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summary(cars)## speed dist
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## Warning: package 'lme4' was built under R version 3.3.2## Loading required package: Matrix## Loading required package: nlme##
## Attaching package: 'nlme'## The following object is masked from 'package:lme4':
##
## lmList## Loading required package: MASS## Warning in checkMatrixPackageVersion(): Package version inconsistency detected.
## TMB was built with Matrix version 1.2.12
## Current Matrix version is 1.2.7.1
## Please re-install 'TMB' from source or ask CRAN for a binary version of 'TMB' matching CRAN's 'Matrix' package## neighid schid attain p7vrq p7read dadocc dadunemp daded momed male
## 1 675 0 0.7350 21.972 12.134 2.316 0 0 0 1
## 2 647 0 0.2641 -7.028 -12.866 16.196 0 0 1 0
## 3 650 0 -1.3276 -11.028 -31.866 -23.454 1 0 0 1
## 4 650 0 0.7350 3.972 3.134 2.316 0 0 0 1
## 5 648 0 -0.1325 -2.028 0.134 -3.454 0 0 0 0
## 6 648 0 0.5610 -5.028 -0.866 -3.454 0 0 0 0
## deprive dummy
## 1 -0.182 1
## 2 0.206 1
## 3 0.534 1
## 4 0.534 1
## 5 0.188 1
## 6 0.188 1### First Model:
first.model <- lmer(attain ~ (1|neighid), data = data, REML = FALSE )
summary (first.model)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: attain ~ (1 | neighid)
## Data: data
##
## AIC BIC logLik deviance df.resid
## 6422.0 6439.2 -3208.0 6416.0 2307
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.33164 -0.65532 0.01513 0.58177 2.96174
##
## Random effects:
## Groups Name Variance Std.Dev.
## neighid (Intercept) 0.2015 0.4489
## Residual 0.8044 0.8969
## Number of obs: 2310, groups: neighid, 524
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.08202 0.02844 2.885### different ways of caculating the Intra Class Correlation:
ICC <- (( 0.2024)/ (0.8044+0.2024))
ICC## [1] 0.201033icc(first.model)##
## Linear mixed model
## Family: gaussian (identity)
## Formula: attain ~ (1 | neighid)
##
## ICC (neighid): 0.200354RanEffects <- as.data.frame(VarCorr(first.model))
RanEffects## grp var1 var2 vcov sdcor
## 1 neighid (Intercept) <NA> 0.2015382 0.4489300
## 2 Residual <NA> <NA> 0.8043706 0.8968671ICC2<- RanEffects[1,4]/(RanEffects[1,4]+RanEffects[2,4])
ICC2## [1] 0.2003543### Second Model:
second.model <- lmer(attain ~ (deprive + 1|neighid), data = data, REML = FALSE)
summary(second.model)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: attain ~ (deprive + 1 | neighid)
## Data: data
##
## AIC BIC logLik deviance df.resid
## 6390.5 6419.3 -3190.3 6380.5 2305
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.49900 -0.63369 0.01618 0.60013 2.94292
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## neighid (Intercept) 0.07474 0.2734
## deprive 0.36897 0.6074 -0.78
## Residual 0.80904 0.8995
## Number of obs: 2310, groups: neighid, 524
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.002947 0.025754 0.114second.model2 <- lmer(attain ~ deprive + (1|neighid), data = data, REML = FALSE)
summary(second.model2)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: attain ~ deprive + (1 | neighid)
## Data: data
##
## AIC BIC logLik deviance df.resid
## 6273.6 6296.6 -3132.8 6265.6 2306
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.2846 -0.6513 0.0081 0.5848 3.4957
##
## Random effects:
## Groups Name Variance Std.Dev.
## neighid (Intercept) 0.08579 0.2929
## Residual 0.81220 0.9012
## Number of obs: 2310, groups: neighid, 524
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.09995 0.02367 4.222
## deprive -0.52077 0.03824 -13.619
##
## Correlation of Fixed Effects:
## (Intr)
## deprive -0.045## Third Model:
third.model <- lmer(attain ~ p7vrq+ p7read + dadocc + dadunemp + daded + momed + male + (1|deprive) + (1|neighid), data = data, REML = FALSE)
summary(third.model)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: attain ~ p7vrq + p7read + dadocc + dadunemp + daded + momed +
## male + (1 | deprive) + (1 | neighid)
## Data: data
##
## AIC BIC logLik deviance df.resid
## 4829.9 4893.1 -2403.9 4807.9 2299
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.1591 -0.6369 -0.0514 0.5938 3.5332
##
## Random effects:
## Groups Name Variance Std.Dev.
## neighid (Intercept) 1.344e-02 1.159e-01
## deprive (Intercept) 7.173e-16 2.678e-08
## Residual 4.567e-01 6.758e-01
## Number of obs: 2310, groups: neighid, 524; deprive, 458
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.077383 0.023439 3.301
## p7vrq 0.028441 0.002268 12.540
## p7read 0.026825 0.001753 15.298
## dadocc 0.009311 0.001359 6.852
## dadunemp -0.143593 0.046878 -3.063
## daded 0.148176 0.041067 3.608
## momed 0.067291 0.037698 1.785
## male -0.054457 0.028607 -1.904
##
## Correlation of Fixed Effects:
## (Intr) p7vrq p7read dadocc dadnmp daded momed
## p7vrq -0.105
## p7read 0.099 -0.775
## dadocc 0.103 -0.065 -0.095
## dadunemp -0.229 0.044 0.026 0.143
## daded -0.210 0.000 -0.066 -0.220 -0.005
## momed -0.236 -0.018 -0.025 -0.067 0.004 -0.420
## male -0.587 0.085 -0.051 0.010 0.021 -0.006 -0.013third.model2 <- lmer(attain ~ p7vrq+ p7read + dadocc + dadunemp + daded + momed + male + (deprive |neighid), data = data, REML = FALSE)
summary(third.model2)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: attain ~ p7vrq + p7read + dadocc + dadunemp + daded + momed +
## male + (deprive | neighid)
## Data: data
##
## AIC BIC logLik deviance df.resid
## 4828.8 4897.7 -2402.4 4804.8 2298
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.1819 -0.6364 -0.0511 0.5831 3.5409
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## neighid (Intercept) 0.006719 0.08197
## deprive 0.019078 0.13812 -0.92
## Residual 0.456744 0.67583
## Number of obs: 2310, groups: neighid, 524
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.069266 0.023331 2.969
## p7vrq 0.028439 0.002268 12.542
## p7read 0.026653 0.001754 15.198
## dadocc 0.009052 0.001362 6.646
## dadunemp -0.142212 0.046655 -3.048
## daded 0.145361 0.041163 3.531
## momed 0.066344 0.037743 1.758
## male -0.054007 0.028573 -1.890
##
## Correlation of Fixed Effects:
## (Intr) p7vrq p7read dadocc dadnmp daded momed
## p7vrq -0.104
## p7read 0.103 -0.775
## dadocc 0.118 -0.064 -0.094
## dadunemp -0.232 0.044 0.025 0.141
## daded -0.207 -0.001 -0.063 -0.218 -0.006
## momed -0.235 -0.017 -0.026 -0.065 0.004 -0.421
## male -0.590 0.084 -0.049 0.010 0.020 -0.006 -0.014third.model22 <- lmer(attain ~ p7vrq+ p7read + dadocc + dadunemp + daded + momed + male + deprive + (1|neighid), data = data, REML = FALSE)
summary(third.model22)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: attain ~ p7vrq + p7read + dadocc + dadunemp + daded + momed +
## male + deprive + (1 | neighid)
## Data: data
##
## AIC BIC logLik deviance df.resid
## 4797.0 4860.2 -2387.5 4775.0 2299
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.9354 -0.6413 -0.0348 0.5706 3.5381
##
## Random effects:
## Groups Name Variance Std.Dev.
## neighid (Intercept) 0.006228 0.07892
## Residual 0.456631 0.67574
## Number of obs: 2310, groups: neighid, 524
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.080731 0.022959 3.516
## p7vrq 0.027763 0.002256 12.306
## p7read 0.026065 0.001746 14.928
## dadocc 0.008239 0.001363 6.044
## dadunemp -0.114896 0.046830 -2.453
## daded 0.140966 0.040810 3.454
## momed 0.062405 0.037454 1.666
## male -0.055381 0.028434 -1.948
## deprive -0.148123 0.025331 -5.848
##
## Correlation of Fixed Effects:
## (Intr) p7vrq p7read dadocc dadnmp daded momed male
## p7vrq -0.108
## p7read 0.097 -0.767
## dadocc 0.100 -0.056 -0.083
## dadunemp -0.228 0.038 0.017 0.123
## daded -0.214 0.002 -0.063 -0.212 -0.009
## momed -0.240 -0.017 -0.023 -0.065 0.002 -0.419
## male -0.596 0.085 -0.050 0.011 0.020 -0.005 -0.013
## deprive -0.026 0.057 0.083 0.155 -0.110 0.038 0.023 0.006third.model222 <- lme(attain ~ p7vrq+ p7read + dadocc + dadunemp + daded + momed + male + deprive, random = ~ 1|neighid, data = data, method = "ML")
intervals(third.model222)## Approximate 95% confidence intervals
##
## Fixed effects:
## lower est. upper
## (Intercept) 0.03570236 0.080731083 0.1257598101
## p7vrq 0.02333831 0.027762947 0.0321875819
## p7read 0.02264061 0.026065173 0.0294897392
## dadocc 0.00556540 0.008238936 0.0109124723
## dadunemp -0.20674426 -0.114895833 -0.0230474062
## daded 0.06092473 0.140965706 0.2210066817
## momed -0.01105306 0.062405000 0.1358630632
## male -0.11114846 -0.055381414 0.0003856343
## deprive -0.19788602 -0.148123268 -0.0983605128
## attr(,"label")
## [1] "Fixed effects:"
##
## Random Effects:
## Level: neighid
## lower est. upper
## sd((Intercept)) 0.02669044 0.07891699 0.2333379
##
## Within-group standard error:
## lower est. upper
## 0.6544745 0.6757445 0.6977058