# threecommonfactors

From cSEM v0.1.0
by Manuel Rademaker

##### Data: threecommonfactors

A dataset containing 500 standardized observations on 9 indicator generated from a population model with three concepts modeled as common factors.

- Keywords
- datasets

##### Usage

`threecommonfactors`

##### Format

A matrix with 500 rows and 9 variables:

- y11-y13
Indicators attachted to the first common factor (

`eta1`

). Population loadings are: 0.7; 0.7; 0.7- y21-y23
Indicators attachted to the second common factor (

`eta2`

). Population loadings are: 0.5; 0.7; 0.8- y31-y33
Indicators attachted to the third common factor (

`eta3`

). Population loadings are: 0.8; 0.75; 0.7

The model is: $$`eta2` = gamma1 * `eta1` + zeta1$$ $$`eta3` = gamma2 * `eta1` + beta * `eta2` + zeta2$$

with population values `gamma1`

= 0.6, `gamma2`

= 0.4 and `beta`

= 0.35.

##### Examples

```
# NOT RUN {
#============================================================================
# Correct model (the model used to generate the data)
#============================================================================
model_correct <- "
# Structural model
eta2 ~ eta1
eta3 ~ eta1 + eta2
# Measurement model
eta1 =~ y11 + y12 + y13
eta2 =~ y21 + y22 + y23
eta3 =~ y31 + y32 + y33
"
a <- csem(threecommonfactors, model_correct)
## The overall model fit is evidently almost perfect:
testOMF(a, .R = 50, .verbose = FALSE) # .R = 50 to speed up the example
# }
```

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

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