An Illustration of Mixed-effects Models on Taiwanese Students’ Math Literacy (A Brief Version)
陳思妤，吳靜芳
12/28 2020
1 Introduction
Note. A long version of this report was presented in class, which covered models and graphs with more details,
for more information, please refer to Final project01.Rmd. Thanks
- Multilevel mixed effects models are widely used in education and relevant disciplines,
to account for the correlated responses within clusters.
- the present study is an illustration of mixed effects model using the PISA 2012 data.
- The Program for International Student Assessment (PISA) is an international assessment that measures 15-year-old students’ reading, mathematics, and science literacy every three years.
- PISA was launched by the OECD in 1997, first administered in 2000 and now covers over 80 countries.
- PISA focuses on the application of skills and knowledge and presents problems in real-world contexts. It is intended to provide a measure of students’ overall preparedness for the future, not just their academic achievement.
- the literacy score was estimated using 3PL-IRT
2 Research variables:
DV: Math literacy
Random effect(School): (1| School)
Fixed effect(Students): Gender, problem-solving style, motivation, Anxiety
Problem-solving style(Approach/Avoidance):
1. Approach
2. Combo
3. No preference
Motivation:
1. Extrinsic
2. Intrinsic
3. Combo
4. Neither
Anxiety: Composite score
## StIDStd School AGE LMINS Gender ESCS Grade Mathlevel Anxiety Anxiety2
## 1 30 1 16.00 9997 1 -0.24 10 2 15 225
## 2 12 1 15.75 9997 1 -0.45 10 3 13 169
## 3 25 1 15.75 9997 1 0.10 10 4 13 169
## 4 23 1 16.17 9997 1 0.26 10 4 14 196
## 5 8 1 15.58 9997 1 0.71 10 5 15 225
## 6 24 1 16.25 9997 1 -0.31 10 5 20 400
## Anxiety3 Anxiety_Group Math_Group Math Grand_Math PS Motivation Remedial
## 1 3375 13.08333 623.0734 434.6549 -125.39966 3 1 0
## 2 2197 13.08333 623.0734 501.0983 -58.95630 3 1 0
## 3 2197 13.08333 623.0734 548.5356 -11.51902 3 4 0
## 4 2744 13.08333 623.0734 585.7688 25.71420 2 1 0
## 5 3375 13.08333 623.0734 666.6225 106.56794 3 1 0
## 6 8000 13.08333 623.0734 624.1704 64.11582 3 1 0
## low Excellence level_3 allmethod approach nopreference avoidance Intrinsic
## 1 1 0 1 1 0 0 0 0
## 2 0 0 2 1 0 0 0 0
## 3 0 0 2 1 0 0 0 0
## 4 0 0 2 0 1 0 0 0
## 5 0 0 3 1 0 0 0 0
## 6 0 0 3 1 0 0 0 0
## extrinsic combo NoMotivation Dicipline Q79_5 Q83_2 Q83_1 Q79_4 Q79_10 Q80_1
## 1 0 0 1 8 1 3 3 2 2 2
## 2 0 0 1 8 2 4 4 3 1 4
## 3 1 0 0 7 1 3 3 2 2 3
## 4 0 0 1 10 1 3 2 1 2 2
## 5 0 0 1 4 1 2 3 3 2 1
## 6 0 0 1 7 1 2 3 2 2 2
## Q80_4 Q82_2
## 1 3 4
## 2 2 4
## 3 3 4
## 4 3 3
## 5 2 3
## 6 2 3## 'data.frame': 1897 obs. of 38 variables:
## $ StIDStd : int 30 12 25 23 8 24 1 32 22 6 ...
## $ School : int 1 1 1 1 1 1 1 1 1 1 ...
## $ AGE : num 16 15.8 15.8 16.2 15.6 ...
## $ LMINS : int 9997 9997 9997 9997 9997 9997 9997 9997 9997 9997 ...
## $ Gender : int 1 1 1 1 1 1 1 1 1 1 ...
## $ ESCS : num -0.24 -0.45 0.1 0.26 0.71 -0.31 0.22 0.67 -0.41 -1.73 ...
## $ Grade : int 10 10 10 10 10 10 10 10 10 10 ...
## $ Mathlevel : int 2 3 4 4 5 5 5 5 6 6 ...
## $ Anxiety : int 15 13 13 14 15 20 12 14 9 15 ...
## $ Anxiety2 : int 225 169 169 196 225 400 144 196 81 225 ...
## $ Anxiety3 : int 3375 2197 2197 2744 3375 8000 1728 2744 729 3375 ...
## $ Anxiety_Group: num 13.1 13.1 13.1 13.1 13.1 ...
## $ Math_Group : num 623 623 623 623 623 ...
## $ Math : num 435 501 549 586 667 ...
## $ Grand_Math : num -125.4 -59 -11.5 25.7 106.6 ...
## $ PS : int 3 3 3 2 3 3 3 3 3 3 ...
## $ Motivation : int 1 1 4 1 1 1 4 3 4 3 ...
## $ Remedial : int 0 0 0 0 0 0 0 0 0 0 ...
## $ low : int 1 0 0 0 0 0 0 0 0 0 ...
## $ Excellence : int 0 0 0 0 0 0 0 0 1 1 ...
## $ level_3 : int 1 2 2 2 3 3 3 3 3 3 ...
## $ allmethod : int 1 1 1 0 1 1 1 1 1 1 ...
## $ approach : int 0 0 0 1 0 0 0 0 0 0 ...
## $ nopreference : int 0 0 0 0 0 0 0 0 0 0 ...
## $ avoidance : int 0 0 0 0 0 0 0 0 0 0 ...
## $ Intrinsic : int 0 0 0 0 0 0 0 0 0 0 ...
## $ extrinsic : int 0 0 1 0 0 0 1 0 1 0 ...
## $ combo : int 0 0 0 0 0 0 0 1 0 1 ...
## $ NoMotivation : int 1 1 0 1 1 1 0 0 0 0 ...
## $ Dicipline : int 8 8 7 10 4 7 8 11 5 5 ...
## $ Q79_5 : int 1 2 1 1 1 1 2 4 1 1 ...
## $ Q83_2 : int 3 4 3 3 2 2 3 4 2 3 ...
## $ Q83_1 : int 3 4 3 2 3 3 3 4 3 3 ...
## $ Q79_4 : int 2 3 2 1 3 2 2 2 1 1 ...
## $ Q79_10 : int 2 1 2 2 2 2 2 1 2 1 ...
## $ Q80_1 : int 2 4 3 2 1 2 3 4 2 3 ...
## $ Q80_4 : int 3 2 3 3 2 2 3 2 2 2 ...
## $ Q82_2 : int 4 4 4 3 3 3 3 4 2 3 ...3 Gender Difference in Math
m20<-lme4::lmer(Math ~ Gender+ (1| School), data=dta_project)
sjPlot::tab_model(m20, show.p=TRUE, show.r2 = FALSE )| Math | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 551.73 | 539.23 – 564.23 | <0.001 |
| Gender [Male] | 12.92 | 4.65 – 21.19 | 0.002 |
| Random Effects | |||
| σ2 | 6619.57 | ||
| τ00 School | 5315.91 | ||
| ICC | 0.45 | ||
| N School | 163 | ||
| Observations | 1897 | ||
summary(m20)## Linear mixed model fit by REML ['lmerMod']
## Formula: Math ~ Gender + (1 | School)
## Data: dta_project
##
## REML criterion at convergence: 22439.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.4313 -0.5925 0.0672 0.6664 3.1227
##
## Random effects:
## Groups Name Variance Std.Dev.
## School (Intercept) 5316 72.91
## Residual 6620 81.36
## Number of obs: 1897, groups: School, 163
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 551.730 6.377 86.525
## GenderMale 12.923 4.220 3.063
##
## Correlation of Fixed Effects:
## (Intr)
## GenderMale -0.331
3.1 Gender Difference in Anxiety
m21<-lme4::lmer(Anxiety ~ Gender+(1| School), data=dta_project)
sjPlot::tab_model(m21, show.p=TRUE, show.r2 = FALSE )| Anxiety | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 13.72 | 13.51 – 13.92 | <0.001 |
| Gender [Male] | -1.15 | -1.43 – -0.87 | <0.001 |
| Random Effects | |||
| σ2 | 9.55 | ||
| τ00 School | 0.15 | ||
| ICC | 0.02 | ||
| N School | 163 | ||
| Observations | 1897 | ||
summary(m21)## Linear mixed model fit by REML ['lmerMod']
## Formula: Anxiety ~ Gender + (1 | School)
## Data: dta_project
##
## REML criterion at convergence: 9694.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.8519 -0.5738 -0.1053 0.6457 2.4611
##
## Random effects:
## Groups Name Variance Std.Dev.
## School (Intercept) 0.150 0.3873
## Residual 9.548 3.0900
## Number of obs: 1897, groups: School, 163
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 13.7158 0.1056 129.846
## GenderMale -1.1489 0.1446 -7.944
##
## Correlation of Fixed Effects:
## (Intr)
## GenderMale -0.6824 PS MO and Anxiety with Math (Models with Random intercept)
4.1 PS
m22<-lme4::lmer(Math ~ PS+(1| School), data=dta_project)
sjPlot::tab_model(m22, show.p=TRUE, show.r2 = FALSE )| Math | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 505.06 | 484.12 – 525.99 | <0.001 |
| PS [Approach] | 66.44 | 41.72 – 91.17 | <0.001 |
| PS [Combo] | 55.14 | 36.84 – 73.44 | <0.001 |
| Random Effects | |||
| σ2 | 6539.56 | ||
| τ00 School | 5126.35 | ||
| ICC | 0.44 | ||
| N School | 163 | ||
| Observations | 1897 | ||
summary(m22)## Linear mixed model fit by REML ['lmerMod']
## Formula: Math ~ PS + (1 | School)
## Data: dta_project
##
## REML criterion at convergence: 22404.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3919 -0.5905 0.0591 0.6690 3.0377
##
## Random effects:
## Groups Name Variance Std.Dev.
## School (Intercept) 5126 71.60
## Residual 6540 80.87
## Number of obs: 1897, groups: School, 163
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 505.055 10.683 47.277
## PSApproach 66.443 12.613 5.268
## PSCombo 55.140 9.337 5.905
##
## Correlation of Fixed Effects:
## (Intr) PSAppr
## PSApproach -0.617
## PSCombo -0.832 0.7064.2 MO
m22<-lme4::lmer(Math ~ Motivation+(1| School), data=dta_project)
sjPlot::tab_model(m22, show.p=TRUE, show.r2 = FALSE )| Math | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 528.66 | 516.22 – 541.11 | <0.001 |
| Motivation [Intrinsic] | 58.77 | 45.36 – 72.18 | <0.001 |
| Motivation [Both] | 60.63 | 50.87 – 70.39 | <0.001 |
| Motivation [Extrinsic] | 24.42 | 15.17 – 33.66 | <0.001 |
| Random Effects | |||
| σ2 | 6106.12 | ||
| τ00 School | 4792.00 | ||
| ICC | 0.44 | ||
| N School | 163 | ||
| Observations | 1897 | ||
summary(m22)## Linear mixed model fit by REML ['lmerMod']
## Formula: Math ~ Motivation + (1 | School)
## Data: dta_project
##
## REML criterion at convergence: 22270.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.7568 -0.5943 0.0505 0.6716 2.7790
##
## Random effects:
## Groups Name Variance Std.Dev.
## School (Intercept) 4792 69.22
## Residual 6106 78.14
## Number of obs: 1897, groups: School, 163
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 528.662 6.350 83.251
## MotivationIntrinsic 58.770 6.840 8.592
## MotivationBoth 60.627 4.979 12.176
## MotivationExtrinsic 24.415 4.717 5.176
##
## Correlation of Fixed Effects:
## (Intr) MtvtnI MtvtnB
## MtvtnIntrns -0.256
## MotivatnBth -0.358 0.335
## MtvtnExtrns -0.373 0.348 0.4874.3 Anxiety and Math
m15<- lme4::lmer(Math ~ Anxiety+ (1| School), data=dta_project)
sjPlot::tab_model(m15, show.p=TRUE, show.r2 = FALSE )| Math | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 663.71 | 644.62 – 682.80 | <0.001 |
| Anxiety | -8.03 | -9.19 – -6.86 | <0.001 |
| Random Effects | |||
| σ2 | 6052.94 | ||
| τ00 School | 5008.32 | ||
| ICC | 0.45 | ||
| N School | 163 | ||
| Observations | 1897 | ||
summary(m15)## Linear mixed model fit by REML ['lmerMod']
## Formula: Math ~ Anxiety + (1 | School)
## Data: dta_project
##
## REML criterion at convergence: 22278.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.7688 -0.5768 0.0999 0.6635 2.7423
##
## Random effects:
## Groups Name Variance Std.Dev.
## School (Intercept) 5008 70.77
## Residual 6053 77.80
## Number of obs: 1897, groups: School, 163
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 663.7082 9.7398 68.14
## Anxiety -8.0280 0.5935 -13.53
##
## Correlation of Fixed Effects:
## (Intr)
## Anxiety -0.8015 Question 3-1: the interactive relationship between anxiety and PS
5.1 lm
m19<-lm(Math ~ Gender+ PS*Anxiety, data=dta_project)
sjPlot::tab_model(m19, show.p=TRUE, show.r2 = FALSE )| Math | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 491.09 | 396.68 – 585.49 | <0.001 |
| Gender [Male] | 2.02 | -7.44 – 11.48 | 0.675 |
| PS [Approach] | 157.95 | 32.88 – 283.02 | 0.013 |
| PS [Combo] | 207.62 | 111.53 – 303.71 | <0.001 |
| Anxiety | -1.14 | -8.21 – 5.94 | 0.752 |
| PS [Approach] * Anxiety | -5.21 | -14.93 – 4.50 | 0.293 |
| PS [Combo] * Anxiety | -9.07 | -16.30 – -1.84 | 0.014 |
| Observations | 1897 | ||
summary(m19)##
## Call:
## lm(formula = Math ~ Gender + PS * Anxiety, data = dta_project)
##
## Residuals:
## Min 1Q Median 3Q Max
## -355.89 -66.91 5.92 73.68 300.27
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 491.087 48.135 10.202 < 2e-16 ***
## GenderMale 2.021 4.825 0.419 0.6754
## PSApproach 157.948 63.770 2.477 0.0133 *
## PSCombo 207.622 48.995 4.238 2.37e-05 ***
## Anxiety -1.138 3.607 -0.315 0.7524
## PSApproach:Anxiety -5.215 4.956 -1.052 0.2928
## PSCombo:Anxiety -9.065 3.686 -2.459 0.0140 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 103.1 on 1890 degrees of freedom
## Multiple R-squared: 0.11, Adjusted R-squared: 0.1072
## F-statistic: 38.93 on 6 and 1890 DF, p-value: < 2.2e-165.2 lmm
m18<- lme4::lmer(Math ~ Gender+ PS*Anxiety+ (1| School), data=dta_project)
sjPlot::tab_model(m18, show.p=TRUE, show.r2 = FALSE )| Math | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 546.80 | 472.54 – 621.05 | <0.001 |
| Gender [Male] | 5.72 | -2.24 – 13.68 | 0.159 |
| PS [Approach] | 95.93 | -1.44 – 193.29 | 0.053 |
| PS [Combo] | 119.32 | 44.66 – 193.99 | 0.002 |
| Anxiety | -3.44 | -8.94 – 2.05 | 0.219 |
| PS [Approach] * Anxiety | -2.73 | -10.28 – 4.83 | 0.479 |
| PS [Combo] * Anxiety | -4.79 | -10.40 – 0.82 | 0.095 |
| Random Effects | |||
| σ2 | 5934.41 | ||
| τ00 School | 4809.07 | ||
| ICC | 0.45 | ||
| N School | 163 | ||
| Observations | 1897 | ||
summary(m18)## Linear mixed model fit by REML ['lmerMod']
## Formula: Math ~ Gender + PS * Anxiety + (1 | School)
## Data: dta_project
##
## REML criterion at convergence: 22208.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.5802 -0.5672 0.0814 0.6663 2.7211
##
## Random effects:
## Groups Name Variance Std.Dev.
## School (Intercept) 4809 69.35
## Residual 5934 77.04
## Number of obs: 1897, groups: School, 163
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 546.795 37.884 14.433
## GenderMale 5.718 4.061 1.408
## PSApproach 95.928 49.677 1.931
## PSCombo 119.324 38.097 3.132
## Anxiety -3.444 2.804 -1.228
## PSApproach:Anxiety -2.728 3.855 -0.708
## PSCombo:Anxiety -4.786 2.863 -1.672
##
## Correlation of Fixed Effects:
## (Intr) GndrMl PSAppr PSComb Anxity PSAp:A
## GenderMale -0.125
## PSApproach -0.744 0.043
## PSCombo -0.962 0.038 0.734
## Anxiety -0.960 0.060 0.733 0.948
## PSApprch:An 0.701 -0.032 -0.970 -0.693 -0.731
## PSCmb:Anxty 0.935 -0.024 -0.714 -0.972 -0.976 0.7136 Question 3-2: the 2-way interactive relationship between anxiety and Motivation for different Gender
6.1 lm
m20<-lm(Math ~ Gender+ Motivation*Anxiety, data=dta_project)
summary(m20)##
## Call:
## lm(formula = Math ~ Gender + Motivation * Anxiety, data = dta_project)
##
## Residuals:
## Min 1Q Median 3Q Max
## -334.29 -68.21 4.55 71.13 297.04
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 543.927 18.831 28.884 < 2e-16 ***
## GenderMale -5.398 4.751 -1.136 0.256063
## MotivationIntrinsic 128.493 37.326 3.442 0.000589 ***
## MotivationBoth 203.334 25.674 7.920 4.03e-15 ***
## MotivationExtrinsic 152.680 28.318 5.392 7.86e-08 ***
## Anxiety -1.616 1.284 -1.259 0.208153
## MotivationIntrinsic:Anxiety -4.637 2.922 -1.587 0.112700
## MotivationBoth:Anxiety -10.492 1.967 -5.333 1.08e-07 ***
## MotivationExtrinsic:Anxiety -8.205 1.985 -4.134 3.73e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 100.8 on 1888 degrees of freedom
## Multiple R-squared: 0.1491, Adjusted R-squared: 0.1455
## F-statistic: 41.35 on 8 and 1888 DF, p-value: < 2.2e-166.2 lmm
m21<- lme4::lmer(Math ~ Gender+ Motivation*Anxiety+ (1| School), data=dta_project)
sjPlot::tab_model(m21, show.p=TRUE, show.r2 = FALSE )| Math | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 565.56 | 534.85 – 596.26 | <0.001 |
| Gender [Male] | 0.64 | -7.22 – 8.51 | 0.873 |
| Motivation [Intrinsic] | 102.68 | 45.66 – 159.71 | <0.001 |
| Motivation [Both] | 136.60 | 97.15 – 176.05 | <0.001 |
| Motivation [Extrinsic] | 89.18 | 45.90 – 132.47 | <0.001 |
| Anxiety | -2.65 | -4.61 – -0.68 | 0.008 |
|
Motivation [Intrinsic] * Anxiety |
-4.09 | -8.55 – 0.37 | 0.072 |
|
Motivation [Both] * Anxiety |
-7.12 | -10.13 – -4.10 | <0.001 |
|
Motivation [Extrinsic] * Anxiety |
-4.72 | -7.75 – -1.69 | 0.002 |
| Random Effects | |||
| σ2 | 5734.26 | ||
| τ00 School | 4589.81 | ||
| ICC | 0.44 | ||
| N School | 163 | ||
| Observations | 1897 | ||
summary(m21)## Linear mixed model fit by REML ['lmerMod']
## Formula: Math ~ Gender + Motivation * Anxiety + (1 | School)
## Data: dta_project
##
## REML criterion at convergence: 22135.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.4936 -0.5907 0.0762 0.6634 2.6615
##
## Random effects:
## Groups Name Variance Std.Dev.
## School (Intercept) 4590 67.75
## Residual 5734 75.72
## Number of obs: 1897, groups: School, 163
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 565.5572 15.6655 36.102
## GenderMale 0.6404 4.0128 0.160
## MotivationIntrinsic 102.6822 29.0945 3.529
## MotivationBoth 136.5998 20.1255 6.787
## MotivationExtrinsic 89.1848 22.0860 4.038
## Anxiety -2.6455 1.0039 -2.635
## MotivationIntrinsic:Anxiety -4.0886 2.2747 -1.797
## MotivationBoth:Anxiety -7.1190 1.5384 -4.628
## MotivationExtrinsic:Anxiety -4.7175 1.5466 -3.050
##
## Correlation of Fixed Effects:
## (Intr) GndrMl MtvtnI MtvtnB MtvtnE Anxity MtvI:A MtvB:A
## GenderMale -0.186
## MtvtnIntrns -0.458 -0.005
## MotivatnBth -0.657 -0.016 0.358
## MtvtnExtrns -0.601 0.008 0.325 0.468
## Anxiety -0.911 0.081 0.483 0.694 0.630
## MtvtnIntr:A 0.396 0.000 -0.972 -0.309 -0.278 -0.438
## MtvtnBth:An 0.582 -0.012 -0.314 -0.966 -0.409 -0.645 0.286
## MtvtnExtr:A 0.579 -0.009 -0.312 -0.451 -0.978 -0.639 0.281 0.4166.3 the 2-way interaction graph
- Figure 1a
ggplot(data=dta_project)+geom_smooth(mapping = aes(x=Anxiety, y=Math, color= Motivation))## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
- Figure 1b
ggplot(data=dta_project)+geom_smooth(mapping = aes(x=Anxiety, y=Math))+facet_grid(.~Motivation)## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
# Conclusion & Limitations - To decrease the risk of being classified as remedial students, promoting students to solve problem or
increase any type of Motivation seems to viable approaches. - motivation’ and ‘Anxiety’ were more important to math excellence. - Girls are more likely to exhibit math anxiety and to be devoid of motivation. - Correlated data, exercise caution in interpretation. - missing values issue.
7 Supplementary information：
Remedial students
m9<- lme4::glmer(Remedial ~ Gender+ Motivation +PS+ Anxiety+ (1| School), data=dta_project, family=binomial)## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.0596727 (tol = 0.002, component 1)sjPlot::tab_model(m9, show.p=TRUE, show.r2 = FALSE )| Remedial | |||
|---|---|---|---|
| Predictors | Odds Ratios | CI | p |
| (Intercept) | 0.22 | 0.08 – 0.61 | 0.003 |
| Gender [Male] | 1.22 | 0.86 – 1.73 | 0.265 |
| Motivation [Intrinsic] | 0.24 | 0.11 – 0.51 | <0.001 |
| Motivation [Both] | 0.33 | 0.20 – 0.54 | <0.001 |
| Motivation [Extrinsic] | 0.63 | 0.43 – 0.92 | 0.016 |
| PS [Approach] | 0.21 | 0.08 – 0.54 | 0.001 |
| PS [Combo] | 0.24 | 0.14 – 0.43 | <0.001 |
| Anxiety | 1.05 | 0.99 – 1.11 | 0.085 |
| Random Effects | |||
| σ2 | 3.29 | ||
| τ00 School | 1.69 | ||
| ICC | 0.34 | ||
| N School | 163 | ||
| Observations | 1897 | ||
summary (m9)## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: Remedial ~ Gender + Motivation + PS + Anxiety + (1 | School)
## Data: dta_project
##
## AIC BIC logLik deviance df.resid
## 1213.3 1263.2 -597.7 1195.3 1888
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.5983 -0.3231 -0.2081 -0.1358 5.3702
##
## Random effects:
## Groups Name Variance Std.Dev.
## School (Intercept) 1.695 1.302
## Number of obs: 1897, groups: School, 163
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.50483 0.51349 -2.931 0.003383 **
## GenderMale 0.19804 0.17777 1.114 0.265280
## MotivationIntrinsic -1.43095 0.39111 -3.659 0.000254 ***
## MotivationBoth -1.10529 0.24936 -4.433 9.31e-06 ***
## MotivationExtrinsic -0.45848 0.19107 -2.400 0.016416 *
## PSApproach -1.57978 0.49289 -3.205 0.001350 **
## PSCombo -1.41788 0.29763 -4.764 1.90e-06 ***
## Anxiety 0.04798 0.02782 1.725 0.084579 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) GndrMl MtvtnI MtvtnB MtvtnE PSAppr PSComb
## GenderMale -0.289
## MtvtnIntrns -0.162 -0.011
## MotivatnBth -0.224 -0.134 0.197
## MtvtnExtrns -0.111 -0.015 0.201 0.345
## PSApproach -0.327 0.018 -0.044 0.014 0.002
## PSCombo -0.474 0.080 -0.022 -0.041 -0.068 0.545
## Anxiety -0.756 0.117 0.143 0.194 -0.007 0.023 -0.065
## convergence code: 0
## Model failed to converge with max|grad| = 0.0596727 (tol = 0.002, component 1)Math Excellence students
m10<- lme4::glmer(Excellence ~ Gender+ Motivation +PS+ Anxiety+ (1| School), data=dta_project, family=binomial)## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.135813 (tol = 0.002, component 1)sjPlot::tab_model(m10, show.p=TRUE, show.r2 = FALSE )| Excellence | |||
|---|---|---|---|
| Predictors | Odds Ratios | CI | p |
| (Intercept) | 0.59 | 0.15 – 2.25 | 0.437 |
| Gender [Male] | 1.07 | 0.75 – 1.52 | 0.711 |
| Motivation [Intrinsic] | 2.65 | 1.44 – 4.85 | 0.002 |
| Motivation [Both] | 3.53 | 2.18 – 5.71 | <0.001 |
| Motivation [Extrinsic] | 2.76 | 1.72 – 4.43 | <0.001 |
| PS [Approach] | 1.10 | 0.32 – 3.79 | 0.877 |
| PS [Combo] | 1.52 | 0.55 – 4.18 | 0.422 |
| Anxiety | 0.77 | 0.73 – 0.82 | <0.001 |
| Random Effects | |||
| σ2 | 3.29 | ||
| τ00 School | 3.32 | ||
| ICC | 0.50 | ||
| N School | 163 | ||
| Observations | 1897 | ||
summary (m10)## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: Excellence ~ Gender + Motivation + PS + Anxiety + (1 | School)
## Data: dta_project
##
## AIC BIC logLik deviance df.resid
## 1323.5 1373.5 -652.8 1305.5 1888
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.5271 -0.3311 -0.1729 -0.0828 11.0551
##
## Random effects:
## Groups Name Variance Std.Dev.
## School (Intercept) 3.319 1.822
## Number of obs: 1897, groups: School, 163
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.53229 0.68520 -0.777 0.43725
## GenderMale 0.06679 0.18004 0.371 0.71066
## MotivationIntrinsic 0.97367 0.30928 3.148 0.00164 **
## MotivationBoth 1.26061 0.24528 5.140 2.75e-07 ***
## MotivationExtrinsic 1.01633 0.24077 4.221 2.43e-05 ***
## PSApproach 0.09732 0.63067 0.154 0.87736
## PSCombo 0.41567 0.51808 0.802 0.42236
## Anxiety -0.25624 0.03103 -8.257 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) GndrMl MtvtnI MtvtnB MtvtnE PSAppr PSComb
## GenderMale -0.228
## MtvtnIntrns -0.198 -0.057
## MotivatnBth -0.279 -0.104 0.554
## MtvtnExtrns -0.155 -0.006 0.527 0.659
## PSApproach -0.633 0.073 -0.059 -0.041 -0.066
## PSCombo -0.721 0.063 -0.065 -0.066 -0.085 0.804
## Anxiety -0.566 0.092 0.113 0.183 -0.029 0.074 0.016
## convergence code: 0
## Model failed to converge with max|grad| = 0.135813 (tol = 0.002, component 1)