library(lme4)
## Loading required package: Matrix
str(Penicillin)
## 'data.frame': 144 obs. of 3 variables:
## $ diameter: num 27 23 26 23 23 21 27 23 26 23 ...
## $ plate : Factor w/ 24 levels "a","b","c","d",..: 1 1 1 1 1 1 2 2 2 2 ...
## $ sample : Factor w/ 6 levels "A","B","C","D",..: 1 2 3 4 5 6 1 2 3 4 ...
summary(Penicillin)
## diameter plate sample
## Min. :18.00 a : 6 A:24
## 1st Qu.:22.00 b : 6 B:24
## Median :23.00 c : 6 C:24
## Mean :22.97 d : 6 D:24
## 3rd Qu.:24.00 e : 6 E:24
## Max. :27.00 f : 6 F:24
## (Other):108
xtabs(~ sample + plate, Penicillin)
## plate
## sample a b c d e f g h i j k l m n o p q r s t u v w x
## A 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## B 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## C 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## D 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## E 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## F 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
(model3 <- lmer(diameter ~ 1 + (1|plate) + (1|sample), Penicillin))
## Linear mixed model fit by REML ['lmerMod']
## Formula: diameter ~ 1 + (1 | plate) + (1 | sample)
## Data: Penicillin
## REML criterion at convergence: 330.8606
## Random effects:
## Groups Name Std.Dev.
## plate (Intercept) 0.8467
## sample (Intercept) 1.9316
## Residual 0.5499
## Number of obs: 144, groups: plate, 24; sample, 6
## Fixed Effects:
## (Intercept)
## 22.97
pr03 <- profile(model3)
pr03
## .zeta .sig01 .sig02 .sigma (Intercept) .par
## 1 -3.99417206 0.4838555 1.7651456 0.5678654 22.97222 .sig01
## 2 -3.50158054 0.5155906 1.7655672 0.5632325 22.97222 .sig01
## 3 -3.00593303 0.5501255 1.7660303 0.5595740 22.97222 .sig01
## 4 -2.50732514 0.5879316 1.7665514 0.5567042 22.97222 .sig01
## 5 -2.00578109 0.6295624 1.7670055 0.5544754 22.97222 .sig01
## 6 -1.50127323 0.6756760 1.7678301 0.5527710 22.97222 .sig01
## 7 -0.99382080 0.7270530 1.7686329 0.5514916 22.97222 .sig01
## 8 -0.48494129 0.7844551 1.7695784 0.5505596 22.97222 .sig01
## 9 0.00000000 0.8455722 1.7706463 0.5499322 22.97222 .sig01
## 10 0.06301493 0.8540279 1.7707981 0.5498665 22.97222 .sig01
## 11 0.49239137 0.9151450 1.7719311 0.5495005 22.97222 .sig01
## 12 0.90338547 0.9799755 1.7731886 0.5492655 22.97222 .sig01
## 13 1.31372651 1.0518209 1.7746620 0.5491207 22.97222 .sig01
## 14 1.72258001 1.1315669 1.7763709 0.5490462 22.97222 .sig01
## 15 2.12996848 1.2204044 1.7783627 0.5490252 22.97222 .sig01
## 16 2.53587422 1.3197259 1.7806966 0.5490437 22.97222 .sig01
## 17 2.94028323 1.4311740 1.7834198 0.5490897 22.97222 .sig01
## 18 3.34318380 1.5566924 1.7866022 0.5491539 22.97222 .sig01
## 19 3.74456727 1.6985865 1.7903169 0.5492288 22.97222 .sig01
## 20 -3.72328360 0.8420462 0.7932702 0.5510652 22.97222 .sig02
## 21 -3.18524713 0.8426790 0.8683985 0.5506896 22.97222 .sig02
## 22 -2.63903802 0.8432874 0.9584947 0.5504130 22.97222 .sig02
## 23 -2.08300496 0.8438662 1.0684845 0.5502164 22.97222 .sig02
## 24 -1.51545244 0.8444091 1.2055422 0.5500829 22.97222 .sig02
## 25 -0.93793622 0.8449034 1.3793272 0.5499983 22.97222 .sig02
## 26 -0.37640640 0.8453247 1.5935817 0.5499507 22.97222 .sig02
## 27 0.00000000 0.8455722 1.7706463 0.5499322 22.97222 .sig02
## 28 0.03421088 0.8455933 1.7883528 0.5499309 22.97222 .sig02
## 29 0.34806602 0.8457757 1.9654174 0.5499218 22.97222 .sig02
## 30 0.72945369 0.8459706 2.2223728 0.5499158 22.97222 .sig02
## 31 1.10128662 0.8461330 2.5292370 0.5499134 22.97222 .sig02
## 32 1.46980983 0.8462686 2.9051208 0.5499132 22.97222 .sig02
## 33 1.83438070 0.8463785 3.3696830 0.5499142 22.97222 .sig02
## 34 2.19497627 0.8464658 3.9500691 0.5499159 22.97222 .sig02
## 35 2.55155044 0.8465341 4.6831498 0.5499175 22.97222 .sig02
## 36 2.90409347 0.8465860 5.6195405 0.5499190 22.97222 .sig02
## 37 3.25262538 0.8466240 6.8293029 0.5499202 22.97222 .sig02
## 38 3.59719294 0.8466513 8.4102331 0.5499211 22.97222 .sig02
## 39 3.93786393 0.8466696 10.4999789 0.5499219 22.97222 .sig02
## 40 -3.82024577 0.8565824 1.7721660 0.4358855 22.97222 .sigma
## 41 -3.34296821 0.8555540 1.7720237 0.4478394 22.97222 .sigma
## 42 -2.86530975 0.8544441 1.7718692 0.4603758 22.97222 .sigma
## 43 -2.38726013 0.8532446 1.7717031 0.4735338 22.97222 .sigma
## 44 -1.90880877 0.8519462 1.7715238 0.4873559 22.97222 .sigma
## 45 -1.42994498 0.8505386 1.7713295 0.5018880 22.97222 .sigma
## 46 -0.95066377 0.8490102 1.7711190 0.5171800 22.97222 .sigma
## 47 -0.47118486 0.8473485 1.7708901 0.5332783 22.97222 .sigma
## 48 0.00000000 0.8455722 1.7706463 0.5499322 22.97222 .sigma
## 49 0.15040035 0.8449729 1.7705643 0.5554315 22.97222 .sigma
## 50 0.59114324 0.8431186 1.7703101 0.5720854 22.97222 .sigma
## 51 1.02480250 0.8411404 1.7700397 0.5892956 22.97222 .sigma
## 52 1.45830737 0.8389943 1.7697470 0.6073711 22.97222 .sigma
## 53 1.89149050 0.8366635 1.7694299 0.6263624 22.97222 .sigma
## 54 2.32435026 0.8341281 1.7690868 0.6463305 22.97222 .sigma
## 55 2.75688111 0.8313655 1.7687124 0.6673413 22.97222 .sigma
## 56 3.18907760 0.8283504 1.7683060 0.6894663 22.97222 .sigma
## 57 3.62093430 0.8250542 1.7678624 0.7127824 22.97222 .sigma
## 58 4.05244578 0.8214438 1.7673789 0.7373732 22.97222 .sigma
## 59 -3.89862540 0.8471386 6.2829261 0.5499197 16.91670 (Intercept)
## 60 -3.55323116 0.8473352 5.0646474 0.5499181 18.19415 (Intercept)
## 61 -3.20172214 0.8475661 4.1499639 0.5499164 19.18003 (Intercept)
## 62 -2.84310260 0.8477943 3.4591194 0.5499145 19.95628 (Intercept)
## 63 -2.47610405 0.8479510 2.9359657 0.5499133 20.58176 (Intercept)
## 64 -2.09917760 0.8479419 2.5409791 0.5499133 21.09939 (Intercept)
## 65 -1.71055410 0.8476799 2.2463525 0.5499154 21.54105 (Intercept)
## 66 -1.30836273 0.8471463 2.0326343 0.5499196 21.93105 (Intercept)
## 67 -0.89069537 0.8464498 1.8865555 0.5499252 22.28868 (Intercept)
## 68 -0.45541171 0.8458301 1.8000518 0.5499301 22.63047 (Intercept)
## 69 0.00000000 0.8455722 1.7706463 0.5499322 22.97222 (Intercept)
## 70 0.45198446 0.8458264 1.7996069 0.5499302 23.31136 (Intercept)
## 71 0.88743896 0.8464444 1.8856755 0.5499252 23.65311 (Intercept)
## 72 1.30523154 0.8471413 2.0312748 0.5499197 24.01056 (Intercept)
## 73 1.70753392 0.8476768 2.2444327 0.5499154 24.40025 (Intercept)
## 74 2.09625397 0.8479409 2.5383759 0.5499133 24.84143 (Intercept)
## 75 2.47326291 0.8479517 2.9325026 0.5499133 25.35836 (Intercept)
## 76 2.84033113 0.8477959 3.4545440 0.5499145 25.98287 (Intercept)
## 77 3.19900953 0.8475680 4.1439257 0.5499163 26.75777 (Intercept)
## 78 3.55056880 0.8473372 5.0566141 0.5499181 27.74178 (Intercept)
## 79 3.89600661 0.8471399 6.2722013 0.5499197 29.01661 (Intercept)
library(lattice)
xyplot(pr03, aspect = 1.3)
confint(pr03)
## 2.5 % 97.5 %
## .sig01 0.6335658 1.1821040
## .sig02 1.0957893 3.5562919
## .sigma 0.4858454 0.6294535
## (Intercept) 21.2666274 24.6778176
confint(pr03, level = 0.99)
## 0.5 % 99.5 %
## .sig01 0.5825413 1.3301551
## .sig02 0.9700367 4.7401291
## .sigma 0.4682700 0.6584123
## (Intercept) 20.4255688 25.5188739
splom(pr03)
ranef(model3)
## $plate
## (Intercept)
## a 0.80454704
## b 0.80454704
## c 0.18167191
## d 0.33739069
## e 0.02595313
## f -0.44120322
## g -1.37551591
## h 0.80454704
## i -0.75264078
## j -0.75264078
## k 0.96026582
## l 0.49310948
## m 1.42742217
## n 0.49310948
## o 0.96026582
## p 0.02595313
## q -0.28548443
## r -0.28548443
## s -1.37551591
## t 0.96026582
## u -0.90835956
## v -0.28548443
## w -0.59692200
## x -1.21979713
##
## $sample
## (Intercept)
## A 2.18705797
## B -1.01047615
## C 1.93789946
## D -0.09689497
## E -0.01384214
## F -3.00374417
str(ranef(model3))
## List of 2
## $ plate :'data.frame': 24 obs. of 1 variable:
## ..$ (Intercept): num [1:24] 0.805 0.805 0.182 0.337 0.026 ...
## $ sample:'data.frame': 6 obs. of 1 variable:
## ..$ (Intercept): num [1:6] 2.1871 -1.0105 1.9379 -0.0969 -0.0138 ...
## - attr(*, "class")= chr "ranef.mer"
dotplot(ranef(model3, postVar = TRUE))
## Warning in ranef.merMod(model3, postVar = TRUE): 'postVar' is deprecated:
## please use 'condVar' instead
## $plate
##
## $sample
qqmath(ranef(model3, postVar=TRUE))
## Warning in ranef.merMod(model3, postVar = TRUE): 'postVar' is deprecated:
## please use 'condVar' instead
## $plate
##
## $sample
str(Pastes)
## 'data.frame': 60 obs. of 4 variables:
## $ strength: num 62.8 62.6 60.1 62.3 62.7 63.1 60 61.4 57.5 56.9 ...
## $ batch : Factor w/ 10 levels "A","B","C","D",..: 1 1 1 1 1 1 2 2 2 2 ...
## $ cask : Factor w/ 3 levels "a","b","c": 1 1 2 2 3 3 1 1 2 2 ...
## $ sample : Factor w/ 30 levels "A:a","A:b","A:c",..: 1 1 2 2 3 3 4 4 5 5 ...
summary(Pastes)
## strength batch cask sample
## Min. :54.20 A : 6 a:20 A:a : 2
## 1st Qu.:57.50 B : 6 b:20 A:b : 2
## Median :59.30 C : 6 c:20 A:c : 2
## Mean :60.05 D : 6 B:a : 2
## 3rd Qu.:62.88 E : 6 B:b : 2
## Max. :66.00 F : 6 B:c : 2
## (Other):24 (Other):48
xtabs(~ batch + sample, Pastes, drop = TRUE, sparse = TRUE)
## 10 x 30 sparse Matrix of class "dgCMatrix"
## [[ suppressing 30 column names 'A:a', 'A:b', 'A:c' ... ]]
##
## A 2 2 2 . . . . . . . . . . . . . . . . . . . . . . . . . . .
## B . . . 2 2 2 . . . . . . . . . . . . . . . . . . . . . . . .
## C . . . . . . 2 2 2 . . . . . . . . . . . . . . . . . . . . .
## D . . . . . . . . . 2 2 2 . . . . . . . . . . . . . . . . . .
## E . . . . . . . . . . . . 2 2 2 . . . . . . . . . . . . . . .
## F . . . . . . . . . . . . . . . 2 2 2 . . . . . . . . . . . .
## G . . . . . . . . . . . . . . . . . . 2 2 2 . . . . . . . . .
## H . . . . . . . . . . . . . . . . . . . . . 2 2 2 . . . . . .
## I . . . . . . . . . . . . . . . . . . . . . . . . 2 2 2 . . .
## J . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 2
xtabs(~ cask + batch, Pastes)
## batch
## cask A B C D E F G H I J
## a 2 2 2 2 2 2 2 2 2 2
## b 2 2 2 2 2 2 2 2 2 2
## c 2 2 2 2 2 2 2 2 2 2
Pastes$sample <- with(Pastes, factor(batch:cask))
(model4 <- lmer(strength ~ 1 + (1|sample) + (1|batch), Pastes, REML=FALSE))
## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: strength ~ 1 + (1 | sample) + (1 | batch)
## Data: Pastes
## AIC BIC logLik deviance df.resid
## 255.9945 264.3718 -123.9972 247.9945 56
## Random effects:
## Groups Name Std.Dev.
## sample (Intercept) 2.9041
## batch (Intercept) 1.0951
## Residual 0.8234
## Number of obs: 60, groups: sample, 30; batch, 10
## Fixed Effects:
## (Intercept)
## 60.05
(model4a <- lmer(strength ~ 1 + (1|sample), Pastes, REML=FALSE))
## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: strength ~ 1 + (1 | sample)
## Data: Pastes
## AIC BIC logLik deviance df.resid
## 254.4017 260.6847 -124.2008 248.4017 57
## Random effects:
## Groups Name Std.Dev.
## sample (Intercept) 3.1037
## Residual 0.8234
## Number of obs: 60, groups: sample, 30
## Fixed Effects:
## (Intercept)
## 60.05
anova(model4a, model4)
## Data: Pastes
## Models:
## model4a: strength ~ 1 + (1 | sample)
## model4: strength ~ 1 + (1 | sample) + (1 | batch)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## model4a 3 254.40 260.69 -124.2 248.40
## model4 4 255.99 264.37 -124.0 247.99 0.4072 1 0.5234
pr04 <- profile(model4)
pr04
## .zeta .sig01 .sig02 .sigma (Intercept) .par
## 1 -4.02919334 1.641803 1.757994e+00 0.8977597 60.05333 .sig01
## 2 -3.53448855 1.748506 1.725281e+00 0.8752994 60.05333 .sig01
## 3 -3.03540030 1.865427 1.685340e+00 0.8593031 60.05333 .sig01
## 4 -2.53250465 1.994525 1.636329e+00 0.8476893 60.05333 .sig01
## 5 -2.02604908 2.138075 1.575504e+00 0.8391970 60.05333 .sig01
## 6 -1.51610053 2.298797 1.498746e+00 0.8330053 60.05333 .sig01
## 7 -1.00273559 2.479951 1.399611e+00 0.8285480 60.05333 .sig01
## 8 -0.48787048 2.684729 1.267767e+00 0.8254239 60.05333 .sig01
## 9 0.00000000 2.904078 1.095060e+00 0.8234076 60.05333 .sig01
## 10 0.06030165 2.933118 1.068973e+00 0.8232106 60.05333 .sig01
## 11 0.48747981 3.152467 8.354983e-01 0.8220903 60.05333 .sig01
## 12 0.89469514 3.386340 4.341610e-01 0.8214003 60.05333 .sig01
## 13 1.31900891 3.647924 1.642801e-07 0.8206861 60.05333 .sig01
## 14 1.76895182 3.928712 8.071144e-08 0.8201976 60.05333 .sig01
## 15 2.19306530 4.212947 0.000000e+00 0.8199954 60.05333 .sig01
## 16 2.60941550 4.518193 1.642521e-07 0.8199647 60.05333 .sig01
## 17 3.02216129 4.852116 5.574730e-06 0.8200519 60.05333 .sig01
## 18 3.43255512 5.220600 0.000000e+00 0.8202209 60.05333 .sig01
## 19 3.84110953 5.629553 1.639669e-07 0.8204443 60.05333 .sig01
## 20 -0.63814884 3.103679 0.000000e+00 0.8234076 60.05333 .sig02
## 21 -0.47239338 3.038796 5.433365e-01 0.8234075 60.05333 .sig02
## 22 -0.11278654 2.930001 9.855538e-01 0.8234075 60.05333 .sig02
## 23 0.00000000 2.904078 1.095060e+00 0.8234076 60.05333 .sig02
## 24 0.01165767 2.901600 1.106010e+00 0.8234077 60.05333 .sig02
## 25 0.13136637 2.878217 1.215516e+00 0.8234081 60.05333 .sig02
## 26 0.61459405 2.816115 1.632162e+00 0.8234076 60.05333 .sig02
## 27 1.06372733 2.791920 2.024871e+00 0.8234076 60.05333 .sig02
## 28 1.48108698 2.787499 2.423116e+00 0.8234075 60.05333 .sig02
## 29 1.88409174 2.793391 2.857722e+00 0.8234076 60.05333 .sig02
## 30 2.27809830 2.804811 3.348901e+00 0.8234076 60.05333 .sig02
## 31 2.66547853 2.818808 3.916697e+00 0.8234076 60.05333 .sig02
## 32 3.04746455 2.833440 4.584286e+00 0.8234076 60.05333 .sig02
## 33 3.42476567 2.847437 5.380294e+00 0.8234072 60.05333 .sig02
## 34 3.79783131 2.860005 6.341207e+00 0.8234074 60.05333 .sig02
## 35 -3.98723581 2.938020 1.095060e+00 0.5304859 60.05333 .sigma
## 36 -3.49135556 2.935626 1.095060e+00 0.5563558 60.05333 .sigma
## 37 -2.99400652 2.932880 1.095060e+00 0.5846046 60.05333 .sigma
## 38 -2.49509669 2.929713 1.095060e+00 0.6155479 60.05333 .sigma
## 39 -1.99452698 2.926039 1.095060e+00 0.6495556 60.05333 .sigma
## 40 -1.49219407 2.921753 1.095060e+00 0.6870627 60.05333 .sigma
## 41 -0.98805474 2.916720 1.095059e+00 0.7285780 60.05333 .sigma
## 42 -0.48327976 2.910786 1.095060e+00 0.7745879 60.05333 .sigma
## 43 0.00000000 2.904078 1.095060e+00 0.8234076 60.05333 .sigma
## 44 0.07682017 2.902904 1.095060e+00 0.8316416 60.05333 .sigma
## 45 0.50760409 2.895697 1.095059e+00 0.8804613 60.05333 .sigma
## 46 0.92213889 2.887608 1.095060e+00 0.9320780 60.05333 .sigma
## 47 1.33629036 2.878161 1.095060e+00 0.9887913 60.05333 .sigma
## 48 1.74934993 2.867088 1.095060e+00 1.0511619 60.05333 .sigma
## 49 2.16131960 2.854039 1.095060e+00 1.1199357 60.05333 .sigma
## 50 2.57217092 2.838572 1.095060e+00 1.1959706 60.05333 .sigma
## 51 2.98187781 2.820130 1.095059e+00 1.2802620 60.05333 .sigma
## 52 3.39041533 2.797995 1.095060e+00 1.3739676 60.05333 .sigma
## 53 3.79775995 2.771241 1.095060e+00 1.4784368 60.05333 .sigma
## 54 -3.71631976 2.904078 3.672042e+00 0.8234075 56.54837 (Intercept)
## 55 -3.33599332 2.904078 3.102214e+00 0.8234075 57.15082 (Intercept)
## 56 -2.94953822 2.904078 2.630150e+00 0.8234076 57.66199 (Intercept)
## 57 -2.55625757 2.904078 2.236411e+00 0.8234075 58.10336 (Intercept)
## 58 -2.15536070 2.904078 1.907184e+00 0.8234076 58.49186 (Intercept)
## 59 -1.74594742 2.904078 1.633622e+00 0.8234076 58.84108 (Intercept)
## 60 -1.32698609 2.904078 1.411768e+00 0.8234075 59.16230 (Intercept)
## 61 -0.89728335 2.904078 1.242926e+00 0.8234076 59.46536 (Intercept)
## 62 -0.45544115 2.904078 1.133834e+00 0.8234075 59.75936 (Intercept)
## 63 0.00000000 2.904078 1.095060e+00 0.8234076 60.05333 (Intercept)
## 64 0.45312920 2.904078 1.133444e+00 0.8234075 60.34580 (Intercept)
## 65 0.89504959 2.904078 1.242207e+00 0.8234076 60.63978 (Intercept)
## 66 1.32481060 2.904078 1.410763e+00 0.8234075 60.94277 (Intercept)
## 67 1.74382384 2.904078 1.632354e+00 0.8234076 61.26388 (Intercept)
## 68 2.15328334 2.904078 1.905645e+00 0.8234076 61.61293 (Intercept)
## 69 2.55422149 2.904078 2.234568e+00 0.8234076 62.00119 (Intercept)
## 70 2.94753909 2.904078 2.627945e+00 0.8234076 62.44225 (Intercept)
## 71 3.33402736 2.904078 3.099563e+00 0.8234075 62.95301 (Intercept)
## 72 3.71438360 2.904078 3.668828e+00 0.8234076 63.55493 (Intercept)
library(lattice)
xyplot(pr04, aspect = 1.3)
confint(pr04)
## 2.5 % 97.5 %
## .sig01 2.1579337 4.053589
## .sig02 0.0000000 2.946591
## .sigma 0.6520234 1.085448
## (Intercept) 58.6636504 61.443016
confint(pr04, level = 0.99)
## 0.5 % 99.5 %
## .sig01 1.9829151 4.492471
## .sig02 0.0000000 3.776505
## .sigma 0.6103545 1.196684
## (Intercept) 58.0829453 62.023723
splom(pr04)
ranef(model4)
## $sample
## (Intercept)
## A:a 1.92558677
## A:b 0.48355090
## A:c 2.11785822
## B:a 0.83229519
## B:b -2.53245517
## B:c 0.15934512
## C:a -2.43608072
## C:b 2.75524839
## C:c 3.76467350
## D:a -3.07689823
## D:b -2.11554099
## D:c 4.46975614
## E:a -3.60073081
## E:b -4.22561302
## E:c -0.66859122
## F:a 3.66437104
## F:b -1.57502594
## F:c -0.08492222
## G:a 2.44305764
## G:b -0.15260692
## G:c -2.60406790
## H:a -1.58067150
## H:b 4.47587914
## H:c 3.37031831
## I:a -4.66730442
## I:b 4.17718223
## I:c -2.31197917
## J:a -0.79391737
## J:b -0.40937447
## J:c -1.80334248
##
## $batch
## (Intercept)
## A 0.64367893
## B -0.21908349
## C 0.58066819
## D -0.10275597
## E -1.20786739
## F 0.28500242
## G -0.04459222
## H 0.89087491
## I -0.39842175
## J -0.42750363
str(ranef(model4))
## List of 2
## $ sample:'data.frame': 30 obs. of 1 variable:
## ..$ (Intercept): num [1:30] 1.926 0.484 2.118 0.832 -2.532 ...
## $ batch :'data.frame': 10 obs. of 1 variable:
## ..$ (Intercept): num [1:10] 0.644 -0.219 0.581 -0.103 -1.208 ...
## - attr(*, "class")= chr "ranef.mer"
dotplot(ranef(model4, postVar = TRUE))
## Warning in ranef.merMod(model4, postVar = TRUE): 'postVar' is deprecated:
## please use 'condVar' instead
## $sample
##
## $batch
qqmath(ranef(model4, postVar=TRUE))
## Warning in ranef.merMod(model4, postVar = TRUE): 'postVar' is deprecated:
## please use 'condVar' instead
## $sample
##
## $batch
pr04a <- profile(model4a)
pr04a
## .zeta .sig01 .sigma (Intercept) .par
## 1 -3.64513976 2.015095 0.8710798 60.05333 .sig01
## 2 -3.19290153 2.115684 0.8587105 60.05333 .sig01
## 3 -2.73883044 2.224168 0.8491433 60.05333 .sig01
## 4 -2.28303876 2.341610 0.8416941 60.05333 .sig01
## 5 -1.82557607 2.469215 0.8358877 60.05333 .sig01
## 6 -1.36645284 2.608366 0.8313796 60.05333 .sig01
## 7 -0.90569450 2.760649 0.8279113 60.05333 .sig01
## 8 -0.44419079 2.927572 0.8252865 60.05333 .sig01
## 9 0.00000000 3.103679 0.8234076 60.05333 .sig01
## 10 0.07420110 3.134716 0.8231466 60.05333 .sig01
## 11 0.47437374 3.310822 0.8219653 60.05333 .sig01
## 12 0.86085303 3.496107 0.8211398 60.05333 .sig01
## 13 1.24693170 3.697954 0.8205702 60.05333 .sig01
## 14 1.63207449 3.918072 0.8202099 60.05333 .sig01
## 15 2.01628706 4.158698 0.8200180 60.05333 .sig01
## 16 2.39955258 4.422381 0.8199596 60.05333 .sig01
## 17 2.78185490 4.712043 0.8200046 60.05333 .sig01
## 18 3.16317792 5.031046 0.8201277 60.05333 .sig01
## 19 3.54350595 5.383264 0.8203073 60.05333 .sig01
## 20 -3.66186562 3.134023 0.5472150 60.05333 .sigma
## 21 -3.20598215 3.131785 0.5722652 60.05333 .sigma
## 22 -2.74893711 3.129241 0.5994584 60.05333 .sigma
## 23 -2.29066484 3.126334 0.6290572 60.05333 .sigma
## 24 -1.83109520 3.122999 0.6613657 60.05333 .sigma
## 25 -1.37015548 3.119151 0.6967369 60.05333 .sigma
## 26 -0.90781542 3.114688 0.7355790 60.05333 .sigma
## 27 -0.44496857 3.109496 0.7782792 60.05333 .sigma
## 28 0.00000000 3.103679 0.8234076 60.05333 .sigma
## 29 0.07682014 3.102581 0.8316416 60.05333 .sigma
## 30 0.47642433 3.096362 0.8767700 60.05333 .sigma
## 31 0.86225156 3.089440 0.9243176 60.05333 .sigma
## 32 1.24776053 3.081450 0.9762031 60.05333 .sigma
## 33 1.63239072 3.072200 1.0328690 60.05333 .sigma
## 34 2.01614257 3.061441 1.0948969 60.05333 .sigma
## 35 2.39899396 3.048868 1.1629499 60.05333 .sigma
## 36 2.78092434 3.034100 1.2377886 60.05333 .sigma
## 37 3.16191388 3.016661 1.3202882 60.05333 .sigma
## 38 3.54194361 2.995950 1.4114574 60.05333 .sigma
## 39 -3.66716408 3.908055 0.8234076 57.67845 (Intercept)
## 40 -3.27207835 3.729535 0.8234076 57.98534 (Intercept)
## 41 -2.87418831 3.576871 0.8234076 58.27536 (Intercept)
## 42 -2.47337343 3.447962 0.8234076 58.55146 (Intercept)
## 43 -2.06951050 3.341116 0.8234076 58.81631 (Intercept)
## 44 -1.66247367 3.255019 0.8234076 59.07235 (Intercept)
## 45 -1.25213464 3.188702 0.8234076 59.32190 (Intercept)
## 46 -0.83836269 3.141529 0.8234076 59.56714 (Intercept)
## 47 -0.42102495 3.113184 0.8234076 59.81024 (Intercept)
## 48 0.00000000 3.103679 0.8234076 60.05333 (Intercept)
## 49 0.42040682 3.113157 0.8234076 60.29607 (Intercept)
## 50 0.83775082 3.141473 0.8234075 60.53917 (Intercept)
## 51 1.25152791 3.188619 0.8234076 60.78441 (Intercept)
## 52 1.66187191 3.254907 0.8234076 61.03394 (Intercept)
## 53 2.06891350 3.340974 0.8234076 61.28998 (Intercept)
## 54 2.47278102 3.447788 0.8234076 61.55481 (Intercept)
## 55 2.87360029 3.576664 0.8234076 61.83089 (Intercept)
## 56 3.27149455 3.729291 0.8234076 62.12089 (Intercept)
## 57 3.66658432 3.907772 0.8234076 62.42775 (Intercept)
library(lattice)
xyplot(pr04a, aspect = 1.3)
confint(pr04a)
## 2.5 % 97.5 %
## .sig01 2.4306377 4.122011
## .sigma 0.6520207 1.085448
## (Intercept) 58.8861831 61.220484
confint(pr04a, level = 0.99)
## 0.5 % 99.5 %
## .sig01 2.2651645 4.552495
## .sigma 0.6103609 1.196701
## (Intercept) 58.4822254 61.624441
splom(pr04a)
ranef(model4a)
## $sample
## (Intercept)
## A:a 2.55669114
## A:b 1.10768482
## A:c 2.74989198
## B:a 0.62468272
## B:b -2.75633201
## B:c -0.05152022
## C:a -1.88692822
## C:b 3.32949450
## C:c 4.34379892
## D:a -3.19103390
## D:b -2.22502969
## D:c 4.39209913
## E:a -4.78494084
## E:b -5.41284358
## E:c -1.83862801
## F:a 3.95739724
## F:b -1.30732569
## F:c 0.18998083
## G:a 2.41179050
## G:b -0.19642086
## G:c -2.65973158
## H:a -0.72772317
## H:b 5.35810334
## H:c 4.24719850
## I:a -5.07474210
## I:b 3.81249661
## I:c -2.70803179
## J:a -1.21072527
## J:b -0.82432359
## J:c -2.22502969
str(ranef(model4a))
## List of 1
## $ sample:'data.frame': 30 obs. of 1 variable:
## ..$ (Intercept): num [1:30] 2.557 1.108 2.75 0.625 -2.756 ...
## - attr(*, "class")= chr "ranef.mer"
dotplot(ranef(model4a, postVar = TRUE))
## Warning in ranef.merMod(model4a, postVar = TRUE): 'postVar' is deprecated:
## please use 'condVar' instead
## $sample
qqmath(ranef(model4a, postVar=TRUE))
## Warning in ranef.merMod(model4a, postVar = TRUE): 'postVar' is deprecated:
## please use 'condVar' instead
## $sample
str(InstEval)
## 'data.frame': 73421 obs. of 7 variables:
## $ s : Factor w/ 2972 levels "1","2","3","4",..: 1 1 1 1 2 2 3 3 3 3 ...
## $ d : Factor w/ 1128 levels "1","6","7","8",..: 525 560 832 1068 62 406 3 6 19 75 ...
## $ studage: Ord.factor w/ 4 levels "2"<"4"<"6"<"8": 1 1 1 1 1 1 1 1 1 1 ...
## $ lectage: Ord.factor w/ 6 levels "1"<"2"<"3"<"4"<..: 2 1 2 2 1 1 1 1 1 1 ...
## $ service: Factor w/ 2 levels "0","1": 1 2 1 2 1 1 2 1 1 1 ...
## $ dept : Factor w/ 14 levels "15","5","10",..: 14 5 14 12 2 2 13 3 3 3 ...
## $ y : int 5 2 5 3 2 4 4 5 5 4 ...
xtabs(~ y, InstEval)
## y
## 1 2 3 4 5
## 10186 12951 17609 16921 15754
(model5 <- lmer(y ~ 1 + (1|s) + (1|d)+(1|dept:service), InstEval, REML=FALSE))
## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: y ~ 1 + (1 | s) + (1 | d) + (1 | dept:service)
## Data: InstEval
## AIC BIC logLik deviance df.resid
## 237663.3 237709.3 -118826.6 237653.3 73416
## Random effects:
## Groups Name Std.Dev.
## s (Intercept) 0.3247
## d (Intercept) 0.5124
## dept:service (Intercept) 0.1101
## Residual 1.1768
## Number of obs: 73421, groups: s, 2972; d, 1128; dept:service, 28
## Fixed Effects:
## (Intercept)
## 3.255
ranef(model5)
## $s
## (Intercept)
## 1 1.479558e-01
## 2 -4.640765e-02
## 3 3.190478e-01
## 4 2.477672e-01
## 5 4.003869e-02
## 6 1.152942e-01
## 7 4.696395e-01
## 8 1.872891e-01
## 9 4.221157e-01
## 10 3.088335e-01
## 11 -3.264982e-02
## 12 -2.378291e-01
## 13 1.119334e-01
## 14 1.538647e-01
## 15 3.173446e-01
## 16 1.317343e-01
## 17 -2.357918e-02
## 18 -4.042113e-02
## 19 -2.160224e-02
## 20 3.218401e-01
## 21 -1.629951e-01
## 22 6.464568e-01
## 23 4.251941e-01
## 24 -1.827652e-01
## 25 -1.248677e-01
## 26 2.748793e-01
## 27 2.533187e-03
## 28 3.984152e-01
## 29 4.834440e-01
## 30 2.546294e-01
## 31 6.371636e-02
## 32 -1.547806e-01
## 33 -2.158216e-01
## 34 -9.950627e-02
## 35 -4.844240e-01
## 36 3.626951e-01
## 37 3.378640e-01
## 38 3.254166e-01
## 39 2.400115e-01
## 40 1.443721e-02
## 41 1.556329e-01
## 42 -4.475789e-01
## 43 -8.485258e-02
## 44 -1.710101e-02
## 45 -8.018243e-02
## 46 -1.641236e-02
## 47 4.837594e-01
## 48 2.194738e-01
## 49 2.752717e-01
## 50 -1.063766e-01
## 51 1.524026e-01
## 52 1.989288e-01
## 53 4.291441e-01
## 54 -2.021065e-01
## 55 3.003342e-01
## 56 -4.207670e-01
## 57 -4.400752e-01
## 58 8.831501e-02
## 59 -2.538611e-01
## 60 3.290818e-02
## 61 2.855285e-01
## 62 3.812364e-01
## 63 6.277453e-02
## 64 2.103735e-01
## 65 3.261628e-01
## 66 6.328381e-02
## 67 -2.116618e-01
## 68 -2.528048e-01
## 69 2.294022e-01
## 70 -2.941338e-01
## 71 -5.699918e-03
## 72 1.027520e-01
## 73 -4.146669e-01
## 74 1.133888e-01
## 75 2.384956e-01
## 76 7.768673e-02
## 77 -2.829046e-01
## 78 -1.708340e-02
## 79 3.671644e-01
## 80 -4.514029e-02
## 81 1.418521e-01
## 82 2.688315e-01
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## 95 5.790346e-01
## 96 8.759331e-02
## 97 -1.173931e-01
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## 99 -1.426815e-01
## 100 5.878465e-01
## 101 8.347451e-02
## 102 -3.545077e-01
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##
## $d
## (Intercept)
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##
## $`dept:service`
## (Intercept)
## 15:0 -0.047839371
## 15:1 0.154602219
## 5:0 0.048720782
## 5:1 0.072421837
## 10:0 -0.165662341
## 10:1 0.057190792
## 12:0 0.023753762
## 12:1 -0.007547317
## 6:0 0.038234172
## 6:1 -0.189710197
## 7:0 0.085236770
## 7:1 -0.027862281
## 4:0 0.092246120
## 4:1 0.066657203
## 8:0 0.027147038
## 8:1 0.097782509
## 9:0 0.053327097
## 9:1 -0.164455636
## 14:0 0.056097413
## 14:1 -0.154664430
## 1:0 0.009956489
## 1:1 0.019533672
## 3:0 0.013598001
## 3:1 0.035621174
## 11:0 0.071008802
## 11:1 -0.182675133
## 2:0 0.018398875
## 2:1 -0.101118021
str(ranef(model5))
## List of 3
## $ s :'data.frame': 2972 obs. of 1 variable:
## ..$ (Intercept): num [1:2972] 0.148 -0.0464 0.319 0.2478 0.04 ...
## $ d :'data.frame': 1128 obs. of 1 variable:
## ..$ (Intercept): num [1:1128] 0.419 -0.472 0.742 -0.587 0.305 ...
## $ dept:service:'data.frame': 28 obs. of 1 variable:
## ..$ (Intercept): num [1:28] -0.0478 0.1546 0.0487 0.0724 -0.1657 ...
## - attr(*, "class")= chr "ranef.mer"
dotplot(ranef(model5, postVar = TRUE))
## Warning in ranef.merMod(model5, postVar = TRUE): 'postVar' is deprecated:
## please use 'condVar' instead
## $s
##
## $d
##
## $`dept:service`
qqmath(ranef(model5, postVar=TRUE))
## Warning in ranef.merMod(model5, postVar = TRUE): 'postVar' is deprecated:
## please use 'condVar' instead
## $s
##
## $d
##
## $`dept:service`
model5a <- lmer(y ~ 1 + (1|s) + (1|d), InstEval, REML=0)
anova(model5a,model5)
## Data: InstEval
## Models:
## model5a: y ~ 1 + (1 | s) + (1 | d)
## model5: y ~ 1 + (1 | s) + (1 | d) + (1 | dept:service)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## model5a 4 237786 237823 -118889 237778
## model5 5 237663 237709 -118827 237653 124.43 1 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1