.se or gpa.tol passed by
the user is kept.
esem_invariance() fits the second start of each
level without rotation and standard errors, since only its fit-function
value is compared, and refits it in full only when it is kept. Results
are unchanged, and the levels fit faster.
besem_ordered() and
esem_ordered(method = "rotation") warn when an item’s
communality exceeds 1 (a Heywood case, negative residual variance) and
return the communalities as communalities.
Their DWLS optimization now starts from two points and keeps a proper solution when one is reached. On data where it previously ran off to a communality far above 1 although a proper solution exists, it now returns that solution. A message says when a solution with a lower discrepancy but a communality above 1 was set aside.
esem_ordered(method = "rotation") no longer stops
with a singular-matrix error at the chi-square step when the solution is
improper.
besem_ordered(),
esem_ordered(method = "rotation"): polychoric correlations
now come from lavaan (same auxiliary fit as the weight matrix and
asymptotic covariance matrix), not psych::polychoric().
psych departs from lavaan and Mplus when items differ in number of
response categories. For those items chi-square, fit indices and
loadings now equal lavaan’s WLSMV fit of the unrotated model.
Standardized loadings were within 0.005 of Mplus 9 in validation runs.
Equal numbers of categories: loadings agree with 0.6.0 to about four
decimals. See test-polychoric_source.R.polychoric_source element ("lavaan" or
"r_obs_override"). r_obs_override warns if it
is more than 0.001 from lavaan’s correlations, since the weight matrix
is lavaan’s either way.missing = "listwise").lavaan_fit keeps the groups for
factor_scores().generate_mplus_syntax(),
generate_mplus_besem_syntax(): semicolon after NAMES and
USEVARIABLES. BY lists wrap at Mplus’s 90 columns. See
test-mplus_syntax.R.ordered argument: TRUE writes
CATEGORICAL and WLSMV. ESEM syntax uses the theta parameterization, as
esem_ordered() does. B-ESEM syntax keeps the Mplus default
(delta), which is the model besem_ordered() fits, so Mplus
reports a negative residual variance when there is one.
generate_mplus_besem_syntax() also gets
estimator.ITERATIONS = 10000 and
CONVERGENCE = 0.000001, like the invariance syntax. Mplus’s
default criterion can stop short of the optimum that R reaches.missing_code = "." writes MISSING = .;
(the NA code of MplusAutomation::prepareMplusData()).Fixes and additions prompted by the review of the Teacher’s Corner
manuscript. The minor version is bumped because reported values change:
SRMR now follows the Mplus definition, composite reliabilities use
absolute loadings, and lavaan >= 0.7-2 is required. Point estimates
and fit of the previously correct paths are unchanged. Prose now says
“ordinal” instead of “ordered-categorical”; function and argument names
(esem_ordered(), ordered = TRUE) are
unchanged.
esem_invariance() passes the sorted group levels to
lavaan as group.label, so the reference group is the first
sorted level in R and in the Mplus syntax written by
run_mplus_besem_invariance() alike. Loadings and factor
covariances are therefore oriented to the same group in both
programs.fit_ewc(var_fixed = FALSE) re-expresses the source ESEM
exactly and is honoured for a B-ESEM source (referent primary loadings
fixed, factor variances free, covariances 0).print() and compare_ewc() agree
with each other and with Mplus.print() of ESEM, B-ESEM and EWC fits,
fit_indices(), compare_ewc(), the
parameters() header and esem_compare() report
the robust chi-square, CFI, TLI and RMSEA, matching the comparison
table.esem_compare() fits its CFA with the ESEM’s estimator,
robust test, standard errors, missing-data setting and, for ordinal
items, parameterization, so both columns are like for like.p(p+1)/2 + p),
polychoric and category-probability residuals for ordinal items
(denominator p(p-1)/2 + total categories), pooled over
groups by sample size. Multi-group values agree with Mplus to three
decimals at every invariance level of the validation runs; single-group
values are unchanged at three decimals. The custom DWLS B-ESEM path uses
the same denominator.compute_indices() sums absolute standardized loadings
in every composite (Morin, Arens & Marsh, 2016), so reverse-scoring
an item or reflecting a factor changes nothing
(test-reliability.R). For CFA and ESEM the residual
variance comes from the model-implied item variance (one minus the
diagonal of Lambda Phi Lambda’), which accounts for the factor
correlations.compute_indices()
help describe the other factor’s variance as an additional source of
error rather than as partialled out (Morin et al., 2020).print() of the reliability indices follows the console
width (80 to 100 columns) instead of a fixed 100, and
alignment_check() wraps its recommendation line.esem_invariance() is
printed in bold blue where the console supports ANSI colour (RStudio, or
a terminal whose TERM is not “dumb”);
options(bifactory.ansi_colour = FALSE) turns it off,
TRUE forces it. Same detection as
parameters().esem_invariance() catches lavaan’s estimation warnings
per level, on the master and on the worker processes, and reports them
reworded in inv$notes and under “Estimation notes” after
the table. Admissibility is read from the reported solution, so a note
names the group and the parameter, e.g. “a negative variance estimate
(Heywood case): 2 (G latent variance -0.120)”. Only the reported fit’s
notes are kept; package warnings are unaffected.print(): levels
fitted and considered, that the table can be interpreted, the most
constrained admissible level supported by dCFI >= -0.010 among all
fitted levels, any note at that level, a tip toward
through = "varcov" / "means" or
partial_invariance() when strict is supported but
inadmissible, and “Remember: print(inv)”.
factor_scores(level = "auto") uses the same rule, so it
never selects an inadmissible level and can select varcov or means when
they were fitted.esem_invariance() gains
through = c("strict", "varcov", "means"): the latent
variance/covariance and latent mean invariance levels of Morin’s
sequence, for ESEM and B-ESEM under MLR and WLSMV. The default sequence
is unchanged; run_mplus_besem_invariance() mirrors the
fitted levels.partial_invariance() follows the partial-invariance
rules for ESEM and B-ESEM. Only level = "strong"
(intercepts or thresholds) and level = "strict" (residual
variances) are accepted; level = "weak" is refused with an
explanation, because the rotated loadings are constrained as a block.
Constraints are released one at a time by score test; an item is
released only if every factor it belongs to keeps at least two items
with invariant intercepts/thresholds (Byrne, Shavelson & Muthén,
1989; van de Schoot, Lugtig & Hox, 2012); releasing more than 20% of
the constraints added at a level warns (Dimitrov, 2010); every released
parameter is listed. On ordinal items at least one threshold per item
stays invariant (Millsap & Yun-Tein, 2004); an item’s last threshold
can be released by hand through
esem_invariance(..., group.partial = "item|t1"). Released
thresholds are honoured on the ordinal path, the continuous refit is
retried from simple starting values, and B-ESEM is supported. A recovery
test plants intercept shifts on two items in one of two simulated groups
and checks that exactly those items are released, as intercepts on the
continuous path and as thresholds on the ordinal path.start = "simple" starting values; the alternative is kept
when its fit function is lower by more than 0.1%. The new
cores argument (default 2) runs the two starts on two
worker processes at the same time with identical results, so a level
takes as long as its slower start; cores = 1 fits
sequentially.align_loadings() compares against another fit, or
against a supplied solution (lambda, psi,
theta per group), by orientation transfer: the
unstandardized loadings are rotated to the reference and the factor
covariances are transformed with the same rotation before standardizing.
This is exact in every group, including groups with free factor
covariances, where Procrustes alignment of standardized loadings is not.
An esem_invariance target is read at the requested
level.run_mplus_besem_invariance() writes
CONVERGENCE = 0.000001 for its first Mplus attempt; if
Mplus does not converge there, the retries start at Mplus’s default and
then loosen (1e-4 to 5e-2). When a level’s Mplus run prints no fit
(singular information matrix, no DIFFTEST derivatives file),
DIFFTEST is omitted from the next level’s input.
extract_mplus_loadings() returns numeric matrices for such
outputs.This release contains defensive fixes; estimation results are unchanged.
parameters() on a Heywood-corrected ESEM fit now
reports NA for standard errors, z-values, and p-values when
the rotation changed after those quantities were computed, while
retaining the corrected standardized loadings.factor_scores() now raises an informative error when
the polychoric correlation or score-information matrix is singular,
instead of exposing a bare solve() failure.NA/0 target
convention, so primary cells in targets built that way are freed
correctly.factor_scores() now warns when one pooled polychoric
matrix is applied across multiple groups.esem_ordered() and besem_ordered() now
stop with a clear message when supplied item names collide
case-insensitively, instead of silently mismatching them.NA rather than
NaN for a degenerate all-zero loading matrix.Changes in response to CRAN review (no changes to estimation results):
efa().print()/summary()
methods now uses message() (or warning() where
appropriate) instead of cat()/print(), so it
can be suppressed with suppressMessages(). Progress output
keeps its verbose gating.parameters() now returns a classed data frame
(bifactory_parameters) that prints the same formatted table
via its own print() method. Assigning the result no longer
prints as a side effect..GlobalEnv; internal fixed-seed sections use
withr::with_seed() (new Import: withr). Draws are
unchanged, so results are identical to 0.5.0.lavaan::HolzingerSwineford1939); \dontrun{}
is retained only for examples that require a licensed Mplus installation
or open an interactive editor. Longer-running examples use
\donttest{}. No runnable example uses a package from
Suggests.efa() blocks
(MLR).