Psychological determinants of test motivation in low-stakes test situations: A longitudinal study of singletrait–multistate models in accounting

Empirical Research in Vocational Education and Training

Table 3 Model fit and parameter estimates of the bivariate “butterfly” models

#	Model	n	Par	χ²	df	χ²/df	CFI	TLI	RMSEA	SRMR	β_{_t} (VALUE)	p	β_{_s11} (VALUE)	p	β_{_s12} (VALUE)	p
Multiconstruct bifactor approach (butterfly models)
1	INTRI	632	85	522.08	320	1.63	0.965	0.962	0.032	0.076	0.370	0.000	0.195	0.013	0.297	0.003
2	IDENT	632	79	356.13	245	1.45	0.971	0.968	0.027	0.064	0.344	0.005	0.053	0.723	0.238	0.201
3	INTRO	632	79	438.62	245	1.79	0.928	0.918	0.035	0.073	0.334	0.000	0.512	0.000	0.295	0.017
4	EXTRI	632	79	362.82	245	1.48	0.944	0.937	0.028	0.063	− 0.096	0.279	0.186	0.107	0.074	0.701
5	ACMOT	796	78	333.37	246	1.36	0.967	0.963	0.021	0.059	0.385	0.000	0.439	0.000	NA	NA
6	ASELF	796	99	981.11	495	1.98	0.912	0.906	0.035	0.083	0.122	0.297	0.241	0.046	NA	NA
Bifactor models using the residual approach
7	GRITG_t	506	63	284.04	126	2.25	0.900	0.879	0.050	0.057	0.600	0.205	–	–	–	–
8	GRITP_t	506	63	197.45	126	1.57	0.958	0.949	0.033	0.062	0.181	0.771	–	–	–	–
9	GRITG _s	506	60	290.39	129	2.25	0.898	0.879	0.050	0.062	–	–	− 0.543	0.025	− 0.545	0.251
10	GRITP_s	506	63	195.21	126	1.55	0.960	0.951	0.033	0.063	–	–	0.430	0.284	0.590	0.238

#	Model	n	Par	χ²	df	χ²/df	CFI	TLI	RMSEA	SRMR	β_{_t} (EFFOR)	p	β_{_s11} (EFFOR)	p	β_{_s12} (EFFOR)	p
Multiconstruct bifactor approach (butterfly models)
11	INTRI	632	102	867.95	492	1.76	0.949	0.945	0.035	0.072	0.296	0.000	− 0.148	0.187	− 0.026	0.776
12	IDENT	632	97	645.05	398	1.62	0.954	0.949	0.031	0.064	0.386	0.001	− 0.074	0.491	0.066	0.716
13	INTRO	632	97	682.05	398	1.71	0.923	0.916	0.034	0.068	0.342	0.000	0.019	0.895	− 0.173	0.277
14	EXTRI	632	97	641.69	398	1.61	0.928	0.921	0.031	0.065	0.030	0.786	− 0.041	0.758	− 0.115	0.515
15	ACMOT	796	96	647.61	399	1.62	0.939	0.933	0.028	0.068	0.256	0.025	0.137	0.326	NA	NA
16	ASELF	796	113	1408.30	706	1.99	0.896	0.891	0.035	0.077	0.103	0.314	0.048	0.720	NA	NA
Bifactor models using the residual approach
17	GRITG_t	506	81	465.48	243	1.92	0.922	0.911	0.043	0.060	− 0.046	0.851	–	–	–	–
18	GRITP _t	506	81	375.03	243	1.54	0.954	0.948	0.033	0.057	0.481	0.002	–	–	–	–
19	GRITG_s	506	79	515.09	245	2.10	0.905	0.893	0.047	0.063	–	–	− 0.005	0.989	-0.292	0.470
20	GRITP_s	506	81	379.13	243	1.56	0.953	0.947	0.033	0.057	–	–	− 0.016	0.973	0.009	0.988

Italic values indicate p value < 0.05
β_{_t}, association between traits; β_{_s11}, association between states at grade 11; β_{_s12}, association between states at grade 12; VALUE, Subjective test value; EFFOR, Effort; INTRI, Intrinsic regulation; IDENT, Identified regulation; INTRO, Introjected regulation; EXTRI, External regulation; ACMOT, Achievement motivation; ASELF, Academic self-concept; GRITG, Passion for long-term goals; GRITP, Perseverance. Subscript t, prediction of the trait factor; s, prediction of the state factors. N, observations; #Par, number of parameters; χ², Chi square value; df, degrees of freedom; CFI, Comparative Fit Index; TLI, Tucker Lewis Index; RMSEA, Root Mean Square Error of Approximation; SRMR, Standardized Root Mean Square Residual. NA, not applicable as the covariate was not measured at that time