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

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

#============================================================================
# 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
#> ________________________________________________________________________________
#> --------- 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    	0.0212
#> 	SRMR                    0.0158    	0.0279
#> 	dL                      0.0112    	0.0349
#> 	dML                     0.0320    	0.1120
#>
#>
#> Decision:
#>
#> 	                    	Significance level
#> 	Distance measure    	     95%
#> 	dG                  	Do not reject
#> 	SRMR                	Do not reject
#> 	dL                  	Do not reject
#> 	dML                 	Do not reject
#>