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	
#> 	
#> Additional information:
#> 
#> 	Out of 30 bootstrap replications 30 are admissible.
#> 	See ?verify() for what constitutes an inadmissible result.
#> 
#> 	The seed used was: 1614705571
#> ________________________________________________________________________________