# testOMF

##### Test for overall model fit

Bootstrap-based test for overall model fit originally proposed by Beran1985;textualcSEM. See also Dijkstra2015;textualcSEM who first suggested the test in the context of PLS-PM.

##### Usage

```
testOMF(
.object = NULL,
.alpha = 0.05,
.handle_inadmissibles = c("drop", "ignore", "replace"),
.R = 499,
.saturated = FALSE,
.seed = NULL,
.verbose = TRUE
)
```

##### Arguments

- .object
An R object of class cSEMResults resulting from a call to

`csem()`

.- .alpha
An integer or a numeric vector of significance levels. Defaults to

`0.05`

.- .handle_inadmissibles
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`.R`

). 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`.R`

). 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*".- .R
Integer. The number of bootstrap replications. Defaults to

`499`

.- .saturated
Logical. Should a saturated structural model be used? Defaults to

`FALSE`

.- .seed
Integer or

`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!- .verbose
Logical. Should information (e.g., progress bar) be printed to the console? Defaults to

`TRUE`

.

##### Details

`testOMF()`

tests the null hypothesis that the population indicator
correlation matrix equals the population model-implied indicator correlation matrix.
Several potential test statistics may be used. `testOMF()`

uses three 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, and the standardized root mean square residual (SRMR).
The reference distribution for each test statistic is obtained by
the bootstrap as proposed by Beran1985;textualcSEM.

If `.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.

##### Value

A list of class `cSEMTestOMF`

containing the following list elements:

`$Test_statistic`

The value of the test statistics.

`$Critical_value`

The corresponding critical values obtained by the bootstrap.

`$Decision`

The test decision. One of:

`FALSE`

(**Reject**) or`TRUE`

(**Do not reject**).`$Information`

The

`.R`

bootstrap values; The number of admissible results; The seed used and the number of total runs.

##### References

##### See Also

`csem()`

, `calculateSRMR()`

, `calculateDG()`

, `calculateDL()`

, cSEMResults,
`testMICOM()`

, `testMGD()`

##### Examples

```
# NOT RUN {
# ===========================================================================
# 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, .verbose = FALSE, .seed = 320)
# }
```

*Documentation reproduced from package cSEM, version 0.1.0, License: GPL-3*