threecommonfactors {cSEM} | R Documentation |

## Data: threecommonfactors

### Description

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

### Usage

```
threecommonfactors
```

### Format

A matrix with 500 rows and 9 variables:

- y11-y13
Indicators attached to the first common factor (`eta1`

).
Population loadings are: 0.7; 0.7; 0.7

- y21-y23
Indicators attached to the second common factor (`eta2`

).
Population loadings are: 0.5; 0.7; 0.8

- y31-y33
Indicators attached 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

```
#============================================================================
# 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 = 30) # .R = 30 to speed up the example
```

[Package

*cSEM* version 0.5.0

Index]