1 分析說明

本研究將以台灣TIMSS2015及2019年的資料檢驗影響臺灣國中生的學校效能（即：數學成就、學校霸凌程度及學校氣氛）之因素

-IDSCHOOL：學校編碼

學校層級變項
- SCH_ACA_IMP：學校對學業的重視
- SCH_MAT_RES：學校資源
- SCH_DIS：學校紀律和安全
- SCH_ADV：學生背景成分
- COM_N：學校所在地人口

學生層級變項
- STU_ENG：數學學習投入
- STU_CON：數學自信
- STU_LIK：喜歡數學
- STU_RES：家庭資源

依變項：
- MATH_PV1：數學成就
- STU_BUL：學校霸凌
- STU_BEL：學校氣氛

2 虛無模型

2.1 TIMSS 2015

2.1.1 數學成就為依變項

m0a <- lme4::lmer(MATH_PV1 ~ (1 | IDSCHOOL), data=subset(TIMSS, Year == 2015))
sjPlot::tab_model(m0a, digits=3, digits.re=3, show.se = TRUE)

	MATH_PV1
Predictors	Estimates	std. Error	CI	p
(Intercept)	596.234	3.427	589.515 – 602.952	<0.001
Random Effects
σ²	7100.259
τ₀₀ _IDSCHOOL	1982.896
ICC	0.218
N _IDSCHOOL	190
Observations	5617
Marginal R² / Conditional R²	0.000 / 0.218

lmerTest::ranova(m0a)

ANOVA-like table for random-effects: Single term deletions

Model:
MATH_PV1 ~ (1 | IDSCHOOL)
               npar logLik   AIC  LRT Df Pr(>Chisq)
<none>            3 -33083 66172                   
(1 | IDSCHOOL)    2 -33610 67224 1054  1     <2e-16

2.1.2 學校霸凌為依變項

m0b <- lme4::lmer(STU_BUL ~ (1 | IDSCHOOL), data=subset(TIMSS, Year == 2015))
sjPlot::tab_model(m0b, digits=3, digits.re=3, show.se = TRUE)

	STU_BUL
Predictors	Estimates	std. Error	CI	p
(Intercept)	2.849	0.007	2.835 – 2.864	<0.001
Random Effects
σ²	0.146
τ₀₀ _IDSCHOOL	0.005
ICC	0.035
N _IDSCHOOL	190
Observations	5617
Marginal R² / Conditional R²	0.000 / 0.035

lmerTest::ranova(m0b)

ANOVA-like table for random-effects: Single term deletions

Model:
STU_BUL ~ (1 | IDSCHOOL)
               npar logLik  AIC   LRT Df Pr(>Chisq)
<none>            3  -2642 5289                    
(1 | IDSCHOOL)    2  -2672 5348 60.78  1   6.38e-15

2.1.3 學校氣氛為依變項

m0c <- lme4::lmer(STU_BEL ~ (1 | IDSCHOOL), data=subset(TIMSS, Year == 2015))
sjPlot::tab_model(m0c, digits=3, digits.re=3, show.se = TRUE)

	STU_BEL
Predictors	Estimates	std. Error	CI	p
(Intercept)	2.814	0.010	2.794 – 2.833	<0.001
Random Effects
σ²	0.331
τ₀₀ _IDSCHOOL	0.007
ICC	0.020
N _IDSCHOOL	190
Observations	5617
Marginal R² / Conditional R²	0.000 / 0.020

lmerTest::ranova(m0c)

ANOVA-like table for random-effects: Single term deletions

Model:
STU_BEL ~ (1 | IDSCHOOL)
               npar logLik  AIC   LRT Df Pr(>Chisq)
<none>            3  -4913 9833                    
(1 | IDSCHOOL)    2  -4926 9855 24.86  1   6.17e-07

2.2 TIMSS 2019

2.2.1 數學成就為依變項

m0a <- lme4::lmer(MATH_PV1 ~ (1 | IDSCHOOL), data=subset(TIMSS, Year == 2019))
sjPlot::tab_model(m0a, digits=3, digits.re=3, show.se = TRUE)

	MATH_PV1
Predictors	Estimates	std. Error	CI	p
(Intercept)	605.457	3.601	598.396 – 612.517	<0.001
Random Effects
σ²	7399.492
τ₀₀ _IDSCHOOL	1977.930
ICC	0.211
N _IDSCHOOL	178
Observations	4180
Marginal R² / Conditional R²	0.000 / 0.211

lmerTest::ranova(m0a)

ANOVA-like table for random-effects: Single term deletions

Model:
MATH_PV1 ~ (1 | IDSCHOOL)
               npar logLik   AIC   LRT Df Pr(>Chisq)
<none>            3 -24723 49453                    
(1 | IDSCHOOL)    2 -25058 50121 669.6  1     <2e-16

2.2.2 學校霸凌為依變項

m0b <- lme4::lmer(STU_BUL ~ (1 | IDSCHOOL), data=subset(TIMSS, Year == 2019))
sjPlot::tab_model(m0b, digits=3, digits.re=3, show.se = TRUE)

	STU_BUL
Predictors	Estimates	std. Error	CI	p
(Intercept)	2.872	0.007	2.858 – 2.886	<0.001
Random Effects
σ²	0.125
τ₀₀ _IDSCHOOL	0.004
ICC	0.030
N _IDSCHOOL	178
Observations	4180
Marginal R² / Conditional R²	0.000 / 0.030

lmerTest::ranova(m0b)

ANOVA-like table for random-effects: Single term deletions

Model:
STU_BUL ~ (1 | IDSCHOOL)
               npar logLik  AIC   LRT Df Pr(>Chisq)
<none>            3  -1639 3283                    
(1 | IDSCHOOL)    2  -1654 3313 31.55  1   1.95e-08

2.2.3 學校氣氛為依變項

m0c <- lme4::lmer(STU_BEL ~ (1 | IDSCHOOL), data=subset(TIMSS, Year == 2019))
sjPlot::tab_model(m0c, digits=3, digits.re=3, show.se = TRUE)

	STU_BEL
Predictors	Estimates	std. Error	CI	p
(Intercept)	2.057	0.016	2.025 – 2.088	<0.001
Random Effects
σ²	0.369
τ₀₀ _IDSCHOOL	0.030
ICC	0.074
N _IDSCHOOL	178
Observations	4180
Marginal R² / Conditional R²	0.000 / 0.074

lmerTest::ranova(m0c)

ANOVA-like table for random-effects: Single term deletions

Model:
STU_BEL ~ (1 | IDSCHOOL)
               npar logLik  AIC   LRT Df Pr(>Chisq)
<none>            3  -3943 7892                    
(1 | IDSCHOOL)    2  -4019 8041 151.3  1     <2e-16

3 完整模型

3.1 TIMSS 2015

3.1.1 數學成就為依變項

m0a <- lme4::lmer(MATH_PV1 ~ STU_ENG+STU_CON+STU_LIK+STU_RES+SCH_ACA_IMP+SCH_MAT_RES+SCH_DIS+SCH_ADV+COM_N+ (1+STU_ENG+STU_CON+STU_LIK+STU_RES|IDSCHOOL), data=subset(TIMSS, Year == 2015),control=lmerControl(optimizer="optimx", 
                                      calc.derivs=FALSE,
                                      optCtrl=list(method="nlminb", 
                                                   starttests=FALSE, 
                                                   kkt=FALSE)))
sjPlot::tab_model(m0a, digits=3, digits.re=3, show.se = TRUE)

	MATH_PV1
Predictors	Estimates	std. Error	CI	p
(Intercept)	310.064	15.728	279.231 – 340.897	<0.001
STU ENG	8.303	1.954	4.473 – 12.134	<0.001
STU CON	49.208	2.072	45.145 – 53.270	<0.001
STU LIK	13.879	2.088	9.785 – 17.972	<0.001
STU RES	34.319	2.089	30.224 – 38.415	<0.001
SCH ACA IMP	14.066	3.671	6.869 – 21.263	<0.001
SCH MAT RES	-3.210	4.490	-12.011 – 5.592	0.475
SCH DIS	7.694	4.184	-0.509 – 15.897	0.066
SCH ADV	15.345	3.947	7.608 – 23.082	<0.001
COM N	7.906	1.467	5.031 – 10.782	<0.001
Random Effects
σ²	4816.688
τ₀₀ _IDSCHOOL	4247.296
τ₁₁ _{IDSCHOOL.STU_ENG}	213.962
τ₁₁ _{IDSCHOOL.STU_CON}	126.025
τ₁₁ _{IDSCHOOL.STU_LIK}	103.034
τ₁₁ _{IDSCHOOL.STU_RES}	88.779
ρ₀₁	-0.670
	0.077
	-0.565
	-0.845
N _IDSCHOOL	190
Observations	5617
Marginal R² / Conditional R²	0.394 / NA

lmerTest::ranova(m0a)

ANOVA-like table for random-effects: Single term deletions

Model:
MATH_PV1 ~ STU_ENG + STU_CON + STU_LIK + STU_RES + SCH_ACA_IMP + SCH_MAT_RES + SCH_DIS + SCH_ADV + COM_N + (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)
                                                                  npar logLik
<none>                                                              26 -31983
STU_ENG in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)   21 -31996
STU_CON in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)   21 -31988
STU_LIK in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)   21 -31988
STU_RES in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)   21 -31989
                                                                    AIC    LRT
<none>                                                            64019       
STU_ENG in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL) 64035 25.979
STU_CON in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL) 64019  9.667
STU_LIK in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL) 64019  9.594
STU_RES in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL) 64019 10.518
                                                                  Df Pr(>Chisq)
<none>                                                                         
STU_ENG in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)  5   9.01e-05
STU_CON in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)  5     0.0852
STU_LIK in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)  5     0.0876
STU_RES in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)  5     0.0618

# ICC
r.squaredGLMM(m0a)[2]

[1] 0.454317

3.1.2 學校霸凌為依變項

m0b <- lme4::lmer(STU_BUL ~ STU_ENG+STU_CON+STU_LIK+STU_RES+SCH_ACA_IMP+SCH_MAT_RES+SCH_DIS+SCH_ADV+COM_N+ (1+STU_ENG+STU_CON+STU_LIK+STU_RES|IDSCHOOL), data=subset(TIMSS, Year == 2015),control=lmerControl(optimizer="optimx", 
                                      calc.derivs=FALSE,
                                      optCtrl=list(method="nlminb", 
                                                   starttests=FALSE, 
                                                   kkt=FALSE)))
sjPlot::tab_model(m0b, digits=3, digits.re=3, show.se = TRUE)

	STU_BUL
Predictors	Estimates	std. Error	CI	p
(Intercept)	2.699	0.056	2.589 – 2.809	<0.001
STU ENG	0.059	0.009	0.040 – 0.077	<0.001
STU CON	0.003	0.011	-0.018 – 0.025	0.763
STU LIK	-0.009	0.012	-0.031 – 0.014	0.452
STU RES	0.002	0.011	-0.019 – 0.023	0.833
SCH ACA IMP	-0.005	0.013	-0.031 – 0.020	0.683
SCH MAT RES	-0.006	0.016	-0.037 – 0.025	0.700
SCH DIS	0.019	0.015	-0.010 – 0.049	0.195
SCH ADV	0.018	0.014	-0.009 – 0.045	0.203
COM N	-0.005	0.005	-0.015 – 0.005	0.348
Random Effects
σ²	0.142
τ₀₀ _IDSCHOOL	0.042
τ₁₁ _{IDSCHOOL.STU_ENG}	0.003
τ₁₁ _{IDSCHOOL.STU_CON}	0.002
τ₁₁ _{IDSCHOOL.STU_LIK}	0.004
τ₁₁ _{IDSCHOOL.STU_RES}	0.001
ρ₀₁	-0.834
	-0.054
	0.099
	-0.860
N _IDSCHOOL	190
Observations	5617
Marginal R² / Conditional R²	0.012 / NA

lmerTest::ranova(m0b)

ANOVA-like table for random-effects: Single term deletions

Model:
STU_BUL ~ STU_ENG + STU_CON + STU_LIK + STU_RES + SCH_ACA_IMP + SCH_MAT_RES + SCH_DIS + SCH_ADV + COM_N + (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)
                                                                  npar logLik
<none>                                                              26  -2634
STU_ENG in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)   21  -2645
STU_CON in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)   21  -2635
STU_LIK in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)   21  -2637
STU_RES in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)   21  -2636
                                                                   AIC    LRT
<none>                                                            5321       
STU_ENG in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL) 5333 22.005
STU_CON in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL) 5312  1.700
STU_LIK in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL) 5316  5.466
STU_RES in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL) 5313  2.599
                                                                  Df Pr(>Chisq)
<none>                                                                         
STU_ENG in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)  5   0.000522
STU_CON in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)  5   0.888940
STU_LIK in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)  5   0.361742
STU_RES in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)  5   0.761535

# ICC
r.squaredGLMM(m0b)[2]

[1] 0.0642393

3.1.3 學校氣氛為依變項

m0c <- lme4::lmer(STU_BEL ~ STU_ENG+STU_CON+STU_LIK+STU_RES+SCH_ACA_IMP+SCH_MAT_RES+SCH_DIS+SCH_ADV+COM_N+ (1+STU_ENG+STU_CON+STU_LIK+STU_RES|IDSCHOOL), data=subset(TIMSS, Year == 2015),control=lmerControl(optimizer="optimx", 
                                      calc.derivs=FALSE,
                                      optCtrl=list(method="nlminb", 
                                                   starttests=FALSE, 
                                                   kkt=FALSE)))
sjPlot::tab_model(m0c, digits=3, digits.re=3, show.se = TRUE)

	STU_BEL
Predictors	Estimates	std. Error	CI	p
(Intercept)	2.503	0.079	2.349 – 2.657	<0.001
STU ENG	0.171	0.015	0.142 – 0.200	<0.001
STU CON	-0.034	0.015	-0.063 – -0.005	0.021
STU LIK	0.055	0.016	0.025 – 0.085	<0.001
STU RES	0.035	0.016	0.003 – 0.067	0.034
SCH ACA IMP	0.008	0.017	-0.024 – 0.041	0.611
SCH MAT RES	-0.039	0.020	-0.078 – -0.000	0.050
SCH DIS	0.009	0.019	-0.029 – 0.047	0.639
SCH ADV	-0.012	0.017	-0.047 – 0.022	0.478
COM N	-0.011	0.007	-0.024 – 0.002	0.090
Random Effects
σ²	0.302
τ₀₀ _IDSCHOOL	0.251
τ₁₁ _{IDSCHOOL.STU_ENG}	0.012
τ₁₁ _{IDSCHOOL.STU_CON}	0.000
τ₁₁ _{IDSCHOOL.STU_LIK}	0.002
τ₁₁ _{IDSCHOOL.STU_RES}	0.008
ρ₀₁	-0.952
	0.997
	-0.900
	-0.959
N _IDSCHOOL	190
Observations	5617
Marginal R² / Conditional R²	0.057 / NA

lmerTest::ranova(m0c)

ANOVA-like table for random-effects: Single term deletions

Model:
STU_BEL ~ STU_ENG + STU_CON + STU_LIK + STU_RES + SCH_ACA_IMP + SCH_MAT_RES + SCH_DIS + SCH_ADV + COM_N + (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)
                                                                  npar logLik
<none>                                                              26  -4736
STU_ENG in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)   21  -4759
STU_CON in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)   21  -4736
STU_LIK in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)   21  -4738
STU_RES in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)   21  -4746
                                                                   AIC   LRT Df
<none>                                                            9523         
STU_ENG in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL) 9559 46.21  5
STU_CON in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL) 9515  1.41  5
STU_LIK in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL) 9518  4.49  5
STU_RES in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL) 9533 19.80  5
                                                                  Pr(>Chisq)
<none>                                                                      
STU_ENG in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)   8.22e-09
STU_CON in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)    0.92316
STU_LIK in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)    0.48077
STU_RES in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)    0.00136

# ICC
r.squaredGLMM(m0c)[2]

[1] 0.109513

3.2 TIMSS 2019

3.2.1 數學成就為依變項

m0a <- lme4::lmer(MATH_PV1 ~ STU_ENG+STU_CON+STU_LIK+STU_RES+SCH_ACA_IMP+SCH_MAT_RES+SCH_DIS+SCH_ADV+COM_N+ (1+STU_ENG+STU_CON+STU_LIK+STU_RES|IDSCHOOL), data=subset(TIMSS, Year == 2019),control=lmerControl(optimizer="optimx", 
                                      calc.derivs=FALSE,
                                      optCtrl=list(method="nlminb", 
                                                   starttests=FALSE, 
                                                   kkt=FALSE)))
summary(m0a)

Linear mixed model fit by REML ['lmerMod']
Formula: MATH_PV1 ~ STU_ENG + STU_CON + STU_LIK + STU_RES + SCH_ACA_IMP +  
    SCH_MAT_RES + SCH_DIS + SCH_ADV + COM_N + (1 + STU_ENG +  
    STU_CON + STU_LIK + STU_RES | IDSCHOOL)
   Data: subset(TIMSS, Year == 2019)
Control: 
lmerControl(optimizer = "optimx", calc.derivs = FALSE, optCtrl = list(method = "nlminb",  
    starttests = FALSE, kkt = FALSE))

REML criterion at convergence: 47886.6

Scaled residuals: 
   Min     1Q Median     3Q    Max 
-4.883 -0.612  0.057  0.652  2.898 

Random effects:
 Groups   Name        Variance Std.Dev. Corr                   
 IDSCHOOL (Intercept) 3347.4   57.86                           
          STU_ENG      131.5   11.47    -0.82                  
          STU_CON       21.5    4.63    -0.03 -0.23            
          STU_LIK       21.1    4.60    -0.98  0.73  0.05      
          STU_RES      155.5   12.47    -0.48  0.29 -0.62  0.50
 Residual             5214.0   72.21                           
Number of obs: 4180, groups:  IDSCHOOL, 178

Fixed effects:
            Estimate Std. Error t value
(Intercept)   313.62      18.03   17.39
STU_ENG        13.13       2.15    6.12
STU_CON        47.82       2.29   20.89
STU_LIK        15.07       2.28    6.62
STU_RES        31.18       2.47   12.60
SCH_ACA_IMP    12.78       3.98    3.21
SCH_MAT_RES    -3.66       4.70   -0.78
SCH_DIS         8.17       4.66    1.75
SCH_ADV        20.41       3.91    5.22
COM_N           6.37       1.47    4.33

Correlation of Fixed Effects:
            (Intr) STU_EN STU_CO STU_LI STU_RE SCH_AC SCH_MA SCH_DI SCH_AD
STU_ENG     -0.226                                                        
STU_CON     -0.015 -0.042                                                 
STU_LIK     -0.068 -0.185 -0.589                                          
STU_RES     -0.185 -0.018 -0.113  0.020                                   
SCH_ACA_IMP  0.049  0.011 -0.022 -0.004 -0.043                            
SCH_MAT_RES -0.436 -0.006  0.003  0.004  0.021 -0.240                     
SCH_DIS     -0.644 -0.018 -0.012  0.020  0.002 -0.091 -0.080              
SCH_ADV     -0.134 -0.001 -0.002 -0.020 -0.068 -0.304  0.008 -0.037       
 [ 達到了 getOption("max.print") -- 省略最後 1 列 ]]
optimizer (optimx) convergence code: 1 (none)

sjPlot::tab_model(m0a, digits=3, digits.re=3, show.se = TRUE)

	MATH_PV1
Predictors	Estimates	std. Error	CI	p
(Intercept)	313.621	18.031	278.270 – 348.972	<0.001
STU ENG	13.131	2.147	8.922 – 17.341	<0.001
STU CON	47.822	2.290	43.333 – 52.311	<0.001
STU LIK	15.070	2.277	10.606 – 19.534	<0.001
STU RES	31.184	2.474	26.333 – 36.035	<0.001
SCH ACA IMP	12.776	3.981	4.972 – 20.580	0.001
SCH MAT RES	-3.658	4.699	-12.869 – 5.554	0.436
SCH DIS	8.174	4.662	-0.966 – 17.313	0.080
SCH ADV	20.414	3.910	12.748 – 28.081	<0.001
COM N	6.374	1.473	3.486 – 9.262	<0.001
Random Effects
σ²	5214.005
τ₀₀ _IDSCHOOL	3347.375
τ₁₁ _{IDSCHOOL.STU_ENG}	131.466
τ₁₁ _{IDSCHOOL.STU_CON}	21.457
τ₁₁ _{IDSCHOOL.STU_LIK}	21.129
τ₁₁ _{IDSCHOOL.STU_RES}	155.456
ρ₀₁	-0.825
	-0.033
	-0.979
	-0.476
ICC	0.122
N _IDSCHOOL	178
Observations	4180
Marginal R² / Conditional R²	0.352 / 0.431

lmerTest::ranova(m0a)

ANOVA-like table for random-effects: Single term deletions

Model:
MATH_PV1 ~ STU_ENG + STU_CON + STU_LIK + STU_RES + SCH_ACA_IMP + SCH_MAT_RES + SCH_DIS + SCH_ADV + COM_N + (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)
                                                                  npar logLik
<none>                                                              26 -23943
STU_ENG in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)   21 -23948
STU_CON in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)   21 -23944
STU_LIK in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)   21 -23945
STU_RES in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)   21 -23946
                                                                    AIC   LRT
<none>                                                            47939      
STU_ENG in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL) 47938 9.238
STU_CON in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL) 47930 1.551
STU_LIK in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL) 47931 2.609
STU_RES in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL) 47933 4.594
                                                                  Df Pr(>Chisq)
<none>                                                                         
STU_ENG in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)  5     0.0999
STU_CON in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)  5     0.9071
STU_LIK in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)  5     0.7600
STU_RES in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)  5     0.4674

# ICC
r.squaredGLMM(m0a)[2]

[1] 0.430879

3.2.2 學校霸凌為依變項

m0b <- lme4::lmer(STU_BUL ~ STU_ENG+STU_CON+STU_LIK+STU_RES+SCH_ACA_IMP+SCH_MAT_RES+SCH_DIS+SCH_ADV+COM_N+ (1+STU_ENG+STU_CON+STU_LIK+STU_RES|IDSCHOOL), data=subset(TIMSS, Year == 2019),control=lmerControl(optimizer="optimx", 
                                      calc.derivs=FALSE,
                                      optCtrl=list(method="nlminb", 
                                                   starttests=FALSE, 
                                                   kkt=FALSE)))
sjPlot::tab_model(m0b, digits=3, digits.re=3, show.se = TRUE)

	STU_BUL
Predictors	Estimates	std. Error	CI	p
(Intercept)	2.777	0.063	2.652 – 2.901	<0.001
STU ENG	0.031	0.010	0.011 – 0.052	0.002
STU CON	-0.015	0.011	-0.037 – 0.007	0.173
STU LIK	-0.001	0.011	-0.022 – 0.021	0.932
STU RES	0.011	0.011	-0.011 – 0.033	0.334
SCH ACA IMP	-0.015	0.013	-0.042 – 0.011	0.251
SCH MAT RES	0.003	0.016	-0.028 – 0.035	0.827
SCH DIS	0.014	0.016	-0.017 – 0.045	0.367
SCH ADV	0.011	0.013	-0.015 – 0.036	0.413
COM N	-0.003	0.005	-0.013 – 0.007	0.607
Random Effects
σ²	0.123
τ₀₀ _IDSCHOOL	0.041
τ₁₁ _{IDSCHOOL.STU_ENG}	0.003
τ₁₁ _{IDSCHOOL.STU_CON}	0.001
τ₁₁ _{IDSCHOOL.STU_LIK}	0.000
τ₁₁ _{IDSCHOOL.STU_RES}	0.002
ρ₀₁	-0.845
	-0.419
	0.806
	-0.597
N _IDSCHOOL	178
Observations	4180
Marginal R² / Conditional R²	0.005 / NA

lmerTest::ranova(m0b)

ANOVA-like table for random-effects: Single term deletions

Model:
STU_BUL ~ STU_ENG + STU_CON + STU_LIK + STU_RES + SCH_ACA_IMP + SCH_MAT_RES + SCH_DIS + SCH_ADV + COM_N + (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)
                                                                  npar logLik
<none>                                                              26  -1654
STU_ENG in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)   21  -1660
STU_CON in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)   21  -1655
STU_LIK in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)   21  -1654
STU_RES in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)   21  -1656
                                                                   AIC    LRT
<none>                                                            3360       
STU_ENG in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL) 3362 11.840
STU_CON in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL) 3351  0.852
STU_LIK in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL) 3351  0.742
STU_RES in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL) 3353  2.683
                                                                  Df Pr(>Chisq)
<none>                                                                         
STU_ENG in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)  5      0.037
STU_CON in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)  5      0.974
STU_LIK in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)  5      0.981
STU_RES in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)  5      0.749

# ICC
r.squaredGLMM(m0b)[2]

[1] 0.0482729

3.2.3 學校氣氛為依變項

m0c <- lme4::lmer(STU_BEL ~ STU_ENG+STU_CON+STU_LIK+STU_RES+SCH_ACA_IMP+SCH_MAT_RES+SCH_DIS+SCH_ADV+COM_N+ (1+STU_ENG+STU_CON+STU_LIK+STU_RES|IDSCHOOL), data=subset(TIMSS, Year == 2019),control=lmerControl(optimizer="optimx", 
                                      calc.derivs=FALSE,
                                      optCtrl=list(method="nlminb", 
                                                   starttests=FALSE, 
                                                   kkt=FALSE)))
sjPlot::tab_model(m0c, digits=3, digits.re=3, show.se = TRUE)

	STU_BEL
Predictors	Estimates	std. Error	CI	p
(Intercept)	1.095	0.127	0.847 – 1.344	<0.001
STU ENG	0.261	0.017	0.228 – 0.294	<0.001
STU CON	-0.113	0.018	-0.149 – -0.077	<0.001
STU LIK	0.167	0.019	0.129 – 0.204	<0.001
STU RES	0.029	0.018	-0.006 – 0.064	0.109
SCH ACA IMP	0.002	0.028	-0.054 – 0.057	0.954
SCH MAT RES	0.014	0.033	-0.051 – 0.079	0.675
SCH DIS	0.042	0.033	-0.022 – 0.107	0.201
SCH ADV	0.044	0.028	-0.010 – 0.098	0.113
COM N	-0.002	0.011	-0.023 – 0.019	0.880
Random Effects
σ²	0.322
τ₀₀ _IDSCHOOL	0.023
τ₁₁ _{IDSCHOOL.STU_ENG}	0.009
τ₁₁ _{IDSCHOOL.STU_CON}	0.003
τ₁₁ _{IDSCHOOL.STU_LIK}	0.009
τ₁₁ _{IDSCHOOL.STU_RES}	0.002
ρ₀₁	-0.616
	-0.358
	0.217
	0.696
ICC	0.087
N _IDSCHOOL	178
Observations	4180
Marginal R² / Conditional R²	0.119 / 0.196

lmerTest::ranova(m0c)

ANOVA-like table for random-effects: Single term deletions

Model:
STU_BEL ~ STU_ENG + STU_CON + STU_LIK + STU_RES + SCH_ACA_IMP + SCH_MAT_RES + SCH_DIS + SCH_ADV + COM_N + (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)
                                                                  npar logLik
<none>                                                              26  -3711
STU_ENG in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)   21  -3714
STU_CON in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)   21  -3712
STU_LIK in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)   21  -3712
STU_RES in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)   21  -3711
                                                                   AIC   LRT Df
<none>                                                            7473         
STU_ENG in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL) 7470 6.964  5
STU_CON in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL) 7467 3.511  5
STU_LIK in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL) 7466 3.078  5
STU_RES in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL) 7465 1.678  5
                                                                  Pr(>Chisq)
<none>                                                                      
STU_ENG in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)      0.223
STU_CON in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)      0.622
STU_LIK in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)      0.688
STU_RES in (1 + STU_ENG + STU_CON + STU_LIK + STU_RES | IDSCHOOL)      0.892

# ICC
r.squaredGLMM(m0c)[2]

[1] 0.195793

TIMSS 2015 & 2019

Ching-Yuan Chang

2023-01-07