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Table 4 Model fit and parameter estimates of the bivariate LST-AR-“butterfly” models

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

# Model n Par χ2 df χ2/df CFI TLI RMSEA SRMR β_t (VALUE) p β_s11
(VALUE)
p β_s12
(VALUE)
p
1 INTRI 632 68 822.79 337 2.44 0.917 0.913 0.048 0.127 0.549 0.001 0.101 0.263 0.238 0.000
2 IDENT 632 59 630.25 265 2.38 0.906 0.902 0.047 0.137 0.387 0.057 0.099 0.365 0.248 0.140
3 INTRO 632 59 602.72 265 2.27 0.874 0.868 0.045 0.119 0.499 0.004 0.264 0.023 0.275 0.009
4 EXTRI 632 59 548.76 265 2.07 0.866 0.861 0.041 0.116 − 0.039 0.764 0.091 0.491 − 0.131 0.464
5 ACMOT 796 58 616.24 266 2.32 0.869 0.864 0.041 0.127 0.300 0.123 0.347 0.001 NA NA
6 ASELF 796 88 1478.13 506 2.92 0.823 0.815 0.049 0.279 0.167 0.151 0.045 0.670 NA NA
7 GRITG t 506 52 414.82 137 3.03 0.825 0.804 0.063 0.109 0.618 0.000
8 GRITP t 506 55 325.72 134 2.43 0.888 0.872 0.053 0.110 0.634 0.000
9 GRITG s 506 50 412.28 139 2.97 0.827 0.810 0.062 0.108 0.243 0.200 0.381 0.070
10 GRITPs 506 53 324.87 136 2.39 0.890 0.876 0.052 0.111 − 0.293 0.229 − 0.223 0.543
# Model n Par χ2 df χ2/df CFI TLI RMSEA SRMR β_t (EFFOR) p β_s11 (EFFOR) p β_s12 (EFFOR) p
11 INTRI 632 87 1096.25 507 2.16 0.920 0.917 0.043 0.121 0.552 0.001 − 0.004 0.970 − 0.058 0.538
12 IDENT 632 78 855.87 417 2.05 0.918 0.914 0.041 0.128 0.603 0.008 0.007 0.955 0.101 0.564
13 INTRO 632 78 763.54 417 1.83 0.906 0.902 0.036 0.117 0.403 0.001 0.287 0.005 0.094 0.473
14 EXTRI 632 78 758.878 417 1.82 0.898 0.894 0.036 0.114 − 0.079 0.596 0.181 0.192 0.027 0.896
15 ACMOT 796 77 844.88 418 2.02 0.894 0.890 0.036 0.122 0.338 0.074 0.269 0.003 NA NA
16 ASELF 796 107 1747.64 712 2.45 0.846 0.840 0.043 0.242 − 0.046 0.784 0.098 0.364 NA NA
17 GRITG t 506 70 551.65 254 2.17 0.895 0.886 0.048 0.106 − 0.497 0.011
18 GRITP t 506 74 411.22 250 1.64 0.944 0.938 0.036 0.102 0.813 0.000
19 GRITGs 506 68 563.41 256 2.20 0.892 0.884 0.049 0.119 0.017 0.849 − 0.156 0.354
20 GRITPs 506 71 427.58 253 1.69 0.940 0.934 0.037 0.117 0.092 0.167 0.137 0.297
  1. Italic values indicate p value < 0.05
  2. 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; 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