# Stability of Peer Acceptance and Rejection and Their Effect on Academic Performance in Primary Education: A Longitudinal Research

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## Abstract

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## 1. Introduction

#### 1.1. Acceptance and Rejection

#### 1.1.1. Acceptance and Rejection: Different, Yet Related

#### 1.1.2. The Expansiveness of Acceptance with Respect to Rejection or Positive Bias

#### 1.1.3. The Predictive Power of Acceptance and Rejection Experiences. Negative Asymmetry

#### 1.1.4. The Evolution of Acceptance and Rejection: Stability or Change

#### 1.2. School Adjustment: Academic Performance

#### 1.3. Acceptance and Rejection as Predictors of Performance

#### 1.4. Our Study

## 2. Materials and Methods

#### 2.1. Participants

_{LongitudinalT1}= 80.53 months, SD

_{LongitudinalT1}= 3.34; M

_{LongitudinalGirlsT1}= 80.36 months, SD

_{LongitudinalGirlsT1}= 3.36; M

_{LongitudinalBoysT1}= 80.72 months, SD

_{LongitudinalBoysT1}= 3.33; M

_{LongitudinalT2}= 94.53 months; M

_{LongitudinalT3}= 118.53 months; M

_{LongitudinalT4}= 142.53 months). The total sample of children present at T1 (n = 229, 49.8% girls) showed no differences of age with the subsample of the participants in the longitudinal study: M

_{T1}= 80.52 months, SD

_{T1}= 3.33; M

_{GirlsT1}= 80.34 months, SD

_{GirlsT1}= 3.34; M

_{BoysT1}= 80.72 months, SD

_{BoysT1}= 3.33. However, the total sample of students present at T4 (n = 206, 52.9% girls) were slightly older (M

_{T4}= 143.63 months, SD

_{T4}= 4.77, M

_{GirlsT4}= 143.51 months, SD

_{GirlsT4}= 4.82; M

_{BoysT4}= 143.75 months, SD

_{BoysT4}= 4.74) than the subsample of the students who participated in the longitudinal group, due to the presence of repeater students in the same school between T1 and T4 or the arrival of older students from other schools. That is, the students belonging to the non-longitudinal sample who were present at T4 (n = 37) were significantly older (M

_{NonLongitudinalT4}= 148.62 months, SD

_{NonLongitudinalT4}= 6.88, t

_{(204)}=8.046) than the 169 students of the longitudinal group.

#### 2.2. Measures

#### 2.3. Model

## 3. Results

^{2}SB) should have a p > 0.05, although, since it depends on the sample size, the Relative Chi-square (χ

^{2}SB/df) was also used (df: Degrees of freedom), which should be smaller than 2; (2) the Bentler–Bonnet Nonnormed Fit Index (NNFI), the Comparative Fit Index (CFI), the Bollen Fit Index (BFI), and the McDonald Fit Index (MFI) were used, and they would be between 0.85 and 0.90 to be considered poor, between 0.90 and 0.95 to be acceptable, between 0.95 and 0.99 to be very good, and >0.99 to be outstanding; and (3) the value of the Root Mean Square Error of Approximation (RMSEA) should be between 0.10 and 0.08 to be considered a poor fit, between 0.08 and 0.05 to be an acceptable fit, between 0.05 and 0.02 to be a good fit, and < 0.02 to be considered a great fit. Due to the absence of multivariate normality in the variables (Normalized Estimate Multivariate Kurtosis = 16.482), it was decided to use the Satorra–Bentler robust estimation [59,65]. To compare the degree of fit between two models, the Akaike Information Criterion (AIC) was used. AIC is a criterion of relative comparison between two models, thus the lower its value, the better its relative fit. For the comparison of two models that contain the same data (regardless of whether these are nested or not) we used the Burnham, Anderson and Huyvaert [66] criterion, which establishes that, if Δ

_{i(AIC)}=AIC

_{i}− AIC

_{min}, when Δ

_{i(AIC)}> 7, then the model with the highest value is not supported.

#### 3.1. Objective 1a: The Evolution of Social Relationships among Peers

_{i(AIC)}(M3-M2) = 195.38 − 174.13 = 21.25, which is a value of Δi(

_{AIC}) higher than 7, thus the means of F_PrefT are different from each other and there is no strong factorial invariance of F_PrefT. This mean comparison procedure in SEM is equivalent to a RANOVA (analysis of variance with repeated measures). The range of M(F_PrefT) in M2 goes from 25.401 at T2 to 28.194 at T1 (Table 3). Considering that the SE of M(F_PrefT) = 0.869, the differences between two factorial means are statistically different (α = 0.05) from a difference between them greater than 1.703 (=1.96*0.869), thus M(F_Pref2) < M(F_Pref1) and M(F_Pref4) < M(F_Pref1), and the other contrasts are not different from each other (Table 3).

#### 3.2. Objective 1b: The Evolution of Academic Performance

_{(AIC)}(M5-M4) = 174.05 − 116.70 = 57.35, thus the means of F_APT are different from each other, and there is no strong factorial invariance of F_APT. The range of M(F_APT) (Table 3) goes from 3.733 at T2 to 4.106 at T3. Since SE[M(F_APT)] = 0.062, the differences between two means would be significant when their value is higher than 0.122 (=1.96*0.062); therefore, all the mean differences are significant, except M(F_AP1) = M(F_AP2), see Table 3.

_{i(AIC)}(M7-M6) = −12.72 − (–12.80) = 0.08 when compared, thus both models are practically equivalent. We selected the simplest of these two models, that is, the one with the largest number of degrees of freedom: M7 (“a” = “g” = 0.481, t = 3.47, p < 0.001). To sum up, under similar conditions, i.e., if the “l” effect of F_PrefT toward each F_AQT did not exist, the AR effects would be similar in both temporal factors.

_{0(Mats1)}= … = b

_{0(Mats4)}) (see M8 in Table 2). In M8, all the indicators are worse than in M1; AIC(M8) = −27.70, when comparing this model with M1 (Δ

_{i(AIC)}(M8-M1) = −27.70 − (−48.04) = 20.34), it was observed to be higher than 7, thus we accepted that the means of MatsT are not equal (there is at least one of them that differs from another). The intercepts of Mats have a range between 3.769 at T2 and 4.077 at T3. Considering SE = 0.061 for the equality of means, from a mean difference of 0.120 (=1.96*0.061), the differences would be significant if they involve T4 and T3: M(Mat2) = M(Mat1) < M(Mat4) < M(Mat3), see Table 3.

_{0(Lang1)}= … = b

_{0(Lang4)}, producing AIC(M9) = 45.27. Compared to M1 (Δ

_{i(AIC)}(M9-M1) = 45.27 − (−48.04) = 93.31), the difference between these two models is considerable, in favor of M1, thus we reject the equality of M(LangT). Table 3 shows that the means range between 3.793 (T2) and 4.213 (T3). In M9, the SE of the marks in LangT is 0.059, thus the differences greater than 0.116 (= 1.96*0.059) would be significant, with no differences between T1 and T2; however, there would be differences between these two and the others and between T3 and T4: M(Lang1) = M(Lang2) < M(Lang4) < M(Lang3).

_{0(Mats1)}= … = b

_{0(Mats4)}and b

_{0(Lang1)}= … = b

_{0(Lang4)}. This model, with AIC(M10) = 16.41, is considerably worse than M1 (Table 2), and showed that the means of MatsT and those of LangT differ internally, with M1 being better (independent means). We calculated M11 with all the means equalized, b

_{0(Mats1)}= … = b

_{0(Mats4)}= b

_{0(Lang1)}= … = b

_{0(Lang4)}, obtaining AIC(M11) = 3.19, with Δ

_{i(AIC)}(M11-M1) = 16.41 − (−48.04) = 64.45, thus M1, with independent means, is better than the model of equal means for MatsT and LangT.

#### 3.3. Objective 2: The Effects of Social Relationships on Academic Performance

_{i(AIC)}(M12-M1) = −37.85 − (−48.04) = 10.19, thus M1 is better than M12; moreover, in M12, neither the “i” effects nor the “a” effects are significant. Likewise, there were simultaneous reciprocal effects between both temporal factors, that is, from F_PrefT to F_APT and vice versa, for equal values of T (M13 in Table 2); however, the model does not fit, all the set indicators are worse (AIC(M13) = 39.31), and there are non-significant effects. Of the three models, M1 is the one that responds to the hypothesis and best fits the data.

#### 3.4. Objective 3: The Positive Bias and Negative Asymmetry of Social Relationships

_{0(Like1)}= … = b

_{0(Like4)}). In M14 (Table 2), all the indicators are worse than in M1 M1; AIC(M14) = − 33.91, and, when comparing this model with M1, Δ

_{i(AIC)}(M14-M1) = −33.91 − (−48.04) = 14.13, thus we accept that M1 is better than M14, and that the means of LikeT differ from each other. The intercepts of Like range between 24.669 at T3 and 29.621 at T4 (Table 3). With the aim of determining which means differ from each other, M14 showed that SE[M(LikeT)] = 0.879, indicating that there were significant differences from 1.723 points LikeT (=1.96*0.879); therefore, M(Like3) < M(Like1) = M(Like2) < M(Like4), see Table 3.

_{0(Dislike1)}= … = b

_{0(Dislike4)}). When equalizing these 4 intercepts (M15, Table 2), it was observed that all the set fit indicators were worse, and Δ

_{i(AIC)}(M15-M1) = 26.68 − (−48.04) = 74.72, indicating that the means differ. Table 3 shows that the intercepts of DislikeT range between 6.882 at T3 and 15.556 at T1. In M15, SE[M(DislikeT)] = 0.692, thus there is a significant difference between two means from 1.356 (=1.96*0.692), with all differences being significant in the following order: M(Dislike3) < M(Dislike4) < M(Dislike2) < M(Dislike1), see Table 3.

_{i(AIC)}(M16-M1) = 93.74 − (−48.04) = 141.78. This result is reached in M17, with constraints Like1 = Like2 =…= Like4, and Dislike1 =…= Dislike4, producing AIC(M17) = 261.67, thus it is also worse than M1.

_{α}*SE(–b)|= |−1.405 ± 1.96*0.260|, in absolute value: |CI(–b)| = |0.896 < b < 1.915|. This means that the value 1 is within its confidence interval, indicating that there are no significant differences among the absolute effects of F_Pref on Likes or Dislikes in any time point T. (b) With the aim of verifying whether the “c” effects (of F_Like on LikeT, with T= 2, 3 or 4) and the “d” effects (of F_Dislike on DislikeT, with T= 2, 3 or 4) are equal (“c” = “d”), we equalised these parameters (Table 2, M18), producing AIC = −49.77, which compared with M1: Δ

_{i(AIC)}(M18-M1) = −49.77 − (−48.04) = 1.73, not allowing us to reject the equality of effects. We accepted the original model, M1, since it is the one that responds to our hypothesis, as F_Like is better defined than F_Dislike.

_{i(AIC)}(M19-M1) = −10.27 − (−48.04) = 37.77, indicating that M1 is better than M19. Moreover, paradoxical and non-significant direct effects were obtained: “m” = −0.132, SE = 0.088, t= −1.492, p = 0.136; and “n” = 0.019, SE = 0.029, t = 0.651, p = 0.516. Therefore, the direct effects of F_Like and F_Dislike on each F_APT are not met.

_{i(AIC)}(M20–M1) = –30.69 − (−48.04) = 17.35; moreover, the effects of F_Like on F_Mats and F_Lang were not significant (“q” = 0.044, SE(q) = 0.026, t = 1.700, p = 0.091), as well as the effects of F_Dislike on F_Mats and F_Lang (“r” = 0.017, SE(r) = 0.026, t =0.669, p = 0.504).

_{i(AIC)}(M21-M1) = 7.65 − (−48.04) = 55.69, thus M1 is better than M21. However, the effects were consistent and significant: Those of LikeT on MatsT and LangT (“s” = 0.004, SE(s) = 0.002, t = 2.17, p = 0.031) and those of DislikeT on MatsT and LangT (u = −0.013, SE(u) = 0.003, t = −4.50, p < 0.001).

#### 3.5. Ojective 4: The Multilevel Effect

## 4. Discussion

#### 4.1. Evolution and Stability of Social Relationships and Academic Performance

#### 4.1.1. Evolution and Stability of Academic Performance

#### 4.1.2. Evolution and Stability of Social Acceptance: Likes, Dislikes, Social Preference, and Positive Bias

#### 4.2. Effects of Social Relationships on Academic Performance

#### The Predictive Power of Rejection: Negative Asymmetry

## 5. Conclusions, Future Research Lines, and Educational Implications

#### 5.1. Conclusions, Limitations and Future Research Lines

#### 5.2. Educational Implications

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

_{i}(Figure 1) is shown to only receive an effect from its previous factor score F_Pref3

_{i}:

_{i}= a·F_Pref3

_{i}+ D

_{i(F_Pref4)},

_{i(F_Pref4)}is the prediction error (or disturbance) of the same child “i” in factor F_Pref4. To simplify the demonstration, let us suppose that we do it with predicted values at each time point and without considering the means; thus, instead of operating with the direct values, we enter the predicted values F_Pref4

_{i}’ and F_Pref3

_{i}’, therefore, the error D

_{i(F_Pref4)}is equal to zero:

_{i}’ = a·F_Pref3

_{i}’,

_{i}’ = a·F_Pref2

_{i}’:

_{i}’ = a·(a·F_Pref2

_{i}’) = a

^{2}·F_Pref2

_{i}’,

_{i}’ = a

^{2}·(a·F_Pref1

_{i}’) = a

^{3}·F_Pref1

_{i}.

_{i}we did not include the indicator of prediction (superscript quotation mark), since these are primitive values, without prediction and without prediction error. However, statistically and substantively, immediate values must exert greater influence than remote values; therefore, the value of the AR coefficient must be lower than 1. In our case (Figure 3), we have that F_Pref4

_{i}’ = 0.681·F_Pref3

_{i}’ (applying Equation (A2)), although using Equation (A4): F_Pref4

_{i}’ = 0.681

^{3}·F_Pref1

_{i}’ = 0.316·F_Pref1

_{i}’, which indicates that the effect of F_Pref3 on F_Pref4 is 0.681, whereas the effect of F_Pref2 on F_Pref4 is 0.464, and the effect of F_Pref1 on F_Pref4 is 0.316, which is becomes much smaller along time. In the case that the “a” effect was greater than one, remote values of F_PrefT would exert greater influence than near values, which would make no sense.

^{2}·Var(F_Pref3′),

^{2}·a

^{2}·Var(F_Pref2′)) = a

^{4}·Var(F_Pref2′) = a

^{6}·Var(F_Pref1),

^{6}·Var(F_Pref1) = 0.100·Var(F_Pref1), although, if it had produced an “a” value greater than 1 (e.g., 1.319), then Var(F_Pref4′) = 1.319

^{6}·Var(F_Pref1) = 5.266·Var(F_Pref1), thus Var(F_Pref1) would exert greater influence than Var(F_Pref3′), and the farther away from the initial time point, the greater the expected variance would be and the greater the influence on remote values, which would make no sense.

## Appendix B

_{i}), in Figure 1:

_{i}= b

_{0(Lang2)}+ h·F_AP2

_{i}+ j·F_Lang

_{i}+ E

_{i(Lang2)},

_{0(Lang2)}is the value of the intercept of Lang2, common to the entire sample, “h” and “j” are the respective coefficients of the factor scores of child “i” for F_AP2

_{i}and F_Lang

_{i}, respectively, and E

_{i(Lang2)}is the prediction error of the variable Lang2 of child “i”. If we calculate expected values in Equation (A8):

_{i}) = E(b

_{0(Lang2)}+ h·F_AP2

_{i}+ j·F_Lang

_{i}+ E

_{i}).

_{0(Lang2)}) is the constant itself, the value of any factor (F_AP2 and F_Lang) is zero, and that of any measurement error (E) is also zero, Equation (A9) would be:

_{i}) = b

_{0(Lang2)}+ h·0 + j·0 + 0 = b

_{0(Lang2)},

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**Figure 1.**Representation of the effects model proposed in the hypotheses. Notes. The errors of the variables (E

_{j}) and of the factors (D

_{k}) are not represented, in order to keep the figure simple. The effects identified with 1(f) indicate that they are values fixed to 1, to ensure the convergence of the model; the rest of the effects and covariances are free, although with values “a”, “b”,…, “l” constrained to be equal.

**Figure 2.**Representation of the submodels present in Figure 1. (

**a**) AR dynamic factor model of the latent variables of social relationships; (

**b**) AR model of the latent variables of academic performance; (

**c**) MTMT model for the variables of social relationships; (

**d**) MTMT model for the variables of academic performance; (

**e**) structural model of temporal effects between social preference and academic performance.

**Figure 3.**Representation of the results obtained with the model hypothesized in Figure 1. Notes. Effects with 1(f) are values fixed to 1. ns: Non-significant effect. ** p < 0.010. All the other effects obtained p < 0.001.

**Table 1.**Correlations, means and standard deviations of the variables with the subjects participating in the longitudinal study (N = 169).

Like1 | Dislike1 | Mats1 | Lang1 | Like2 | Dislike2 | Mats2 | Lang2 | Like3 | Dislike3 | Mats3 | Lang3 | Like4 | Dislike4 | MatsT4 | Lang4 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Like1 | 1 | |||||||||||||||

Dislike1 | −0.406 *** | 1 | ||||||||||||||

Mats1 | 0.333 *** | −0.271 *** | 1 | |||||||||||||

Lang1 | 0.313 *** | −0.377 *** | 0.767 *** | 1 | ||||||||||||

Like2 | 0.672 *** | −0.374 *** | 0.244 ** | 0.195 * | 1 | |||||||||||

Dislike2 | −0.268 *** | 0.592 *** | −0.280 *** | −0.296 *** | −0.391 *** | 1 | ||||||||||

Mats2 | 0.268 *** | −0.256 ** | 0.658 *** | 0.530 *** | 0.257 ** | −0.263 ** | 1 | |||||||||

Lang2 | 0.346 *** | −0.412 *** | 0.611 *** | 0.681 *** | 0.292 *** | −0.350 *** | 0.712 *** | 1 | ||||||||

Like3 | 0.521 *** | −0.210 ** | 0.300 ** | 0.279 *** | 0.563 *** | −0.320 *** | 0.286 *** | 0.309 *** | 1 | |||||||

Dislike3 | −0.166 * | 0.527 *** | −0.154 * | −0.177 * | −0.173 * | 0.615 *** | −0.217 ** | −0.283 *** | −0.288 *** | 1 | ||||||

Mats3 | 0.186 * | −0.255 ** | 0.582 *** | 0.514 *** | 0.127 | −0.257 ** | 0.559 *** | 0.535 *** | 0.223 ** | −0.301 *** | 1 | |||||

Lang3 | 0.116 | −0.442 *** | 0.522 *** | 0.651 *** | 0.130 | −0.360 *** | 0.533 *** | 0.695 *** | 0.181 * | −0.392 *** | 0.643 *** | 1 | ||||

Like4 | 0.450 *** | −0.142 | 0.236 ** | 0.167 * | 0.469 *** | −0.282 *** | 0.321 *** | 0.262 ** | 0.590 *** | −0.226 ** | 0.110 | 0.091 | 1 | |||

Dislike4 | −0.209 ** | 0.425 *** | −0.203 ** | −0.190 * | −0.274 *** | 0.568 *** | −0.188 * | −0.240 ** | −0.345 *** | 0.488 *** | −0.280 *** | −0.315 *** | −0.355 *** | 1 | ||

Mats4 | 0.223 ** | −0.186 * | 0.435 *** | 0.322 *** | 0.138 | −0.205 ** | 0.508 *** | 0.401 *** | 0.254 ** | −0.255 ** | 0.603 *** | 0.447 *** | 0.119 | −0.287 *** | 1 | |

Lang4 | 0.228 ** | −0.344 *** | 0.385 *** | 0.474 *** | 0.168 * | −0.328 *** | 0.421 *** | 0.493 *** | 0.270 *** | −0.317 *** | 0.505 *** | 0.658 *** | 0.173 * | −0.398 *** | 0.709 *** | 1 |

Mean | 27.201 | 15.556 | 3.858 | 3.876 | 27.290 | 11.935 | 3.769 | 3.793 | 24.669 | 6.882 | 4.077 | 4.213 | 29.621 | 8.254 | 3.893 | 4.053 |

SD | 13.255 | 14.747 | 1.002 | 1.030 | 14.128 | 11.644 | 1.069 | 1.040 | 12.694 | 9.762 | 0.906 | 0.901 | 17.887 | 11.096 | 1.018 | 0.915 |

Model Description | χ^{2}SB (df) | P (χ^{2}) | χ^{2}/df | NNFI | CFI | BFI | MFI | RMSEA | AIC |
---|---|---|---|---|---|---|---|---|---|

M1.Figure 1 | 145.96 (97) | <0.001 | 1.50 | 0.937 | 0.949 | 0.950 | 0.865 | 0.055 | −48.04 |

M2. As M1, without “a”, means of LikeT and DislikeT equal to zero, and with free factor means of F_PrefT | 394.13 (110) | <0.001 | 3.58 | 0.781 | 0.821 | 0.825 | 0.601 | 0.102 | 174.13 |

M3. As M2, with equal factor means of F_PrefT | 421.38 (113) | <0.001 | 3.73 | 0.769 | 0.811 | 0.815 | 0.584 | 0.105 | 195.38 |

M4. As M1, with factor means, without “l”, “a” and “g”, and with free F_APT | 332.70 (108) | <0.001 | 3.08 | 0.798 | 0.832 | 0.835 | 0.619 | 0.098 | 116.70 |

M5. As M4, with equal factor means of F_APT | 396.04 (111) | <0.001 | 3.57 | 0.778 | 0.815 | 0.819 | 0.591 | 0.103 | 174.05 |

M6. As M1, without “l” effects | 183.20 (98) | <0.001 | 1.87 | 0.892 | 0.912 | 0.913 | 0.777 | 0.072 | −12.80 |

M7. As M1, without “l” effects, adding “a” = “g” effects | 185.28 (99) | <0.001 | 1.87 | 0.891 | 0.910 | 0.912 | 0.775 | 0.072 | −12.72 |

M8. As M1, with b_{0(Mats1)} = … = b_{0(Mats4)} | 172.30 (100) | <0.001 | 1.72 | 0.927 | 0.942 | 0.944 | 0.846 | 0.059 | −27.70 |

M9. As M1, with b_{0(Lang1)} = … = b_{0(Lang4)} | 245.27 (100) | <0.001 | 2.45 | 0.864 | 0.893 | 0.896 | 0.730 | 0.081 | 45.27 |

M10. As M1, with b_{0(Mats1)} = … = b_{0(Mats4)} and with b_{0(Lang1)} = … = b_{0(Lang4)} | 222.42 (103) | <0.001 | 2.16 | 0.903 | 0.926 | 0.928 | 0.799 | 0.068 | 16.41 |

M11. As M1, with b_{0(Mats1)} = … = b_{0(Mats4)} = b_{0(Lang1)} = … = b_{0(Lang4)} | 211.19 (104) | <0.001 | 2.03 | 0.921 | 0.940 | 0.941 | 0.833 | 0.062 | 3.19 |

M12. Changing the direction of “l” in Figure 1 | 156.14 (97) | <0.001 | 1.61 | 0.924 | 0.939 | 0.940 | 0.839 | 0.060 | −37.85 |

M13. Reciprocal effects between temporal factors | 225.31 (93) | <0.001 | 2.42 | 0.823 | 0.863 | 0.866 | 0.676 | 0.092 | 39.31 |

M14. As M1, with b_{0(Like1)} = … = b_{0(Like4)} | 166.08 (100) | <0.001 | 1.66 | 0.932 | 0.947 | 0.948 | 0.857 | 0.057 | −33.91 |

M15. As M1, with b_{0(Dislike1)} = … = b_{0(Dislike4)} | 226.68 (100) | <0.001 | 2.26 | 0.918 | 0.936 | 0.937 | 0.819 | 0.064 | 26.68 |

M16. As M1, constraining M(Like1) = M(Dislike1); …; M(Like4) = M(Dislike4) | 295.74 (101) | <0.001 | 2.93 | 0.912 | 0.932 | 0.933 | 0.714 | 0.084 | 93.74 |

M17. As M1, with M(Like1) = …= M(Like4), and M(Dislike1) = … = M(Dislike4) | 261.67 (102) | <0.001 | 2.57 | 0.826 | 0.865 | 0.868 | 0.593 | 0.104 | 261.67 |

M18. As M1, with “c” = “d” effects | 146.23 (98) | <0.001 | 1.49 | 0.939 | 0.950 | 0.951 | 0.867 | 0.054 | −49.77 |

M19.Figure 4 (as Figure 1, removing the “l” effects and adding the “m” and “n” effects) | 181.73 (96) | <0.001 | 1.89 | 0.889 | 0.911 | 0.913 | 0.776 | 0.073 | −10.27 |

M20. As M1, removing the “l” effects, adding F_Like on F_Mats and F_Lang (“q” effects), and F_Dislike on F_Mats and F_Lang (“r” effects) | 163.31 (97) | <0.001 | 1.68 | 0.915 | 0.931 | 0.933 | 0.822 | 0.064 | −30.69 |

M21. As M1, removing the “l” effects, adding LikeT on MatsT and LangT (“s” effects), and DislikeT on MatsT and LangT (“u” effects) | 199.65 (96) | <0.001 | 2.08 | 0.865 | 0.892 | 0.895 | 0.736 | 0.080 | 7.65 |

M22. Multilevel M1, with free observable variables | The model does not converge |

^{2}SB, Satorra–Bentler Robust Chi square; df, degrees of freedom; χ

^{2}/df, Relative Satorra–Bentler Chi-square; NNFI, Bentler–Bonnet Nonnormed Fit Index; CFI, Comparative Fit Index; BFI, Bollen Fit Index; MFI, McDonald Fit Index; RMSEA, Root Mean Square Error of Approximation; AIC, Akaike Information Criterion.

**Table 3.**Means of the variables and means of the factors in the models. The means are equivalent to the intercepts.

Models | Variables | Mean Differences | |||
---|---|---|---|---|---|

M1 | Like1 | Like2 | Like3 | Like4 | |

Means | 27.201 | 27.290 | 24.669 | 29.621 | Yes (M14-M1) |

Dislike1 | Dislike2 | Dislike3 | Dislike4 | ||

Means | 15.556 | 11.935 | 6.882 | 8.254 | Yes (M15-M1) |

Mats1 | Mats2 | Mats3 | Mats4 | ||

Means | 3.858 | 3.769 | 4.077 | 3.893 | Yes (M8-M1) |

Lang1 | Lang2 | Lang3 | Lang4 | ||

Means | 3.876 | 3.793 | 4.213 | 4.053 | Yes (M9-M1) |

M2 | F_Pref1 | F_Pref2 | F_Pref3 | F_Pref4 | |

Factor Means | 28.194 | 25.401 | 26.987 | 26.178 | Yes (M3-M2) |

M4 | F_AP1 | F_AP2 | F_AP3 | F_AP4 | |

Factor Means | 3.823 | 3.733 | 4.106 | 3.946 | Yes (M5-M4) |

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García Bacete, F.J.; Muñoz Tinoco, V.; Marande Perrin, G.; Rosel Remírez, J.F.
Stability of Peer Acceptance and Rejection and Their Effect on Academic Performance in Primary Education: A Longitudinal Research. *Sustainability* **2021**, *13*, 2650.
https://doi.org/10.3390/su13052650

**AMA Style**

García Bacete FJ, Muñoz Tinoco V, Marande Perrin G, Rosel Remírez JF.
Stability of Peer Acceptance and Rejection and Their Effect on Academic Performance in Primary Education: A Longitudinal Research. *Sustainability*. 2021; 13(5):2650.
https://doi.org/10.3390/su13052650

**Chicago/Turabian Style**

García Bacete, Francisco J., Victoria Muñoz Tinoco, Ghislaine Marande Perrin, and Jesús F. Rosel Remírez.
2021. "Stability of Peer Acceptance and Rejection and Their Effect on Academic Performance in Primary Education: A Longitudinal Research" *Sustainability* 13, no. 5: 2650.
https://doi.org/10.3390/su13052650