A comparison of three approaches to covariate effects on latent factors

Large-scale Assessments in Education

An IERI – International Educational Research Institute Journal

Table 2 Parameter estimates for terminal nodes from Mplus tree with complexity parameter of 0.001

Parameter	Node 8	Node 9	Node 10	Node 11	Node 6	Node 7
SC.BY BSBM19A	1.000	1.000	1.000	1.000	1.000	1.000
SC.BY BSBM19C	0.367	0.252	0.915	0.956	1.354	1.681
SC.BY BSBM19D	1.085	0.985	1.101	1.119	1.322	1.363
SC.BY BSBM19E	− 0.360	0.095	0.485	0.622	0.655	1.012
SC.BY BSBM19F	0.663	1.023	1.164	1.073	1.328	1.310
SC.BY BSBM19G	0.904	0.906	0.864	0.917	0.926	0.944
SC.BY BSBM19I	0.097	0.322	0.810	0.812	1.118	1.272
BSBM19C.WITH BSBM19E	0.359	0.379	0.303	0.216	0.131	0.101
BSBM19C.WITH BSBM19I	0.498	0.451	0.343	0.261	0.105	0.090
BSBM19E.WITH BSBM19I	0.389	0.424	0.354	0.299	0.241	0.200
Intercepts BSBM19A	2.680	2.506	3.042	2.954	3.539	3.541
Intercepts BSBM19C	2.125	1.845	2.422	2.176	3.161	3.004
Intercepts BSBM19D	2.472	2.211	2.770	2.564	3.224	3.129
Intercepts BSBM19E	2.555	2.310	2.782	2.521	3.188	2.898
Intercepts BSBM19F	2.452	2.017	2.592	2.337	3.101	2.897
Intercepts BSBM19G	2.462	2.310	2.713	2.479	2.895	2.829
Intercepts BSBM19I	1.973	1.926	2.423	2.236	2.950	2.743
Variances SC	0.659	0.589	0.496	0.539	0.262	0.238
Residual.Variances BSBM19A	0.357	0.460	0.309	0.303	0.171	0.188
Residual.Variances BSBM19C	1.035	1.014	0.836	0.721	0.452	0.363
Residual.Variances BSBM19D	0.286	0.463	0.299	0.256	0.217	0.239
Residual.Variances BSBM19E	1.026	1.114	0.951	0.923	0.652	0.716
Residual.Variances BSBM19F	0.803	0.447	0.293	0.346	0.229	0.319
Residual.Variances BSBM19G	0.614	0.623	0.667	0.676	0.694	0.735
Residual.Variances BSBM19I	0.966	0.968	0.809	0.737	0.553	0.512

The stopping criteria for tree growth were a maximum tree depth of four, a minimum number of observations in any terminal node of 100, and complexity parameter (cp) = 0.001. The first factor loading was fixed to 1 for model identification. Node 8 was the group of boys in mathematics achievement category 1. Node 9 was the group of girls in mathematics achievement category 1. Node 10 was the group of boys in mathematics achievement categories 2 and 3. Node 11 was the group of girls in mathematics achievement categories 2 and 3. Node 6 was the group of boys in mathematics achievement categories 4 and 5. Node 7 was the group of girls in mathematics achievement categories 4 and 5