library(lme4)
## Loading required package: Matrix
library(nlme)
##
## Attaching package: 'nlme'
## The following object is masked from 'package:lme4':
##
## lmList
Achieve <- read.csv("Achieve.csv")
Model4.1 <- lme( fixed = geread~1, random = ~1|school/class, data = Achieve)
summary(Model4.1)
## Linear mixed-effects model fit by REML
## Data: Achieve
## AIC BIC logLik
## 46154 46182.97 -23073
##
## Random effects:
## Formula: ~1 | school
## (Intercept)
## StdDev: 0.5583923
##
## Formula: ~1 | class %in% school
## (Intercept) Residual
## StdDev: 0.5221676 2.201589
##
## Fixed effects: geread ~ 1
## Value Std.Error DF t-value p-value
## (Intercept) 4.30806 0.05499164 9752 78.34027 0
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -2.3052003 -0.6289603 -0.2093700 0.3049085 3.8673234
##
## Number of Observations: 10320
## Number of Groups:
## school class %in% school
## 160 568
intervals(Model4.1)
## Approximate 95% confidence intervals
##
## Fixed effects:
## lower est. upper
## (Intercept) 4.200265 4.30806 4.415855
## attr(,"label")
## [1] "Fixed effects:"
##
## Random Effects:
## Level: school
## lower est. upper
## sd((Intercept)) 0.4702517 0.5583923 0.6630533
## Level: class
## lower est. upper
## sd((Intercept)) 0.4545912 0.5221676 0.5997895
##
## Within-group standard error:
## lower est. upper
## 2.170908 2.201589 2.232704
Model4.2 <- lme( fixed = geread~gevocab+clenroll+cenroll, random = ~1|school/class, data = Achieve)
summary(Model4.2)
## Linear mixed-effects model fit by REML
## Data: Achieve
## AIC BIC logLik
## 43144.87 43195.56 -21565.43
##
## Random effects:
## Formula: ~1 | school
## (Intercept)
## StdDev: 0.2766194
##
## Formula: ~1 | class %in% school
## (Intercept) Residual
## StdDev: 0.3007871 1.922991
##
## Fixed effects: geread ~ gevocab + clenroll + cenroll
## Value Std.Error DF t-value p-value
## (Intercept) 1.6751266 0.20809605 9751 8.04978 0.0000
## gevocab 0.5075566 0.00842654 9751 60.23313 0.0000
## clenroll 0.0189860 0.00955860 407 1.98628 0.0477
## cenroll -0.0000037 0.00000364 158 -1.02193 0.3084
## Correlation:
## (Intr) gevocb clnrll
## gevocab -0.124
## clenroll -0.961 -0.062
## cenroll -0.134 0.025 -0.007
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -3.2211629 -0.5672782 -0.2079045 0.3183508 4.4736276
##
## Number of Observations: 10320
## Number of Groups:
## school class %in% school
## 160 568
Model4.3 <- lme( fixed = geread~gevocab+clenroll+cenroll+gevocab*cenroll, random = ~1|school/class, data = Achieve)
summary(Model4.3)
## Linear mixed-effects model fit by REML
## Data: Achieve
## AIC BIC logLik
## 43167.75 43225.69 -21575.88
##
## Random effects:
## Formula: ~1 | school
## (Intercept)
## StdDev: 0.2740961
##
## Formula: ~1 | class %in% school
## (Intercept) Residual
## StdDev: 0.2975919 1.923059
##
## Fixed effects: geread ~ gevocab + clenroll + cenroll + gevocab * cenroll
## Value Std.Error DF t-value p-value
## (Intercept) 1.7515430 0.20999286 9750 8.34096 0.0000
## gevocab 0.4899998 0.01168332 9750 41.94013 0.0000
## clenroll 0.0188007 0.00951172 407 1.97659 0.0488
## cenroll -0.0000132 0.00000563 158 -2.33721 0.0207
## gevocab:cenroll 0.0000023 0.00000107 9750 2.18957 0.0286
## Correlation:
## (Intr) gevocb clnrll cenrll
## gevocab -0.203
## clenroll -0.949 -0.041
## cenroll -0.212 0.542 0.000
## gevocab:cenroll 0.166 -0.693 -0.007 -0.766
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -3.1901563 -0.5682666 -0.2060729 0.3183307 4.4723839
##
## Number of Observations: 10320
## Number of Groups:
## school class %in% school
## 160 568
Model4.4 <- lme( fixed = geread~1, random = ~1|corp/school/class, data = Achieve)
summary(Model4.4)
## Linear mixed-effects model fit by REML
## Data: Achieve
## AIC BIC logLik
## 46113.22 46149.43 -23051.61
##
## Random effects:
## Formula: ~1 | corp
## (Intercept)
## StdDev: 0.4209979
##
## Formula: ~1 | school %in% corp
## (Intercept)
## StdDev: 0.295833
##
## Formula: ~1 | class %in% school %in% corp
## (Intercept) Residual
## StdDev: 0.5247746 2.201587
##
## Fixed effects: geread ~ 1
## Value Std.Error DF t-value p-value
## (Intercept) 4.32583 0.07197848 9752 60.09894 0
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -2.2995234 -0.6304742 -0.2130696 0.3028624 3.9448255
##
## Number of Observations: 10320
## Number of Groups:
## corp school %in% corp
## 59 160
## class %in% school %in% corp
## 568
intervals(Model4.4)
## Approximate 95% confidence intervals
##
## Fixed effects:
## lower est. upper
## (Intercept) 4.184738 4.32583 4.466923
## attr(,"label")
## [1] "Fixed effects:"
##
## Random Effects:
## Level: corp
## lower est. upper
## sd((Intercept)) 0.321723 0.4209979 0.5509065
## Level: school
## lower est. upper
## sd((Intercept)) 0.2003532 0.295833 0.4368144
## Level: class
## lower est. upper
## sd((Intercept)) 0.4578135 0.5247746 0.6015295
##
## Within-group standard error:
## lower est. upper
## 2.170912 2.201587 2.232695
Model4.5 <- lme( fixed = geread~gevocab+gender, random = ~gender|school/class, data = Achieve)
summary(Model4.5)
## Linear mixed-effects model fit by REML
## Data: Achieve
## AIC BIC logLik
## 43127.93 43200.35 -21553.97
##
## Random effects:
## Formula: ~gender | school
## Structure: General positive-definite, Log-Cholesky parametrization
## StdDev Corr
## (Intercept) 0.2207298 (Intr)
## gender 0.1101379 -0.019
##
## Formula: ~gender | class %in% school
## Structure: General positive-definite, Log-Cholesky parametrization
## StdDev Corr
## (Intercept) 0.302941367 (Intr)
## gender 0.004914493 -0.022
## Residual 1.922517135
##
## Fixed effects: geread ~ gevocab + gender
## Value Std.Error DF t-value p-value
## (Intercept) 2.0150114 0.07570370 9750 26.61708 0.0000
## gevocab 0.5091256 0.00840838 9750 60.54976 0.0000
## gender 0.0175517 0.03929581 9750 0.44666 0.6551
## Correlation:
## (Intr) gevocb
## gevocab -0.527
## gender -0.758 0.039
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -3.2117003 -0.5676457 -0.2072293 0.3161412 4.4474380
##
## Number of Observations: 10320
## Number of Groups:
## school class %in% school
## 160 568
Model4.6 <- lme( fixed = geread~gevocab+gender, random = list(school = ~1, class = ~gender), data = Achieve)
summary(Model4.6)
## Linear mixed-effects model fit by REML
## Data: Achieve
## AIC BIC logLik
## 43125.18 43183.11 -21554.59
##
## Random effects:
## Formula: ~1 | school
## (Intercept)
## StdDev: 0.2737238
##
## Formula: ~gender | class %in% school
## Structure: General positive-definite, Log-Cholesky parametrization
## StdDev Corr
## (Intercept) 0.3623693 (Intr)
## gender 0.1651168 -0.563
## Residual 1.9215122
##
## Fixed effects: geread ~ gevocab + gender
## Value Std.Error DF t-value p-value
## (Intercept) 2.0128841 0.07726503 9750 26.05168 0.0000
## gevocab 0.5090473 0.00841459 9750 60.49582 0.0000
## gender 0.0190565 0.03880626 9750 0.49107 0.6234
## Correlation:
## (Intr) gevocb
## gevocab -0.516
## gender -0.768 0.039
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -3.2117225 -0.5676842 -0.2072084 0.3182780 4.4324392
##
## Number of Observations: 10320
## Number of Groups:
## school class %in% school
## 160 568
Model4.7 <- lmer(geread~1+(1|school/class), data = Achieve)
summary(Model4.7)
## Linear mixed model fit by REML ['lmerMod']
## Formula: geread ~ 1 + (1 | school/class)
## Data: Achieve
##
## REML criterion at convergence: 46146
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.3052 -0.6290 -0.2094 0.3049 3.8673
##
## Random effects:
## Groups Name Variance Std.Dev.
## class:school (Intercept) 0.2727 0.5222
## school (Intercept) 0.3118 0.5584
## Residual 4.8470 2.2016
## Number of obs: 10320, groups: class:school, 568; school, 160
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 4.30806 0.05499 78.34
Model4.8 <- lmer( geread~gevocab+clenroll+cenroll+(1|school/class), data = Achieve)
## Warning: Some predictor variables are on very different scales: consider
## rescaling
summary(Model4.8)
## Linear mixed model fit by REML ['lmerMod']
## Formula: geread ~ gevocab + clenroll + cenroll + (1 | school/class)
## Data: Achieve
##
## REML criterion at convergence: 43130.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.2212 -0.5673 -0.2079 0.3184 4.4736
##
## Random effects:
## Groups Name Variance Std.Dev.
## class:school (Intercept) 0.09047 0.3008
## school (Intercept) 0.07652 0.2766
## Residual 3.69790 1.9230
## Number of obs: 10320, groups: class:school, 568; school, 160
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 1.675e+00 2.081e-01 8.05
## gevocab 5.076e-01 8.427e-03 60.23
## clenroll 1.899e-02 9.559e-03 1.99
## cenroll -3.721e-06 3.642e-06 -1.02
##
## Correlation of Fixed Effects:
## (Intr) gevocb clnrll
## gevocab -0.124
## clenroll -0.961 -0.062
## cenroll -0.134 0.025 -0.007
## fit warnings:
## Some predictor variables are on very different scales: consider rescaling
Model4.9 <- lmer( geread~gevocab+clenroll+cenroll+gevocab*cenroll+(1|school/class), data = Achieve)
## Warning: Some predictor variables are on very different scales: consider
## rescaling
summary(Model4.9)
## Linear mixed model fit by REML ['lmerMod']
## Formula: geread ~ gevocab + clenroll + cenroll + gevocab * cenroll + (1 |
## school/class)
## Data: Achieve
##
## REML criterion at convergence: 43151.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.1902 -0.5683 -0.2061 0.3183 4.4724
##
## Random effects:
## Groups Name Variance Std.Dev.
## class:school (Intercept) 0.08856 0.2976
## school (Intercept) 0.07513 0.2741
## Residual 3.69816 1.9231
## Number of obs: 10320, groups: class:school, 568; school, 160
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 1.752e+00 2.100e-01 8.34
## gevocab 4.900e-01 1.168e-02 41.94
## clenroll 1.880e-02 9.512e-03 1.98
## cenroll -1.316e-05 5.628e-06 -2.34
## gevocab:cenroll 2.340e-06 1.069e-06 2.19
##
## Correlation of Fixed Effects:
## (Intr) gevocb clnrll cenrll
## gevocab -0.203
## clenroll -0.949 -0.041
## cenroll -0.212 0.542 0.000
## gevcb:cnrll 0.166 -0.693 -0.007 -0.766
## fit warnings:
## Some predictor variables are on very different scales: consider rescaling
Model4.10 <- lmer( geread~1+(1|corp/school/class), data = Achieve)
summary(Model4.10)
## Linear mixed model fit by REML ['lmerMod']
## Formula: geread ~ 1 + (1 | corp/school/class)
## Data: Achieve
##
## REML criterion at convergence: 46103.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.2995 -0.6305 -0.2131 0.3029 3.9448
##
## Random effects:
## Groups Name Variance Std.Dev.
## class:(school:corp) (Intercept) 0.27539 0.5248
## school:corp (Intercept) 0.08748 0.2958
## corp (Intercept) 0.17726 0.4210
## Residual 4.84699 2.2016
## Number of obs: 10320, groups:
## class:(school:corp), 568; school:corp, 160; corp, 59
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 4.32583 0.07198 60.1
Model4.11 <- lmer( geread~gevocab+gender+(gender|school/class), data = Achieve)
summary(Model4.11)
## Linear mixed model fit by REML ['lmerMod']
## Formula: geread ~ gevocab + gender + (gender | school/class)
## Data: Achieve
##
## REML criterion at convergence: 43107.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.2043 -0.5680 -0.2069 0.3171 4.4455
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## class:school (Intercept) 0.148959 0.38595
## gender 0.019818 0.14078 -0.62
## school (Intercept) 0.033157 0.18209
## gender 0.006802 0.08247 0.58
## Residual 3.692434 1.92157
## Number of obs: 10320, groups: class:school, 568; school, 160
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 2.015564 0.075629 26.65
## gevocab 0.509097 0.008408 60.55
## gender 0.017237 0.039243 0.44
##
## Correlation of Fixed Effects:
## (Intr) gevocb
## gevocab -0.527
## gender -0.757 0.039