testOMF( .object = NULL, .alpha = 0.05, .fit_measures = FALSE, .handle_inadmissibles = c("drop", "ignore", "replace"), .R = 499, .saturated = FALSE, .seed = NULL, ... )
An integer or a numeric vector of significance levels.
Logical. (EXPERIMENTAL) Should additional fit measures
be included? Defaults to
Character string. How should inadmissible results
be treated? One of "drop", "ignore", or "replace". If "drop", all
replications/resamples yielding an inadmissible result will be dropped
(i.e. the number of results returned will potentially be less than
For "ignore" all results are returned even if all or some of the replications
yielded inadmissible results (i.e. number of results returned is equal to
For "replace" resampling continues until there are exactly
.R admissible solutions.
Depending on the frequency of inadmissible solutions this may significantly increase
computing time. Defaults to "drop".
Integer. The number of bootstrap replications. Defaults to
Logical. Should a saturated structural model be used?
NULL. The random seed to use. Defaults to
NULL in which
case an arbitrary seed is chosen. Note that the scope of the seed is limited
to the body of the function it is used in. Hence, the global seed will
not be altered!
Can be used to determine the fitting function used in the calculateGFI function.
A list of class
cSEMTestOMF containing the following list elements:
The value of the test statistics.
The corresponding critical values obtained by the bootstrap.
The test decision. One of:
FALSE (Reject) or
TRUE (Do not reject).
.R bootstrap values; The number of admissible results;
The seed used and the number of total runs.
Bootstrap-based test for overall model fit originally proposed by Beran and Srivastava (1985) . See also Dijkstra and Henseler (2015) who first suggested the test in the context of PLS-PM.
testOMF() tests the null hypothesis that the population indicator
correlation matrix equals the population model-implied indicator correlation matrix.
Several discrepancy measures may be used. By default,
testOMF() uses four distance
measures to assess the distance between the sample indicator correlation matrix
and the estimated model-implied indicator correlation matrix, namely the geodesic distance,
the squared Euclidean distance, the standardized root mean square residual (SRMR),
and the distance based on the maximum likelihood fit function.
The reference distribution for each test statistic is obtained by
the bootstrap as proposed by Beran and Srivastava (1985)
It is possible to perform the bootstrap-based test using fit measures such
as the CFI, RMSEA or the GFI if
.fit_measures = TRUE. This is experimental.
To the best of our knowledge the applicability and usefulness of the fit
measures for model fit assessment have not been formally (statistically)
assessed yet. Theoretically, the logic of the test applies to these fit indices as well.
Hence, their applicability is theoretically justified.
Only use if you know what you are doing.
.saturated = TRUE the original structural model is ignored and replaced by
a saturated model, i.e., a model in which all constructs are allowed to correlate freely.
This is useful to test misspecification of the measurement model in isolation.
Beran R, Srivastava MS (1985).
“Bootstrap Tests and Confidence Regions for Functions of a Covariance Matrix.”
The Annals of Statistics, 13(1), 95--115.
Dijkstra TK, Henseler J (2015). “Consistent and Asymptotically Normal PLS Estimators for Linear Structural Equations.” Computational Statistics & Data Analysis, 81, 10--23.
# =========================================================================== # Basic usage # =========================================================================== model <- " # Structural model eta2 ~ eta1 eta3 ~ eta1 + eta2 # (Reflective) measurement model eta1 =~ y11 + y12 + y13 eta2 =~ y21 + y22 + y23 eta3 =~ y31 + y32 + y33 " ## Estimate out <- csem(threecommonfactors, model, .approach_weights = "PLS-PM") ## Test testOMF(out, .R = 50, .seed = 320) #> ________________________________________________________________________________ #> --------- Test for overall model fit based on Beran & Srivastava (1985) -------- #> #> Null hypothesis: #> #> ┌──────────────────────────────────────────────────────────────────┐ #> │ │ #> │ H0: The model-implied indicator covariance matrix equals the │ #> │ population indicator covariance matrix. │ #> │ │ #> └──────────────────────────────────────────────────────────────────┘ #> #> Test statistic and critical value: #> #> Critical value #> Distance measure Test statistic 95% #> dG 0.0060 0.0192 #> SRMR 0.0158 0.0272 #> dL 0.0112 0.0333 #> dML 0.0320 0.1027 #> #> #> Decision: #> #> Significance level #> Distance measure 95% #> dG Do not reject #> SRMR Do not reject #> dL Do not reject #> dML Do not reject #> #> Additional information: #> #> Out of 50 bootstrap replications 50 are admissible. #> See ?verify() for what constitutes an inadmissible result. #> #> The seed used was: 320 #> ________________________________________________________________________________