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library(foreign)
library(multilevel)## Loading required package: nlme## Loading required package: MASSlibrary(lme4)## Warning: package 'lme4' was built under R version 3.3.2## Loading required package: Matrix##
## Attaching package: 'lme4'## The following object is masked from 'package:nlme':
##
## lmListlibrary(MASS)
library(rockchalk)##
## Attaching package: 'rockchalk'## The following object is masked from 'package:MASS':
##
## mvrnormlibrary(psych)
library(sjstats)## 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##
## Attaching package: 'sjstats'## The following objects are masked from 'package:psych':
##
## pca, phisetwd("/Users/yahyaalshehri/Desktop/PhD Courses/Multilevel Modeling/mlmus3")
high_survey <- read.dta ("hsb.dta")
colnames(high_survey)## [1] "minority" "female" "ses" "mathach" "size" "sector"
## [7] "pracad" "disclim" "himinty" "schoolid" "mean" "sd"
## [13] "sdalt" "junk" "sdalt2" "num" "se" "sealt"
## [19] "sealt2" "t2" "t2alt" "pickone" "mmses" "mnses"
## [25] "xb" "resid"summarize(high_survey)## $numerics
## disclim female himinty junk mathach mean
## 0% -2.4160 0.0000 0.0000 0.0000 -2.8320 4.2398
## 25% -0.8170 0.0000 0.0000 7.0704 7.2750 10.8837
## 50% -0.2310 1.0000 0.0000 30.6254 13.1310 13.1601
## 75% 0.4600 1.0000 1.0000 75.1511 18.3170 14.6967
## 100% 2.7560 1.0000 1.0000 239.2892 24.9930 19.7191
## mean -0.1319 0.5282 0.2800 47.3160 12.7479 12.7479
## sd 0.9440 0.4992 0.4490 48.8976 6.8782 3.0058
## var 0.8911 0.2492 0.2016 2390.9763 47.3103 9.0349
## skewness 0.2394 -0.1129 0.9796 1.2998 -0.1805 -0.2712
## kurtosis -0.1588 -1.9875 -1.0405 1.4620 -0.9216 -0.0507
## NA's 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## N 7185.0000 7185.0000 7185.0000 7185.0000 7185.0000 7185.0000
## minority mmses mnses num pickone pracad
## 0% 0.0000 -1.1939 -1.1939 14.0000 0.0000 0.0000
## 25% 0.0000 -0.3230 -0.3230 41.0000 0.0000 0.3200
## 50% 0.0000 0.0320 0.0320 51.0000 0.0000 0.5300
## 75% 1.0000 0.3269 0.3269 57.0000 0.0000 0.7000
## 100% 1.0000 0.8250 0.8250 67.0000 1.0000 1.0000
## mean 0.2747 0.0001 0.0001 48.0163 0.0223 0.5345
## sd 0.4464 0.4135 0.4135 10.8222 0.1476 0.2512
## var 0.1993 0.1710 0.1710 117.1196 0.0218 0.0631
## skewness 1.0091 -0.2685 -0.2685 -0.5793 6.4739 0.1596
## kurtosis -0.9819 -0.4789 -0.4789 -0.3704 39.9171 -0.8859
## NA's 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## N 7185.0000 7185.0000 7185.0000 7185.0000 7185.0000 7185.0000
## resid schoolid sd sdalt sdalt2 se
## 0% -19.4889 1224.0000 3.5410 6.2563 48.3936 0.5059
## 25% -4.7643 3020.0000 5.5903 6.2563 48.3936 0.7798
## 50% 0.2358 5192.0000 6.2985 6.2563 48.3936 0.8939
## 75% 5.1619 7342.0000 6.7990 6.2563 48.3936 1.0323
## 100% 16.4446 9586.0000 8.4811 6.2563 48.3936 1.8237
## mean 0.0624 5277.8978 6.1975 6.2563 48.3936 0.9190
## sd 6.4595 2499.5778 0.8637 0.0000 0.0000 0.2017
## var 41.7246 6247889.1555 0.7460 0.0000 0.0000 0.0407
## skewness -0.1360 0.1074 -0.2358 NaN NaN 1.1132
## kurtosis -0.6856 -1.2546 0.2158 NaN NaN 2.3226
## NA's 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## N 7185.0000 7185.0000 7185.0000 7185.0000 7185.0000 7185.0000
## sealt sealt2 sector ses size t2
## 0% 0.7643 0.8499 0.0000 -3.7580 100.0000 0.0007
## 25% 0.8287 0.9214 0.0000 -0.5380 565.0000 1.0800
## 50% 0.8761 0.9741 0.0000 0.0020 1016.0000 5.7493
## 75% 0.9771 1.0864 1.0000 0.6020 1436.0000 15.7333
## 100% 1.6721 1.8592 1.0000 2.6920 2713.0000 195.8106
## mean 0.9246 1.0281 0.4931 0.0001 1056.8618 14.6558
## sd 0.1292 0.1437 0.5000 0.7794 604.1725 26.4160
## var 0.0167 0.0206 0.2500 0.6074 365024.4089 697.8054
## skewness 1.5869 1.5869 0.0276 -0.2281 0.5715 3.6684
## kurtosis 3.2496 3.2496 -1.9995 -0.3804 -0.3649 16.8883
## NA's 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## N 7185.0000 7185.0000 7185.0000 7185.0000 7185.0000 7185.0000
## t2alt xb
## 0% 0.0007 5.6839
## 25% 0.9578 10.7907
## 50% 4.3592 12.8722
## 75% 11.4854 14.6015
## 100% 52.8246 17.5219
## mean 8.5376 12.6855
## sd 11.0627 2.4248
## var 122.3842 5.8798
## skewness 2.0632 -0.2685
## kurtosis 4.2433 -0.4789
## NA's 0.0000 0.0000
## N 7185.0000 7185.0000
##
## $factors
## NULLhead(high_survey)## minority female ses mathach size sector pracad disclim himinty
## 1 0 1 -1.528 5.876 842 0 0.35 1.597 0
## 2 0 1 -0.588 19.708 842 0 0.35 1.597 0
## 3 0 0 -0.528 20.349 842 0 0.35 1.597 0
## 4 0 0 -0.668 8.781 842 0 0.35 1.597 0
## 5 0 0 -0.158 17.898 842 0 0.35 1.597 0
## 6 0 0 0.022 4.583 842 0 0.35 1.597 0
## schoolid mean sd sdalt junk sdalt2 num se
## 1 1224 9.715446 7.592785 6.256328 45.71077 48.39363 47 1.107522
## 2 1224 9.715446 7.592785 6.256328 49.99941 48.39363 47 1.107522
## 3 1224 9.715446 7.592785 6.256328 59.47536 48.39363 47 1.107522
## 4 1224 9.715446 7.592785 6.256328 14.86853 48.39363 47 1.107522
## 5 1224 9.715446 7.592785 6.256328 27.67840 48.39363 47 1.107522
## 6 1224 9.715446 7.592785 6.256328 64.86649 48.39363 47 1.107522
## sealt sealt2 t2 t2alt pickone mmses mnses
## 1 0.9125792 1.014718 6.958498 8.289523 1 -0.434383 -0.434383
## 2 0.9125792 1.014718 6.958498 8.289523 0 -0.434383 -0.434383
## 3 0.9125792 1.014718 6.958498 8.289523 0 -0.434383 -0.434383
## 4 0.9125792 1.014718 6.958498 8.289523 0 -0.434383 -0.434383
## 5 0.9125792 1.014718 6.958498 8.289523 0 -0.434383 -0.434383
## 6 0.9125792 1.014718 6.958498 8.289523 0 -0.434383 -0.434383
## xb resid
## 1 10.13759 -4.261589
## 2 10.13759 9.570412
## 3 10.13759 10.211412
## 4 10.13759 -1.356588
## 5 10.13759 7.760412
## 6 10.13759 -5.554588describe(high_survey)## vars n mean sd median trimmed mad min max
## minority 1 7185 0.27 0.45 0.00 0.22 0.00 0.00 1.00
## female 2 7185 0.53 0.50 1.00 0.54 0.00 0.00 1.00
## ses 3 7185 0.00 0.78 0.00 0.02 0.85 -3.76 2.69
## mathach 4 7185 12.75 6.88 13.13 12.91 8.12 -2.83 24.99
## size 5 7185 1056.86 604.17 1016.00 1011.71 661.24 100.00 2713.00
## sector 6 7185 0.49 0.50 0.00 0.49 0.00 0.00 1.00
## pracad 7 7185 0.53 0.25 0.53 0.53 0.27 0.00 1.00
## disclim 8 7185 -0.13 0.94 -0.23 -0.16 0.94 -2.42 2.76
## himinty 9 7185 0.28 0.45 0.00 0.23 0.00 0.00 1.00
## schoolid 10 7185 5277.90 2499.58 5192.00 5254.46 3192.04 1224.00 9586.00
## mean 11 7185 12.75 3.01 13.16 12.83 3.00 4.24 19.72
## sd 12 7185 6.20 0.86 6.30 6.22 0.95 3.54 8.48
## sdalt 13 7185 6.26 0.00 6.26 6.26 0.00 6.26 6.26
## junk 14 7185 47.32 48.90 30.63 39.84 40.62 0.00 239.29
## sdalt2 15 7185 48.39 0.00 48.39 48.39 0.00 48.39 48.39
## num 16 7185 48.02 10.82 51.00 48.72 10.38 14.00 67.00
## se 17 7185 0.92 0.20 0.89 0.90 0.18 0.51 1.82
## sealt 18 7185 0.92 0.13 0.88 0.91 0.08 0.76 1.67
## sealt2 19 7185 1.03 0.14 0.97 1.01 0.09 0.85 1.86
## t2 20 7185 14.66 26.42 5.75 8.37 7.69 0.00 195.81
## t2alt 21 7185 8.54 11.06 4.36 6.18 5.87 0.00 52.82
## pickone 22 7185 0.02 0.15 0.00 0.00 0.00 0.00 1.00
## mmses 23 7185 0.00 0.41 0.03 0.01 0.47 -1.19 0.82
## mnses 24 7185 0.00 0.41 0.03 0.01 0.47 -1.19 0.82
## xb 25 7185 12.69 2.42 12.87 12.75 2.76 5.68 17.52
## resid 26 7185 0.06 6.46 0.24 0.17 7.35 -19.49 16.44
## range skew kurtosis se
## minority 1.00 1.01 -0.98 0.01
## female 1.00 -0.11 -1.99 0.01
## ses 6.45 -0.23 -0.38 0.01
## mathach 27.83 -0.18 -0.92 0.08
## size 2613.00 0.57 -0.36 7.13
## sector 1.00 0.03 -2.00 0.01
## pracad 1.00 0.16 -0.89 0.00
## disclim 5.17 0.24 -0.16 0.01
## himinty 1.00 0.98 -1.04 0.01
## schoolid 8362.00 0.11 -1.25 29.49
## mean 15.48 -0.27 -0.05 0.04
## sd 4.94 -0.24 0.22 0.01
## sdalt 0.00 NaN NaN 0.00
## junk 239.29 1.30 1.46 0.58
## sdalt2 0.00 NaN NaN 0.00
## num 53.00 -0.58 -0.37 0.13
## se 1.32 1.11 2.32 0.00
## sealt 0.91 1.59 3.25 0.00
## sealt2 1.01 1.59 3.25 0.00
## t2 195.81 3.67 16.89 0.31
## t2alt 52.82 2.06 4.24 0.13
## pickone 1.00 6.47 39.92 0.00
## mmses 2.02 -0.27 -0.48 0.00
## mnses 2.02 -0.27 -0.48 0.00
## xb 11.84 -0.27 -0.48 0.03
## resid 35.93 -0.14 -0.69 0.08str(high_survey)## 'data.frame': 7185 obs. of 26 variables:
## $ minority: int 0 0 0 0 0 0 0 0 0 0 ...
## $ female : int 1 1 0 0 0 0 1 0 1 0 ...
## $ ses : num -1.528 -0.588 -0.528 -0.668 -0.158 ...
## $ mathach : num 5.88 19.71 20.35 8.78 17.9 ...
## $ size : int 842 842 842 842 842 842 842 842 842 842 ...
## $ sector : int 0 0 0 0 0 0 0 0 0 0 ...
## $ pracad : num 0.35 0.35 0.35 0.35 0.35 ...
## $ disclim : num 1.6 1.6 1.6 1.6 1.6 ...
## $ himinty : int 0 0 0 0 0 0 0 0 0 0 ...
## $ schoolid: num 1224 1224 1224 1224 1224 ...
## $ mean : num 9.72 9.72 9.72 9.72 9.72 ...
## $ sd : num 7.59 7.59 7.59 7.59 7.59 ...
## $ sdalt : num 6.26 6.26 6.26 6.26 6.26 ...
## $ junk : num 45.7 50 59.5 14.9 27.7 ...
## $ sdalt2 : num 48.4 48.4 48.4 48.4 48.4 ...
## $ num : num 47 47 47 47 47 47 47 47 47 47 ...
## $ se : num 1.11 1.11 1.11 1.11 1.11 ...
## $ sealt : num 0.913 0.913 0.913 0.913 0.913 ...
## $ sealt2 : num 1.01 1.01 1.01 1.01 1.01 ...
## $ t2 : num 6.96 6.96 6.96 6.96 6.96 ...
## $ t2alt : num 8.29 8.29 8.29 8.29 8.29 ...
## $ pickone : int 1 0 0 0 0 0 0 0 0 0 ...
## $ mmses : num -0.434 -0.434 -0.434 -0.434 -0.434 ...
## $ mnses : num -0.434 -0.434 -0.434 -0.434 -0.434 ...
## $ xb : num 10.1 10.1 10.1 10.1 10.1 ...
## $ resid : num -4.26 9.57 10.21 -1.36 7.76 ...
## - attr(*, "datalabel")= chr ""
## - attr(*, "time.stamp")= chr "23 Nov 2007 10:26"
## - attr(*, "formats")= chr "%8.0g" "%8.0g" "%9.0g" "%9.0g" ...
## - attr(*, "types")= int 251 251 254 254 252 251 254 254 251 254 ...
## - attr(*, "val.labels")= chr "" "" "" "" ...
## - attr(*, "var.labels")= chr "" "" "" "" ...
## - attr(*, "version")= int 12first.model <- lmer(mathach ~ ses + (1|schoolid), data = high_survey, REML = FALSE )
icc(first.model)##
## Linear mixed model
## Family: gaussian (identity)
## Formula: mathach ~ ses + (1 | schoolid)
##
## ICC (schoolid): 0.113235ranef(first.model)## $schoolid
## (Intercept)
## 1224 -1.631506601
## 1288 0.428228846
## 1296 -3.442447786
## 1308 1.678092414
## 1317 -0.262907201
## 1358 -1.113650532
## 1374 -2.265341448
## 1433 4.378982867
## 1436 3.487146179
## 1461 2.072951618
## 1462 -0.493396258
## 1477 1.055844310
## 1499 -3.383122533
## 1637 -3.059222221
## 1906 1.831397282
## 1909 0.916190517
## 1942 3.009565169
## 1946 0.200802861
## 2030 -1.169839905
## 2208 1.534728007
## 2277 -1.362883737
## 2305 -0.016116528
## 2336 2.403568676
## 2458 0.688684599
## 2467 -1.496222460
## 2526 3.177070824
## 2626 0.741285032
## 2629 2.267769625
## 2639 -3.148632702
## 2651 -1.429500891
## 2655 1.186820101
## 2658 -0.264055020
## 2755 2.133608016
## 2768 -1.250730960
## 2771 -0.001495812
## 2818 0.805198844
## 2917 -2.342990217
## 2990 3.631999209
## 2995 -2.042318974
## 3013 0.051382260
## 3020 1.048155028
## 3039 2.530877186
## 3088 -1.983276529
## 3152 0.414728699
## 3332 0.131164456
## 3351 -1.642504084
## 3377 -1.764089741
## 3427 5.769878188
## 3498 1.878028582
## 3499 -0.378929059
## 3533 -1.656729798
## 3610 2.147302243
## 3657 -1.373098559
## 3688 0.871332061
## 3705 -2.459178273
## 3716 -1.077159480
## 3838 2.670365507
## 3881 -0.851031696
## 3967 -0.073164443
## 3992 0.970360559
## 3999 -1.278238203
## 4042 0.620491034
## 4173 -0.008058032
## 4223 1.865205278
## 4253 -2.071401169
## 4292 1.222125962
## 4325 0.609776662
## 4350 -0.943302643
## 4383 -1.040932015
## 4410 0.491043449
## 4420 1.408204696
## 4458 -3.728194581
## 4511 0.887765204
## 4523 -3.580724676
## 4530 -1.934053716
## 4642 1.475857798
## 4868 -0.984338167
## 4931 0.229834467
## 5192 -1.637708063
## 5404 0.689661660
## 5619 1.567411901
## 5640 0.813101168
## 5650 1.330663745
## 5667 0.104973677
## 5720 1.347667986
## 5761 -0.649323353
## 5762 -4.520629593
## 5783 0.062131660
## 5815 -2.863164902
## 5819 -0.823966979
## 5838 0.525045010
## 5937 2.016910173
## 6074 1.564526199
## 6089 2.187351358
## 6144 -2.593804124
## 6170 1.635355657
## 6291 -1.064458886
## 6366 1.989378812
## 6397 0.580473208
## 6415 -0.305312225
## 6443 -1.853939357
## 6464 -3.109104237
## 6469 3.515445397
## 6484 0.570007682
## 6578 0.501610600
## 6600 -0.724398272
## 6808 -2.666842534
## 6816 0.538983817
## 6897 1.383023306
## 6990 -4.800417270
## 7011 0.994809345
## 7101 -0.644248682
## 7172 -3.308800177
## 7232 0.087365043
## 7276 -0.144024742
## 7332 1.090320181
## 7341 -2.142124591
## 7342 -0.370239954
## 7345 -1.227000353
## 7364 1.467108235
## 7635 1.583645683
## 7688 4.646320159
## 7697 1.965537918
## 7734 -0.719417846
## 7890 -2.658287362
## 7919 0.906049585
## 8009 0.166293936
## 8150 1.242182161
## 8165 2.633834671
## 8175 -0.443756810
## 8188 -0.197515797
## 8193 3.381197090
## 8202 -0.939883429
## 8357 1.535404481
## 8367 -5.236724550
## 8477 0.275336523
## 8531 -0.088081805
## 8627 -1.763967217
## 8628 3.726663963
## 8707 -0.124375471
## 8775 -2.044715906
## 8800 -2.912704578
## 8854 -5.308865537
## 8857 1.249627813
## 8874 0.174430144
## 8946 -1.270504595
## 8983 -0.834642285
## 9021 0.474119137
## 9104 2.097816496
## 9158 -2.745098897
## 9198 4.197645133
## 9225 1.152930394
## 9292 -0.677459076
## 9340 -0.416446570
## 9347 0.329677898
## 9359 1.538850228
## 9397 -2.248306683
## 9508 1.019050292
## 9550 -1.334852708
## 9586 0.636148228fixef(first.model)## (Intercept) ses
## 12.65762 2.39150coef(first.model)## $schoolid
## (Intercept) ses
## 1224 11.026117 2.3915
## 1288 13.085852 2.3915
## 1296 9.215176 2.3915
## 1308 14.335716 2.3915
## 1317 12.394716 2.3915
## 1358 11.543973 2.3915
## 1374 10.392282 2.3915
## 1433 17.036606 2.3915
## 1436 16.144770 2.3915
## 1461 14.730575 2.3915
## 1462 12.164227 2.3915
## 1477 13.713468 2.3915
## 1499 9.274501 2.3915
## 1637 9.598401 2.3915
## 1906 14.489021 2.3915
## 1909 13.573814 2.3915
## 1942 15.667188 2.3915
## 1946 12.858426 2.3915
## 2030 11.487783 2.3915
## 2208 14.192351 2.3915
## 2277 11.294740 2.3915
## 2305 12.641507 2.3915
## 2336 15.061192 2.3915
## 2458 13.346308 2.3915
## 2467 11.161401 2.3915
## 2526 15.834694 2.3915
## 2626 13.398908 2.3915
## 2629 14.925393 2.3915
## 2639 9.508991 2.3915
## 2651 11.228122 2.3915
## 2655 13.844443 2.3915
## 2658 12.393568 2.3915
## 2755 14.791231 2.3915
## 2768 11.406892 2.3915
## 2771 12.656128 2.3915
## 2818 13.462822 2.3915
## 2917 10.314633 2.3915
## 2990 16.289623 2.3915
## 2995 10.615304 2.3915
## 3013 12.709006 2.3915
## 3020 13.705778 2.3915
## 3039 15.188501 2.3915
## 3088 10.674347 2.3915
## 3152 13.072352 2.3915
## 3332 12.788788 2.3915
## 3351 11.015119 2.3915
## 3377 10.893534 2.3915
## 3427 18.427502 2.3915
## 3498 14.535652 2.3915
## 3499 12.278694 2.3915
## 3533 11.000894 2.3915
## 3610 14.804926 2.3915
## 3657 11.284525 2.3915
## 3688 13.528955 2.3915
## 3705 10.198445 2.3915
## 3716 11.580464 2.3915
## 3838 15.327989 2.3915
## 3881 11.806592 2.3915
## 3967 12.584459 2.3915
## 3992 13.627984 2.3915
## 3999 11.379385 2.3915
## 4042 13.278114 2.3915
## 4173 12.649565 2.3915
## 4223 14.522829 2.3915
## 4253 10.586222 2.3915
## 4292 13.879749 2.3915
## 4325 13.267400 2.3915
## 4350 11.714321 2.3915
## 4383 11.616691 2.3915
## 4410 13.148667 2.3915
## 4420 14.065828 2.3915
## 4458 8.929429 2.3915
## 4511 13.545389 2.3915
## 4523 9.076899 2.3915
## 4530 10.723570 2.3915
## 4642 14.133481 2.3915
## 4868 11.673285 2.3915
## 4931 12.887458 2.3915
## 5192 11.019915 2.3915
## 5404 13.347285 2.3915
## 5619 14.225035 2.3915
## 5640 13.470724 2.3915
## 5650 13.988287 2.3915
## 5667 12.762597 2.3915
## 5720 14.005291 2.3915
## 5761 12.008300 2.3915
## 5762 8.136994 2.3915
## 5783 12.719755 2.3915
## 5815 9.794458 2.3915
## 5819 11.833656 2.3915
## 5838 13.182668 2.3915
## 5937 14.674533 2.3915
## 6074 14.222150 2.3915
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## 6990 7.857206 2.3915
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## 8628 16.384287 2.3915
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## 9021 13.131742 2.3915
## 9104 14.755440 2.3915
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## 9198 16.855268 2.3915
## 9225 13.810554 2.3915
## 9292 11.980164 2.3915
## 9340 12.241177 2.3915
## 9347 12.987301 2.3915
## 9359 14.196474 2.3915
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## 9550 11.322771 2.3915
## 9586 13.293772 2.3915
##
## attr(,"class")
## [1] "coef.mer"summary(first.model)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: mathach ~ ses + (1 | schoolid)
## Data: high_survey
##
## AIC BIC logLik deviance df.resid
## 46649.0 46676.5 -23320.5 46641.0 7181
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.1263 -0.7277 0.0220 0.7578 2.9186
##
## Random effects:
## Groups Name Variance Std.Dev.
## schoolid (Intercept) 4.729 2.175
## Residual 37.030 6.085
## Number of obs: 7185, groups: schoolid, 160
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 12.6576 0.1873 67.57
## ses 2.3915 0.1057 22.63
##
## Correlation of Fixed Effects:
## (Intr)
## ses 0.003second.model <- lmer(ses ~ (1|schoolid), data = high_survey, REML = FALSE )
summary(second.model)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: ses ~ (1 | schoolid)
## Data: high_survey
##
## AIC BIC logLik deviance df.resid
## 15047.0 15067.7 -7520.5 15041.0 7182
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -5.4793 -0.6724 0.0179 0.7065 4.2632
##
## Random effects:
## Groups Name Variance Std.Dev.
## schoolid (Intercept) 0.1597 0.3997
## Residual 0.4462 0.6680
## Number of obs: 7185, groups: schoolid, 160
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -0.005674 0.032647 -0.174icc(second.model)##
## Linear mixed model
## Family: gaussian (identity)
## Formula: ses ~ (1 | schoolid)
##
## ICC (schoolid): 0.263612Note that the echo = FALSE parameter was added to the code chunk to prevent printing of the R code that generated the plot.