Associations between Student–Teacher Relationship Quality, Class Climate, and Bullying Roles: A Bayesian Multilevel Multinomial Logit Analysis

Figures & data

Table 1. Means, standard deviations, min- and max values for the quantitative variables.

Variable	M	SD	Min	Max
Individual variables
Age	13.67	1.64	10.42	17.33
SES	15.39	1.94	7	19
STRQ	12.31	2.57	3	15
Victimization	1.27	0.49	1	5
Bullying	1.09	0.30	1	5
Class variables
SES	15.28	0.82	12.22	17.28
STRQ	12.35	1.10	8.88	14.67
Class climate	11.77	1.04	8.24	14.00
Victimization	1.28	0.17	1	2.27
Bullying	1.09	0.09	1	1.66

Note: STRQ = student–teacher relationship quality; bullying and victimization are here presented as quantitative variables.

Table 2. Correlations for the Quantitative individual variables.

Variable	Age	SES	STRQ	Vict.	Bul.
Age	1
SES	.02	1
STRQ	−.24	.02	1
Victimization	−.01	−.02	−.21	1
Bullying	.04	−.01	−.12	.38	1

Note: STRQ = student–teacher relationship quality; bullying and victimization are here presented as quantitative variables.

Table 3. Correlations for the quantitative class variables.

Variable	SES	STRQ	Class cl.	Vict.	Bul.
SES	1
STRQ	-.07	1
Class climate	.15	.48	1
Victimization	-.11	-.14	-.39	1
Bullying	-.12	-.13	-.12	.52	1

Note: STRQ = student–teacher relationship quality; bullying and victimization are here presented as quantitative variables.

Table 4. Estimation results for model 1.

	Posterior		Posterior	percentiles	Posterior
Variable/parameter	Mean coefficient	sd	2.5	97.5	Mean eff. size
Gender (BulVic vs Bul)	−0.025	0.304	−0.627	0.567	1.022
Gender (Vic vs Bul)	−1.006	0.250	−1.505	−0.524	0.377
Gender (Un vs Bul)	−0.700	0.240	−1.179	−0.233	0.511
Gender (Vic vs BulVic)	−0.982	0.210	−1.396	−0.573	0.383
Gender (Un vs BulVic)	−0.676	0.198	−1.070	−0.293	0.519
Gender (Un vs Vic)	0.306	0.097	0.117	0.495	1.364
Foreign backgr (BulVic vs Bul)	−0.291	0.338	−0.952	0.373	0.792
Foreign backgr (Vic vs Bul)	−0.361	0.277	−0.895	0.190	0.725
Foreign backgr (Un vs Bul)	−0.419	0.265	−0.929	0.111	0.682
Foreign backgr (Vic vs BulVic)	−0.070	0.247	−0.543	0.425	0.961
Foreign backgr (Un vs BulVic)	−0.128	0.233	−0.573	0.339	0.904
Foreign backgr (Un vs Vic)	−0.058	0.121	−0.293	0.181	0.951
Age (BulVic vs Bul)	−0.244	0.165	−0.570	0.079	0.794
Age (Vic vs Bul)	−0.461	0.137	−0.736	−0.198	0.636
Age (Un vs Bul)	−0.319	0.135	−0.588	−0.058	0.734
Age (Vic vs BulVic)	−0.217	0.114	−0.440	0.004	0.810
Age (Un vs BulVic)	−0.075	0.112	−0.295	0.145	0.934
Age (Un vs Vic)	0.142	0.059	0.026	0.258	1.155
SES (BulVic vs Bul)	−0.127	0.148	−0.419	0.164	0.890
SES (Vic vs Bul)	−0.126	0.124	−0.371	0.114	0.889
SES (Un vs Bul)	−0.154	0.119	−0.389	0.074	0.863
SES (Vic vs BulVic)	0.001	0.104	−0.205	0.202	1.007
SES (Un vs BulVic)	−0.027	0.098	−0.221	0.162	0.978
SES (Un vs Vic)	−0.028	0.050	−0.126	0.070	0.973
STRQ (BulVic vs Bul)	−0.063	0.123	−0.305	0.174	0.946
STRQ (Vic vs Bul)	0.064	0.103	−0.142	0.263	1.071
STRQ (Un vs Bul)	0.479	0.099	0.282	0.671	1.623
STRQ (Vic vs BulVic)	0.127	0.088	−0.048	0.299	1.140
STRQ (Un vs BulVic)	0.543	0.083	0.377	0.705	1.727
STRQ (Un vs Vic)	0.416	0.047	0.324	0.508	1.517
μ (BulVic)	0.484	0.286	−0.074	1.041
μ (Vic)	2.732	0.227	2.299	3.187
μ (Un)	4.315	0.224	3.896	4.763
σ (BulVic)	0.381	0.206	0.059	0.821
σ (Vic)	0.220	0.132	0.040	0.521
σ (Un)	0.465	0.110	0.236	0.685
ρ (BulVic vs Vic)	0.047	0.393	−0.704	0.751
ρ (BulVic vs Un)	−0.128	0.347	−0.766	0.548
ρ (Vic vs Un)	0.147	0.385	−0.640	0.779

Note: Posterior mean, standard deviation (sd), and percentiles of the parameters ${\beta }_{lv}-{\beta }_{mv}$ and the mean effective size (MES), defined in Section Analytical Techniques, are shown for each explanatory variable $x_v$ and categories l and m. Corresponding posterior measures are also shown for the parameters ${\mu }_l,{\sigma }_l,{\rho }_{lm}$. Values in bold mean that the current variable regarding categories l versus m has a very likely effect on the outcome. A very likely effect corresponds to a 95% credibility interval that does not include 0, which is equivalent to a positive/negative slope being at least 39 times more likely than a negative/positive slope.

Table 5. Estimation results for model 2.

	Posterior		Posterior	percentiles	Posterior
Variable/parameter	Mean coefficient	sd	2.5	97.5	Mean eff. size
Individual variables
Gender (BulVic vs Bul)	−0.007	0.305	−0.614	0.581	1.040
Gender (Vic vs Bul)	−0.988	0.256	−1.510	−0.518	0.384
Gender (Un vs Bul)	−0.674	0.240	−1.166	−0.214	0.525
Gender (Vic vs BulVic)	−0.981	0.212	−1.405	−0.581	0.383
Gender (Un vs BulVic)	−0.667	0.196	−1.059	−0.291	0.523
Gender (Un vs Vic)	0.315	0.099	0.124	0.508	1.376
Foreign backgr (BulVic vs Bul)	−0.292	0.367	−0.950	0.426	0.799
Foreign backgr (Vic vs Bul)	−0.314	0.289	−0.855	0.279	0.762
Foreign backgr (Un vs Bul)	−0.355	0.278	−0.859	0.207	0.729
Foreign backgr (Vic vs BulVic)	−0.022	0.258	−0.517	0.471	1.012
Foreign backgr (Un vs BulVic)	−0.063	0.240	−0.526	0.399	0.966
Foreign backgr (Un vs Vic)	−0.042	0.123	−0.279	0.209	0.967
Age (BulVic vs Bul)	−0.260	0.189	−0.637	0.098	0.785
Age (Vic vs Bul)	−0.458	0.153	−0.754	−0.153	0.640
Age (Un vs Bul)	−0.350	0.148	−0.645	−0.062	0.712
Age (Vic vs BulVic)	−0.199	0.145	−0.496	0.077	0.828
Age (Un vs BulVic)	−0.091	0.135	−0.342	0.173	0.921
Age (Un vs Vic)	0.108	0.073	−0.033	0.254	1.117
SESd (BulVic vs Bul)	−0.140	0.143	−0.422	0.143	0.878
SESd (Vic vs Bul)	−0.168	0.119	−0.407	0.068	0.851
SESd (Un vs Bul)	−0.200	0.114	−0.430	0.024	0.824
SESd (Vic vs BulVic)	−0.029	0.100	−0.227	0.169	0.977
SESd (Un vs BulVic)	−0.060	0.093	−0.245	0.124	0.946
SESd (Un vs Vic)	−0.032	0.047	−0.125	0.062	0.970
STRQd (BulVic vs Bul)	−0.043	0.118	−0.276	0.186	0.964
STRQd (Vic vs Bul)	0.056	0.101	−0.136	0.252	1.063
STRQd (Un vs Bul)	0.432	0.096	0.248	0.623	1.547
STRQd (Vic vs BulVic)	0.099	0.088	−0.076	0.271	1.108
STRQd (Un vs BulVic)	0.475	0.082	0.317	0.635	1.614
STRQd (Un vs Vic)	0.376	0.045	0.289	0.464	1.458
Class variables
Class climate (BulVic vs Bul)	−0.107	0.166	−0.429	0.227	0.911
Class climate (Vic vs Bul)	−0.092	0.134	−0.363	0.169	0.920
Class climate (Un vs Bul)	0.172	0.131	−0.090	0.431	1.198
Class climate (Vic vs BulVic)	0.015	0.126	−0.239	0.253	1.023
Class climate (Un vs BulVic)	0.279	0.121	0.038	0.512	1.331
Class climate (Un vs Vic)	0.264	0.066	0.139	0.396	1.305
SES (BulVic vs Bul)	0.018	0.157	−0.292	0.310	1.031
SES (Vic vs Bul)	0.104	0.126	−0.153	0.344	1.118
SES (Un vs Bul)	0.088	0.123	−0.160	0.322	1.101
SES (Vic vs BulVic)	0.086	0.115	−0.133	0.312	1.097
SES (Un vs BulVic)	0.070	0.112	−0.147	0.289	1.080
SES (Un vs Vic)	−0.016	0.058	−0.131	0.098	0.986
STRQ (BulVic vs Bul)	−0.037	0.196	−0.435	0.340	0.982
STRQ (Vic vs Bul)	0.068	0.161	−0.241	0.387	1.084
STRQ (Un vs Bul)	0.118	0.154	−0.191	0.419	1.139
STRQ (Vic vs BulVic)	0.105	0.158	−0.204	0.408	1.125
STRQ (Un vs BulVic)	0.155	0.145	−0.125	0.446	1.180
STRQ (Un vs Vic)	0.050	0.085	−0.111	0.230	1.055
μ (BulVic vs Bul)	0.445	0.283	−0.127	1.005
μ (Vic vs Bul)	2.719	0.230	2.317	3.207
μ (Un vs Bul)	4.303	0.221	3.907	4.777
σ (BulVic)	0.439	0.217	0.081	0.879
σ (Vic)	0.217	0.124	0.047	0.493
σ (Un)	0.416	0.117	0.163	0.638
ρBulVic.Vic	0.065	0.399	−0.688	0.769
ρBulVic.Un	−0.104	0.351	−0.741	0.531
ρVic.Un	0.122	0.390	−0.653	0.785

Note: Posterior mean, standard deviation (sd), and percentiles of the parameters ${\beta }_{lv}-{\beta }_{mv}$ and the Mean Effective Size (MES), as defined in Section Analytical Techniques, are shown for each explanatory variable $x_v$ and categories l and m. Corresponding posterior measures are also shown for the parameters ${\mu }_l,{\sigma }_l,{\rho }_{lm}$. Values in bold indicate that the current variable regarding categories l versus m has a very likely effect on the outcome. A very likely effect corresponds to a 95% credibility interval that does not include 0, which is equivalent to a positive/negative slope being at least 39 times more likely than a negative/positive slope. $x_d=x-\bar{x}$ is the deviation for the individual variable $x$ to its class mean.