| Literature DB >> 34807340 |
Ziwen Teuber1, Xin Tang2,3, Lena Sielemann4, Nantje Otterpohl5, Elke Wild4.
Abstract
The important role of parenting is widely acknowledged, but as most studies have understood and examined it as a stable attribute (e.g., parenting style), the stability of and changes in parenting are less well understood. Using longitudinal person-oriented approaches (i.e., latent profile analyses and latent transition analyses), this study aimed to examine the stability of and changes in autonomy-related parenting profiles and their effects on adolescents' academic and psychological development. Four autonomy-related dimensions (i.e., autonomy support, warmth, psychological control, conditional regard) were chosen to identify parenting profiles on the basis of Self-Determination Theory. Using five-year longitudinal data from 789 German secondary school students (50.06% female, Mage at T1 = 10.82 years, age span = 10-17), four autonomy-related parenting profiles were found: Supportive (~17%), Controlling (~31%), Unsupportive-Uncontrolling (~17%), and Limited Supportive (~35%). The results suggest that the Supportive profile contributes to adolescents' positive academic and psychological development, whereas the Controlling profile, which thwarts autonomy development, exacerbates the development of psychopathology, and impairs academic achievement. More importantly, the Limited Supportive profile is as maladaptive as the Unsupportive-Uncontrolling profile. Regarding parenting profiles' stability and changes, the results showed that about half of each profile stayed in the same group. Overall, it could be observed that parents became more supportive and less controlling over time. However, the findings also indicate that parenting profiles are less stable than expected and can still change during early-to-mid adolescence.Entities:
Keywords: Latent profile and latent transition analyses; Multiple informants; Parental conditional regard; Psychopathology; Self-determination
Mesh:
Year: 2021 PMID: 34807340 PMCID: PMC9135772 DOI: 10.1007/s10964-021-01538-5
Source DB: PubMed Journal: J Youth Adolesc ISSN: 0047-2891
Scale means (in parentheses) and zero-order correlations between variables used in present study
| Variable | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | ||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| T1 | 1 | AKNO | (3.17) | |||||||||||||||
| 2 | INIT | 0.40** | (2.95) | |||||||||||||||
| 3 | WARM | 0.57** | 0.33** | (3.48) | ||||||||||||||
| 4 | PSY.CONT | −0.23** | −0.14** | −0.34** | (2.33) | |||||||||||||
| 5 | PCNR | −0.16** | −0.09* | −0.19** | 0.27** | (1.84) | ||||||||||||
| 6 | PCPR | −0.16** | −0.11** | −0.28** | 0.36** | 0.56** | (2.11) | |||||||||||
| T3 | 7 | AKNO | 0.32** | 0.15** | 0.39** | −0.22** | −0.19** | −0.19** | (3.14) | |||||||||
| 8 | INIT | 0.17** | 0.19** | 0.20** | −0.11** | −0.08* | −0.07* | 0.41** | (2.77) | |||||||||
| 9 | WARM | 0.30** | 0.14** | 0.47** | −0.27** | −0.23** | −0.24** | 0.60** | 0.36** | (3.40) | ||||||||
| 10 | PSY.CONT | −0.16** | −0.09* | −0.23** | 0.39** | 0.18** | 0.23** | −0.29** | −0.12** | −0.34** | (2.13) | |||||||
| 11 | PCNR | −0.10** | −0.13** | −0.20** | 0.24** | 0.34** | 0.38** | −0.23** | −0.11** | −0.32** | 0.29** | (1.58) | ||||||
| 12 | PCPR | −0.17** | −0.14** | −0.25** | 0.28** | 0.32** | 0.46** | −0.22** | −0.08* | −0.32** | 0.36** | 0.61** | (1.81) | |||||
| 13 | EXTa | −0.19** | −0.06 | −0.27** | 0.25** | 0.13** | 0.21** | −0.34** | −0.18** | −0.35** | 0.28** | 0.13** | 0.25** | (0.65) | ||||
| 14 | INTa | −0.11** | −0.08* | −0.18** | 0.20** | 0.10** | 0.14** | −0.12** | 0.0 | −0.19** | 0.26** | 0.12** | 0.21** | 0.22** | (0.51) | |||
| 15 | PROa | 0.12** | 0.04 | 0.16** | −0.15** | −0.09** | −0.10** | 0.35** | 0.29** | 0.33** | −0.11** | −0.02 | −0.07 | −0.39** | −0.02 | (1.49) | ||
| 16 | EXTp | −0.02 | −0.04 | −0.18** | 0.23** | 0.17** | 0.21** | −0.23** | −0.10* | −0.24** | 0.20** | 0.16** | 0.22** | 0.42** | 0.06 | −0.16** | (0.38) | |
| 17 | INTp | 0.05 | 0.0 | −0.12** | 0.15** | 0.11** | 0.14** | −0.02 | −0.04 | −0.06 | 0.06 | 0.1** | 0.16** | 0.08 | 0.37** | −0.07 | 0.09 | |
| 18 | PROp | 0.10* | 0.02 | 0.13** | −0.20** | −0.05 | −0.07 | 0.19** | 0.17** | 0.22** | −0.11** | −0.13** | −0.13** | −0.23** | 0.00 | 0.30** | −0.23** | |
| 19 | ACH | −0.07 | −0.07* | −0.13** | 0.12** | 0.13** | 0.21** | −0.15** | −0.15** | −0.15** | 0.09* | 0.14** | 0.22** | 0.26** | 0.10** | −0.19** | 0.38** | |
| T4 | 21 | AKNO | 0.23 | 0.14** | 0.23** | −0.18** | −0.10** | −0.08* | 0.41** | 0.25** | 0.35** | −0.20** | −0.13** | −0.11** | −0.16** | −0.12** | 0.20** | −0.16** |
| 22 | INIT | 0.14** | 0.17** | 0.15** | −0.07 | −0.04 | −0.04 | 0.27** | 0.37** | 0.22** | −0.06 | −0.09** | −0.07 | −0.10** | −0.02 | 0.18** | −0.10** | |
| 23 | WARM | 0.21** | 0.08* | 0.32** | −0.20** | −0.13** | −0.17** | 0.34** | 0.23** | 0.48** | −0.21** | −0.22** | −0.20** | −0.22** | −0.16** | 0.15** | −0.22** | |
| 24 | PSY.CONT | −0.01 | −0.06 | −0.08* | 0.31** | 0.19** | 0.20** | −0.13** | −0.07* | −0.14** | 0.42** | 0.20** | 0.24** | 0.16** | 0.18** | −0.04 | 0.16** | |
| 25 | PCNR | −0.12** | −0.14** | −0.20** | 0.27** | 0.28** | 0.33** | −0.16** | −0.10** | −0.24** | 0.22** | 0.37** | 0.43** | 0.15** | 0.16** | −0.07* | 0.15** | |
| 26 | PCPR | −0.14** | −0.11** | −0.20** | 0.20** | 0.28** | 0.38** | −0.15** | −0.08* | −0.20** | 0.19** | 0.34** | 0.48** | 0.14** | 0.19** | −0.08* | 0.14** | |
| 27 | EXTa | −0.13** | −0.06 | −0.15** | 0.15** | 0.05 | 0.09* | −0.22** | −0.09* | −0.20** | 0.16** | 0.06 | 0.09* | 0.57** | 0.18** | −0.23** | 0.57** | |
| 28 | INTa | −0.07* | −0.08* | −0.11** | 0.11** | 0.05 | 0.07 | −0.06 | 0.02 | −0.11** | 0.09* | 0.08* | 0.13** | 0.12** | 0.57** | 0.05 | 0.12** | |
| 29 | PROa | 0.10** | 0.03 | 0.07 | −0.10** | −0.07 | −0.07 | 0.26** | 0.19** | 0.19** | −0.03 | −0.03 | −0.04 | −0.26** | −0.01 | 0.47** | −0.26** | |
| 30 | EXTp | −0.08 | −0.06 | −0.12** | 0.21** | 0.06 | 0.14** | −0.17** | −0.11** | −0.13** | 0.19** | 0.14** | 0.21** | 0.43** | 0.08 | −0.16** | 0.43** | |
| 31 | INTp | 0.00 | −0.02 | −0.09* | 0.10* | 0.08 | 0.14** | −0.08 | −0.05 | −0.09* | 0.05 | 0.09 | 0.15** | 0.12** | 0.29** | −0.02 | 0.12** | |
| 32 | PROp | 0.04 | 0.09* | 0.03* | −0.08 | 0.00 | 0.00 | 0.11* | 0.19** | 0.12** | −0.06 | −0.05 | −0.09* | −0.16** | 0.00 | 0.28** | −0.16** | |
| 33 | ACH | −0.08* | −0.04 | −0.12** | 0.12** | 0.09* | 0.16** | −0.17** | −0.12** | −0.13** | 0.06 | 0.07* | 0.20* | 0.30** | 0.04 | −0.20** | 0.38** | |
Note. AKNO acknowledgment of child’s view, INIT encouragement of child-initiated activities, WARM warmth, PSY.CONT psychological control, PCNR parental conditional negative regard, PCPR parental conditional positive regard, EXTa externalizing problems (adolescent report), INTa internalizing problems (adolescent report), PROa prosocial behavior (adolescent report), EXTp externalizing problems (parent report), INTp internalizing problems (parent report), PROp prosocial behavior (parent report), ACH average school grade
*p < 0.05
**p < 0.01
Results from final latent profile analysis models and latent transition analysis models
| Model | LL | #fp | Scaling | AIC | CAIC | BIC | ABIC | Entropy |
|---|---|---|---|---|---|---|---|---|
| T1: 5th grade (4 profiles)ns | −4469.287 | 51 | 1.2971 | 9040.575 | 9329.783 | 9278.784 | 9116.832 | 0.919 |
| T3: 7th grade (4 profiles) | −4127.932 | 51 | 1.3443 | 8357.863 | 8647.073 | 8596.073 | 8434.121 | 0.905 |
| T4: 9th grade (4 profiles)ns | −3885.527 | 51 | 1.3471 | 7873.055 | 8162.263 | 8111.264 | 7949.312 | 0.894 |
| Configural Similarity | −12482.746 | 153 | 1.3295 | 25271.493 | 26139.119 | 25986.120 | 25500.265 | 0.906 |
| Structural Similarity | −12733.970 | 105 | 1.5164 | 25677.940 | 26273.370 | 26168.370 | 25834.940 | 0.898 |
| Partial Structural Similarity | −12696.352 | 111 | 1.5822 | 25614.704 | 26244.159 | 26133.159 | 25780.676 | 0.886 |
| Partial Dispersion Similarity | −12792.742 | 63 | 1.7724 | 25711.484 | 26068.742 | 26005.742 | 25805.684 | 0.898 |
| Partial Distributional Similarity | −12798.198 | 59 | 1.8730 | 25714.395 | 26048.971 | 25989.970 | 25802.614 | 0.897 |
|
| −2813.584 | 36 | 1.0174 | 5699.169 | 5903.316 | 5867.270 | 5752.952 | 0.856 |
| Externalizing problems (S) | −3125.301 | 42 | 1.0249 | 6334.601 | 6572.454 | 6530.453 | 6397.082 | 0.857 |
| Internalizing problems (S) | −3028.965 | 42 | 1.0234 | 6141.931 | 6380.049 | 6337.782 | 6204.411 | 0.854 |
| Prosocial behavior (S) | −3415.236 | 42 | 1.0178 | 6914.472 | 7152.324 | 7110.324 | 6976.953 | 0.856 |
| Externalizing problems (P) | −2842.455 | 42 | 1.0295 | 5768.909 | 6006.762 | 5964.761 | 5831.390 | 0.854 |
| Internalizing problems (P) | −2823.317 | 42 | 1.0639 | 5730.634 | 5968.486 | 5926.486 | 5793.115 | 0.854 |
| Prosocial behavior (P) | −3073.152 | 42 | 1.0283 | 6230.303 | 6468.156 | 6426.155 | 6292.784 | 0.855 |
| Achievement (S) | −4954.033 | 49 | 0.9920 | 10006.067 | 10229.918 | 10234.560 | 10078.961 | 0.854 |
Note. nsLo–Mendell–Rubin adjusted LRT Test was not significant. In explanatory similarity analysis models, invariant relations with outcome (with covariates) showed the best model fit for all outcomes. S self-report, P parent report, LL model loglikelihood, #fp number of free parameters. Scaling scaling correction factor associated with robust maximum likelihood estimates, AIC Akaike information criteria, CAIC consistent AIC, BIC Bayesian information criteria, ABIC sample size adjusted BIC
Fig. 1Parenting profiles at T1, T3, and T4 based on partial distributional similarity model. Note. AKNO acknowledgment of child’s view, INIT encouragement of child-initiated activities, WARM warmth, PSY.CONT psychological control, PCNR parental conditional negative regard, PCPR parental conditional positive regard
Transition probabilities (in %) of parenting profiles over time
| 1 | 2 | 3 | 4 | 1 | 2 | 3 | 4 | |
|---|---|---|---|---|---|---|---|---|
| From T1 to T3 | From T3 to T4 | |||||||
| 1 Supportive | 0.2 | 25.5 | 23.8 | 1.6 | 18.2 | 21.1 | ||
| 2 Controlling | 2.6 | 16.8 | 25.1 | 0.5 | 14.9 | 34.1 | ||
| 3 Unsupportive-Uncontrolling | 20.6 | 18.3 | 20.4 | 16.5 | 8 | 32.6 | ||
| 4 Limited Supportive | 22.5 | 16.6 | 14.7 | 17.2 | 14.3 | 17.7 | ||
Note. Stability estimates are in boldface. Transition probabilities add up to 100% across rows for each measurement point
Associations between profile membership and outcomes after controlling for covariates
| Supportive (P1) | Controlling (P2) | Unsupportive-uncontrolling (P3) | Limited supportive (P4) | Summary of significant differences | |
|---|---|---|---|---|---|
| Outcome | |||||
| Externalizing problems (S) | 0.447 [0.359; 0.534] | 0.762 [0.673; 0.852] | 0.624 [0.534; 0.713] | 0.560 [0.474; 0.645] | P1 < P4 < P3 < P2 |
| Internalizing problems (S) | 0.498 [0.419; 0.577] | 0.701 [0.620; 0.781] | 0.585 [0.503; 0.666] | 0.597 [0.522; 0.672] | P1 < P3 = P4 < P2 |
| Prosocial behavior (S) | 1.791 [1.692; 1.890] | 1.496 [1.397; 1.596] | 1.556 [1.451; 1.660] | 1.699 [1.605; 1.793] | P2 = P3 < P4 < P1 |
| Externalizing problems (P) | 0.260 [0.175; 0.345] | 0.413 [0.322; 0.503] | 0.306 [0.215; 0.397] | 0.314 [0.231; 0.387] | P1 < P4 < P2; P1 = P3; P3 = P4 |
| Internalizing problems (P) | 0.275 [0.185; 0.366] | 0.351 [0.270; 0.432] | 0.302 [0.215; 0.388] | 0.306 [0.224; 0.387] | P1 < P2 = P3 = P4 |
| Prosocial behavior (P) | 1.882 [1.743; 2.021] | 1.656 [1.507; 1.804] | 1.758 [1.608; 1.908] | 1.749 [1.611; 1.886] | P3 = P4 < P2 < P1 |
| Academic achievement (S)a | 2.993 [2.820; 3.166] | 3.187 [3.016; 3.357] | 3.159 [2.979; 3.339] | 3.103 [2.936; 3.270] | P1 < P4 < P3 = P2 |
Note. M mean value, CI 95% confidence interval of mean value, S self-report, P parent report
aIt should be noted that lower school grades indicate higher academic achievement in Germany
| Subsample | Sample size | T1 | T3 | T4 |
|---|---|---|---|---|
|
| ||||
| Original | Total | 1465 | 1378 | 1441 |
| Girls | 662 | 624 | 663 | |
| 885 | 858 | 803 | ||
| Immigrant students | 579 | 531 | 594 | |
| In this study | Total | 789 | 789 | 789 |
| Girls | 395 | 395 | 395 | |
| 584 | 584 | 584 | ||
| Immigrant students | 245 | 245 | 245 | |
|
| ||||
| Original | Total | 1014 | 871 | 769 |
| Girls | 455 | 415 | 397 | |
| 703 | 615 | 538 | ||
| Immigrant families | 296 | 249 | 221 | |
| In this study | Total | – | 579 | 533 |
| Girls | – | 291 | 271 | |
| – | 452 | 425 | ||
|
| 427 | 411 | ||
| Immigrant families | – | 138 | 137 | |
Note. T1 5th grade, in Spring 2010. T3 7th grade, in Spring 2012. T4 9th grade, in Spring 2014
| Model |
|
|
| CFI | RMSEA | 90% CI for RMSEA | SRMR |
|---|---|---|---|---|---|---|---|
|
| |||||||
| T1: 5th grade | 564.925 | 215 | <0.001 | 0.929 | 0.045 | 0.041/0.050 | 0.044 |
| T3: 7th grade | 507.657 | 215 | <0.001 | 0.949 | 0.042 | 0.037/0.046 | 0.037 |
| T4: 9th grade | 633.055 | 215 | <0.001 | 0.936 | 0.0.050 | 0.045/0.054 | 0.043 |
|
| |||||||
| Configural MI | 3478.376 | 2055 | <0.001 | 0.933 | 0.030 | 0.028/0.031 | 0.039 |
| Weak MI | 3649.920 | 2101 | <0.001 | 0.927 | 0.031 | 0.029/0.032 | 0.050 |
|
| 3904.132 | 2128 | <0.001 | 0.917 | 0.033 | 0.031/0.034 | 0.053 |
| Strong MI | 4279.501 | 2147 | <0.001 | 0.900 | 0.035 | 0.034/0.037 | 0.058 |
Note. N 789
The final model is in boldface
| #profiles | LL | #fp | Scaling | AIC | CAIC | BIC | ABIC | Entropy | LMR-LTR | |
|---|---|---|---|---|---|---|---|---|---|---|
| T1: 5th grade | 1 | −6190.052 | 12 | 1.1136 | 12404.103 | 12472.153 | 12460.152 | 12422.046 | N/A | |
| 2 | −5292.387 | 25 | 1.7083 | 10634.774 | 10776.543 | 10751.543 | 10672.155 | 0.889 | 0.045 | |
| 3 | −4795.169 | 38 | 1.6892 | 9666.339 | 9881.827 | 9843.828 | 9723.158 | 0.901 | 0.012 | |
|
| −4469.287 | 51 | 1.2971 | 9040.575 | 9329.783 | 9278.784 | 9116.832 | 0.919 | 0.012 | |
| 5 | −4256.795 | 64 | 1.5628 | 8641.589 | 9004.519 | 8940.518 | 8737.285 | 0.922 | 0.410 | |
| 6 | −4095.962 | 77 | 1.3101 | 8345.924 | 8782.573 | 8705.573 | 8461.058 | 0.905 | 0.012 | |
| 7 | −3981.074 | 90 | 1.2536 | 8142.148 | 8652.517 | 8562.517 | 8276.720 | 0.895 | 0.163 | |
| T3: 7th grade | 1 | −6264.295 | 12 | 1.0988 | 12552.589 | 12620.639 | 12608.638 | 12570.532 | N/A | |
| 2 | −4879.568 | 25 | 1.4602 | 9809.137 | 9950.905 | 9925.906 | 9846.518 | 0.961 | 0.000 | |
| 3 | −4422.782 | 38 | 1.3240 | 8921.564 | 9137.053 | 9099.053 | 8978.383 | 0.907 | 0.040 | |
|
| −4127.932 | 51 | 1.3443 | 8357.863 | 8647.073 | 8596.073 | 8434.121 | 0.905 | 0.004 | |
| 5 | −3934.059 | 64 | 1.3448 | 7996.119 | 8359.047 | 8295.048 | 8091.815 | 0.898 | 0.036 | |
| 6 | −3785.641 | 77 | 1.2221 | 7725.282 | 8161.931 | 8084.931 | 7840.415 | 0.912 | 0.002 | |
| 7 | −3641.266 | 90 | 1.3114 | 7462.531 | 7972.901 | 7882.900 | 7597.103 | 0.905 | 0.098 | |
| T4: 9th grade | 1 | −6138.414 | 12 | 1.1472 | 12300.828 | 12368.877 | 12356.877 | 12318.771 | N/A | |
| 2 | −4529.918 | 25 | 1.1545 | 9109.837 | 9251.605 | 9226.606 | 9147.218 | 0.969 | 0.000 | |
| 3 | −4140.347 | 38 | 1.4877 | 8356.693 | 8572.183 | 8534.182 | 8413.512 | 0.887 | 0.040 | |
|
| −3885.527 | 51 | 1.3471 | 7873.055 | 8162.263 | 8111.264 | 7949.312 | 0.894 | 0.003 | |
| 5 | −3689.991 | 64 | 1.4471 | 7507.983 | 7870.911 | 7806.912 | 7806.912 | 0.899 | 0.120 | |
| 6 | −3558.511 | 77 | 1.5839 | 7271.022 | 7707.671 | 7630.671 | 7386.155 | 0.882 | 0.593 | |
| 7 | −3452.284 | 90 | 1.2327 | 7084.568 | 7594.937 | 7504.937 | 7219.140 | 0.892 | 0.208 |
Note. #profiles number of profiles, LL model loglikelihood, #fp number of free parameters, Scaling scaling correction factor associated with robust maximum likelihood estimates, AIC Akaike information criteria, CAIC consistent AIC, BIC Bayesian information criteria, ABIC sample size adjusted BIC, LMR-LTR Lo–Mendell–Rubin adjusted LRT Test
The selected profile solutions are in boldface
| Outcome | Model | LL | #fp | Scaling | AIC | CAIC | BIC | ABIC | Entropy |
|---|---|---|---|---|---|---|---|---|---|
| Externalizing problems (S) | M1 | −3266.799 | 37 | 1.0044 | 6607.597 | 6817.134 | 6780.369 | 6662.875 | 0.858 |
| M2 | −3271.166 | 33 | 1.0365 | 6608.331 | 6795.215 | 6762.425 | 6657.632 | 0.858 | |
| M3 | −3120.685 | 46 | 1.0209 | 6333.370 | 6593.874 | 6547.874 | 6401.801 | 0.857 | |
|
| −3125.301 | 42 | 1.0249 | 6334.601 | 6572.454 | 6530.453 | 6397.082 | 0.857 | |
| Internalizing problems (S) | M1 | −3202.642 | 37 | 1.0129 | 6479.284 | 6689.055 | 6652.055 | 6534.561 | 0.855 |
| M2 | −3204.774 | 33 | 1.0436 | 6475.548 | 6662.641 | 6629.641 | 6524.849 | 0.855 | |
| M3 | −3028.650 | 46 | 1.0229 | 6149.299 | 6410.097 | 6363.803 | 6217.730 | 0.855 | |
|
| −3028.965 | 42 | 1.0234 | 6141.931 | 6380.049 | 6337.782 | 6204.411 | 0.854 | |
| Prosocial behavior (S) | M1 | −3539.489 | 37 | 0.9911 | 7152.978 | 7362.514 | 7325.749 | 7208.255 | 0.857 |
| M2 | −3545.371 | 33 | 1.0107 | 7156.742 | 7343.625 | 7310.835 | 7206.043 | 0.857 | |
| M3 | −3410.552 | 46 | 1.0183 | 6913.105 | 7173.608 | 7127.609 | 6981.536 | 0.856 | |
|
| −3415.236 | 42 | 1.0178 | 6914.472 | 7152.324 | 7110.324 | 6976.953 | 0.856 | |
| Externalizing problems (P) | M1 | −2997.710 | 37 | 1.0285 | 6069.420 | 6278.956 | 6242.191 | 6124.697 | 0.855 |
| M2 | −2999.422 | 33 | 1.0593 | 6064.845 | 6251.727 | 6218.938 | 6114.146 | 0.855 | |
| M3 | −2841.306 | 46 | 1.0357 | 5774.612 | 6035.116 | 5989.116 | 5843.043 | 0.854 | |
|
| −2842.455 | 42 | 1.0295 | 5768.909 | 6006.762 | 5964.761 | 5831.390 | 0.854 | |
| Internalizing problems (P) | M1 | −2963.942 | 37 | 1.0515 | 6001.883 | 6211.42 | 6174.654 | 6057.160 | 0.855 |
| M2 | −2966.737 | 33 | 1.0865 | 5999.473 | 6186.357 | 6153.567 | 6048.775 | 0.854 | |
| M3 | −2820.613 | 46 | 1.0620 | 5733.226 | 5993.73 | 5947.730 | 5801.657 | 0.854 | |
|
| −2823.317 | 42 | 1.0639 | 5730.634 | 5968.486 | 5926.486 | 5793.115 | 0.854 | |
| Prosocial behavior (P) | M1 | −3187.298 | 37 | 1.0231 | 6448.596 | 6658.132 | 6621.368 | 6503.873 | 0.866 |
| M2 | −3188.256 | 33 | 1.0501 | 6442.511 | 6629.395 | 6596.605 | 6491.813 | 0.855 | |
| M3 | −3071.482 | 46 | 1.0308 | 6234.964 | 6495.468 | 6449.468 | 6303.395 | 0.855 | |
|
| −3073.152 | 42 | 1.0283 | 6230.303 | 6468.156 | 6426.155 | 6292.784 | 0.855 | |
| Achievement (S) | M1 | −5377.741 | 42 | 0.9830 | 10839.481 | 11039.018 | 11035.600 | 10902.228 | 0.855 |
| M2 | −5451.447 | 34 | 1.0289 | 10970.895 | 11155.777 | 11129.657 | 11021.690 | 0.854 | |
| M3 | −4945.892 | 57 | 1.0043 | 10005.784 | 10244.288 | 10271.582 | 10090.579 | 0.854 | |
|
| −4954.033 | 49 | 0.9920 | 10006.067 | 10229.918 | 10234.560 | 10078.961 | 0.854 |
Note. LL model loglikelihood, #fp number of free parameters, Scaling scaling correction factor associated with robust maximum likelihood estimates. AIC Akaike information criteria, CAIC consistent AIC, BIC Bayesian information criteria, ABIC sample size adjusted BIC. M1 free relations with outcome (without covariates), M2 invariant relations with outcome (without covariates), M3 free relations with outcome (with covariates), M4 invariant relations with outcome (with covariates)
The final models are in boldface