A dataset containing 500 standardized observations on 19 indicator generated from a
population model with 6 concepts, three of which (c1-c3) are composites
forming a second order common factor (c4). The remaining two (eta1, eta2)
are concepts modeled as common factors .
dgp_2ndorder_cf_of_cA matrix with 500 rows and 19 variables:
Indicators attached to c1.
Population weights are: 0.8; 0.4.
Population loadings are: 0.925; 0.65
Indicators attached to c2.
Population weights are: 0.5; 0.3; 0.2; 0.4.
Population loadings are: 0.804; 0.68; 0.554; 0.708
Indicators attached to c3.
Population weights are: 0.3; 0.3; 0.1; 0.1; 0.2; 0.3; 0.4; 0.2.
Population loadings are: 0.496; 0.61; 0.535; 0.391; 0.391; 0.6; 0.5285; 0.53
Indicators attached to eta1.
Population loadings are: 0.8; 0.7; 0.7
Indicators attached to eta1.
Population loadings are: 0.8; 0.8; 0.7
The model is: $$`c4` = gamma1 * `eta1` + zeta1$$ $$`eta2` = gamma2 * `eta1` + beta * `c4` + zeta2$$
with population values gamma1 = 0.6, gamma2 = 0.4 and beta = 0.35.
The second order common factor is
$$`c4` = lambdac1 * `c1` + lambdac2 * `c2` + lambdac3 * `c3` + epsilon$$