############################Split-plot experiment##########################
library(lmerTest) #this is the package suggested
## Loading required package: Matrix
## Loading required package: lme4
##
## Attaching package: 'lmerTest'
## The following object is masked from 'package:lme4':
##
## lmer
## The following object is masked from 'package:stats':
##
## step
library(nlme) #for random effects, degrees of freedom has some problem
##
## Attaching package: 'nlme'
## The following object is masked from 'package:lme4':
##
## lmList
require(ggplot2)
## Loading required package: ggplot2
require(reshape2) #to change long format to wide format or change from wide format to long format
## Loading required package: reshape2
library(heplots) #test equivalence of covariance matrix
## Loading required package: car
library(multcomp) #for multiple comparison
## Loading required package: mvtnorm
## Loading required package: survival
## Loading required package: TH.data
## Loading required package: MASS
##
## Attaching package: 'TH.data'
## The following object is masked from 'package:MASS':
##
## geyser
library(xtable)
library(lsmeans)
## Loading required package: estimability
##
## Attaching package: 'lsmeans'
## The following object is masked from 'package:lmerTest':
##
## lsmeans
#hrate is in long format
hrate<-read.table("C:/jenn/teaching/stat579/data/heartrate.txt",header=TRUE)
nrow(hrate) #120
## [1] 120
hrate
## drug subject time rate
## 1 a 11 time1 81
## 2 a 11 time2 81
## 3 a 11 time3 82
## 4 a 11 time4 82
## 5 a 12 time1 82
## 6 a 12 time2 83
## 7 a 12 time3 80
## 8 a 12 time4 81
## 9 a 13 time1 81
## 10 a 13 time2 77
## 11 a 13 time3 80
## 12 a 13 time4 80
## 13 a 14 time1 84
## 14 a 14 time2 86
## 15 a 14 time3 85
## 16 a 14 time4 85
## 17 a 15 time1 88
## 18 a 15 time2 90
## 19 a 15 time3 88
## 20 a 15 time4 86
## 21 a 16 time1 83
## 22 a 16 time2 82
## 23 a 16 time3 86
## 24 a 16 time4 85
## 25 a 17 time1 85
## 26 a 17 time2 83
## 27 a 17 time3 87
## 28 a 17 time4 86
## 29 a 18 time1 81
## 30 a 18 time2 85
## 31 a 18 time3 86
## 32 a 18 time4 85
## 33 a 19 time1 87
## 34 a 19 time2 89
## 35 a 19 time3 87
## 36 a 19 time4 82
## 37 a 20 time1 77
## 38 a 20 time2 75
## 39 a 20 time3 73
## 40 a 20 time4 77
## 41 b 21 time1 76
## 42 b 21 time2 83
## 43 b 21 time3 85
## 44 b 21 time4 79
## 45 b 22 time1 75
## 46 b 22 time2 81
## 47 b 22 time3 85
## 48 b 22 time4 73
## 49 b 23 time1 75
## 50 b 23 time2 82
## 51 b 23 time3 80
## 52 b 23 time4 77
## 53 b 24 time1 68
## 54 b 24 time2 73
## 55 b 24 time3 72
## 56 b 24 time4 69
## 57 b 25 time1 78
## 58 b 25 time2 87
## 59 b 25 time3 86
## 60 b 25 time4 77
## 61 b 26 time1 81
## 62 b 26 time2 85
## 63 b 26 time3 81
## 64 b 26 time4 74
## 65 b 27 time1 67
## 66 b 27 time2 73
## 67 b 27 time3 75
## 68 b 27 time4 66
## 69 b 28 time1 68
## 70 b 28 time2 73
## 71 b 28 time3 73
## 72 b 28 time4 66
## 73 b 29 time1 68
## 74 b 29 time2 75
## 75 b 29 time3 79
## 76 b 29 time4 69
## 77 b 30 time1 73
## 78 b 30 time2 78
## 79 b 30 time3 80
## 80 b 30 time4 70
## 81 p 1 time1 80
## 82 p 1 time2 77
## 83 p 1 time3 73
## 84 p 1 time4 69
## 85 p 2 time1 64
## 86 p 2 time2 66
## 87 p 2 time3 68
## 88 p 2 time4 71
## 89 p 3 time1 75
## 90 p 3 time2 73
## 91 p 3 time3 73
## 92 p 3 time4 69
## 93 p 4 time1 72
## 94 p 4 time2 70
## 95 p 4 time3 74
## 96 p 4 time4 73
## 97 p 5 time1 74
## 98 p 5 time2 74
## 99 p 5 time3 71
## 100 p 5 time4 67
## 101 p 6 time1 71
## 102 p 6 time2 71
## 103 p 6 time3 72
## 104 p 6 time4 70
## 105 p 7 time1 76
## 106 p 7 time2 78
## 107 p 7 time3 74
## 108 p 7 time4 71
## 109 p 8 time1 73
## 110 p 8 time2 68
## 111 p 8 time3 64
## 112 p 8 time4 64
## 113 p 9 time1 76
## 114 p 9 time2 73
## 115 p 9 time3 74
## 116 p 9 time4 76
## 117 p 10 time1 77
## 118 p 10 time2 78
## 119 p 10 time3 77
## 120 p 10 time4 73
hrate$time<-factor(hrate$time)
hrate$drug<-factor(hrate$drug)
hrate$subject<-factor(hrate$subject)
boxplot(rate~drug, data=hrate, main="boxplot of rate vs drug")
![](data:image/png;base64,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)
#use ggplot for rate vs drug for each time period
p <- ggplot(hrate, aes(factor(time), rate)) + geom_boxplot(aes(fill = drug))
p
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)
## d2 is a data set in wide format, with 30 variables and 6 columns, drug,
#subject, time1-time4, you can change d2 to the long format, such as the data
#hrate with 120 obsn and 4 columns drug, subject, time, and rate
d2<-read.table("C:/jenn/teaching/stat579/data/splitd2.txt",header=TRUE)
d2.long <- melt(d2,
# id.vars: ID variables
# all variables to keep but not split apart on
id.vars=c("subject","drug"),
# measure.vars: The source columns
# (if unspecified then all other variables are measure.vars)
measure.vars = c("time1", "time2", "time3", "time4"),
# variable.name: Name of the destination column identifying each
# original column that the measurement came from
variable.name = "time",
# value.name: column name for values in table
value.name = "rate"
)
nrow(d2)
## [1] 30
d2
## drug subject time1 time2 time3 time4
## 1 p 11 80 77 73 69
## 2 p 12 64 66 68 71
## 3 p 13 75 73 73 69
## 4 p 14 72 70 74 73
## 5 p 15 74 74 71 67
## 6 p 16 71 71 72 70
## 7 p 17 76 78 74 71
## 8 p 18 73 68 64 64
## 9 p 19 76 73 74 76
## 10 p 20 77 78 77 73
## 11 a 21 81 81 82 82
## 12 a 22 82 83 80 81
## 13 a 23 81 77 80 80
## 14 a 24 84 86 85 85
## 15 a 25 88 90 88 86
## 16 a 26 83 82 86 85
## 17 a 27 85 83 87 86
## 18 a 28 81 85 86 85
## 19 a 29 87 89 87 82
## 20 a 30 77 75 73 77
## 21 b 1 76 83 85 79
## 22 b 2 75 81 85 73
## 23 b 3 75 82 80 77
## 24 b 4 68 73 72 69
## 25 b 5 78 87 86 77
## 26 b 6 81 85 81 74
## 27 b 7 67 73 75 66
## 28 b 8 68 73 73 66
## 29 b 9 68 75 79 69
## 30 b 10 73 78 80 70
nrow(d2.long)
## [1] 120
d2.long[1:20,]
## subject drug time rate
## 1 11 p time1 80
## 2 12 p time1 64
## 3 13 p time1 75
## 4 14 p time1 72
## 5 15 p time1 74
## 6 16 p time1 71
## 7 17 p time1 76
## 8 18 p time1 73
## 9 19 p time1 76
## 10 20 p time1 77
## 11 21 a time1 81
## 12 22 a time1 82
## 13 23 a time1 81
## 14 24 a time1 84
## 15 25 a time1 88
## 16 26 a time1 83
## 17 27 a time1 85
## 18 28 a time1 81
## 19 29 a time1 87
## 20 30 a time1 77
d2p<-d2[1:10,3:6]
d2a<-d2[11:20,3:6]
d2b<-d2[21:30,3:6]
cov(d2p)
## time1 time2 time3 time4
## time1 18.6222222 15.066667 8.222222 0.7333333
## time2 15.0666667 17.066667 11.111111 3.0666667
## time3 8.2222222 11.111111 13.333333 8.8888889
## time4 0.7333333 3.066667 8.888889 11.3444444
cov(d2a)
## time1 time2 time3 time4
## time1 10.544444 13.56667 12.93333 6.766667
## time2 13.566667 22.54444 18.62222 10.122222
## time3 12.933333 18.62222 21.82222 12.822222
## time4 6.766667 10.12222 12.82222 8.988889
cov(d2b)
## time1 time2 time3 time4
## time1 24.10000 25.11111 19.17778 18.88889
## time2 25.11111 28.22222 23.11111 22.33333
## time3 19.17778 23.11111 24.93333 19.00000
## time4 18.88889 22.33333 19.00000 22.00000
##test if the three covariance matrices are equivalent across the groups
tres <- boxM(d2[, 3:6], d2[, "drug"])
tres
##
## Box's M-test for Homogeneity of Covariance Matrices
##
## data: d2[, 3:6]
## Chi-Sq (approx.) = 24.408, df = 20, p-value = 0.225
summary(tres)
## Summary for Box's M-test of Equality of Covariance Matrices
##
## Chi-Sq: 24.40793
## df: 20
## p-value: 0.225
##
## log of Covariance determinants:
## a b p pooled
## 5.821413 6.824833 7.334394 7.807921
##
## Eigenvalues:
## a b p pooled
## 1 56.2796579 89.0611189 41.3959082 61.387858
## 2 5.1989142 5.7388204 15.3936986 8.675867
## 3 1.7697531 4.0060892 2.6799066 2.785441
## 4 0.6516748 0.4495271 0.8971533 1.658242
##
## Statistics based on eigenvalues:
## a b p pooled
## product 337.4486511 920.4226490 1532.0986435 2460.0118833
## sum 63.9000000 99.2555556 60.3666667 74.5074074
## precision 0.4329614 0.3759879 0.6341546 0.9144028
## max 56.2796579 89.0611189 41.3959082 61.3878580
##checking interactions #seems interaction is significant
interaction.plot(hrate$drug,hrate$time,hrate$rate)
![](data:image/png;base64,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)
##fit full model with two treatments
##note that there are 30 subjects with 1-30, identifiable betweent the groups
##adding nested structure or not doesn't make difference
myfit<-lmer(rate~drug*time+(1|subject),data=hrate)
summary(myfit)
## Linear mixed model fit by REML t-tests use Satterthwaite approximations
## to degrees of freedom [lmerMod]
## Formula: rate ~ drug * time + (1 | subject)
## Data: hrate
##
## REML criterion at convergence: 571.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.39109 -0.52260 -0.05669 0.50612 2.41993
##
## Random effects:
## Groups Name Variance Std.Dev.
## subject (Intercept) 13.864 3.723
## Residual 4.763 2.182
## Number of obs: 120, groups: subject, 30
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 8.290e+01 1.365e+00 4.057e+01 60.741 < 2e-16 ***
## drugb -1.000e+01 1.930e+00 4.057e+01 -5.181 6.41e-06 ***
## drugp -9.100e+00 1.930e+00 4.057e+01 -4.715 2.85e-05 ***
## timetime2 2.000e-01 9.760e-01 8.100e+01 0.205 0.8382
## timetime3 5.000e-01 9.760e-01 8.100e+01 0.512 0.6099
## timetime4 1.057e-14 9.760e-01 8.100e+01 0.000 1.0000
## drugb:timetime2 5.900e+00 1.380e+00 8.100e+01 4.274 5.20e-05 ***
## drugp:timetime2 -1.200e+00 1.380e+00 8.100e+01 -0.869 0.3872
## drugb:timetime3 6.200e+00 1.380e+00 8.100e+01 4.492 2.32e-05 ***
## drugp:timetime3 -2.300e+00 1.380e+00 8.100e+01 -1.666 0.0995 .
## drugb:timetime4 -9.000e-01 1.380e+00 8.100e+01 -0.652 0.5162
## drugp:timetime4 -3.500e+00 1.380e+00 8.100e+01 -2.536 0.0131 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) drugb drugp timtm2 timtm3 timtm4 drgb:2 drgp:2 drgb:3
## drugb -0.707
## drugp -0.707 0.500
## timetime2 -0.358 0.253 0.253
## timetime3 -0.358 0.253 0.253 0.500
## timetime4 -0.358 0.253 0.253 0.500 0.500
## drugb:tmtm2 0.253 -0.358 -0.179 -0.707 -0.354 -0.354
## drugp:tmtm2 0.253 -0.179 -0.358 -0.707 -0.354 -0.354 0.500
## drugb:tmtm3 0.253 -0.358 -0.179 -0.354 -0.707 -0.354 0.500 0.250
## drugp:tmtm3 0.253 -0.179 -0.358 -0.354 -0.707 -0.354 0.250 0.500 0.500
## drugb:tmtm4 0.253 -0.358 -0.179 -0.354 -0.354 -0.707 0.500 0.250 0.500
## drugp:tmtm4 0.253 -0.179 -0.358 -0.354 -0.354 -0.707 0.250 0.500 0.250
## drgp:3 drgb:4
## drugb
## drugp
## timetime2
## timetime3
## timetime4
## drugb:tmtm2
## drugp:tmtm2
## drugb:tmtm3
## drugp:tmtm3
## drugb:tmtm4 0.250
## drugp:tmtm4 0.500 0.500
print(xtable(anova(myfit))) #this is for the latex version to enter the table
## % latex table generated in R 3.2.5 by xtable 1.8-2 package
## % Tue Mar 27 00:04:06 2018
## \begin{table}[ht]
## \centering
## \begin{tabular}{lrrrrrr}
## \hline
## & Sum Sq & Mean Sq & NumDF & DenDF & F.value & Pr($>$F) \\
## \hline
## drug & 192.89 & 96.44 & 2.00 & 27.00 & 20.25 & 0.0000 \\
## time & 222.29 & 74.10 & 3.00 & 81.00 & 15.56 & 0.0000 \\
## drug:time & 320.13 & 53.36 & 6.00 & 81.00 & 11.20 & 0.0000 \\
## \hline
## \end{tabular}
## \end{table}
anova(myfit)
## Analysis of Variance Table of type III with Satterthwaite
## approximation for degrees of freedom
## Sum Sq Mean Sq NumDF DenDF F.value Pr(>F)
## drug 192.89 96.443 2 27 20.247 4.249e-06 ***
## time 222.29 74.097 3 81 15.556 4.444e-08 ***
## drug:time 320.13 53.356 6 81 11.201 4.539e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
myfit2<-lmer(rate~drug*time+(1|subject/drug),data=hrate)
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: large eigenvalue ratio
## - Rescale variables?
summary(myfit2)
## Linear mixed model fit by REML t-tests use Satterthwaite approximations
## to degrees of freedom [lmerMod]
## Formula: rate ~ drug * time + (1 | subject/drug)
## Data: hrate
##
## REML criterion at convergence: 571.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.39109 -0.52260 -0.05669 0.50612 2.41993
##
## Random effects:
## Groups Name Variance Std.Dev.
## drug:subject (Intercept) 6.773 2.602
## subject (Intercept) 7.091 2.663
## Residual 4.763 2.182
## Number of obs: 120, groups: drug:subject, 30; subject, 30
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 8.290e+01 1.365e+00 4.057e+01 60.741 < 2e-16 ***
## drugb -1.000e+01 1.930e+00 4.057e+01 -5.181 6.41e-06 ***
## drugp -9.100e+00 1.930e+00 4.057e+01 -4.715 2.85e-05 ***
## timetime2 2.000e-01 9.760e-01 8.100e+01 0.205 0.8382
## timetime3 5.000e-01 9.760e-01 8.100e+01 0.512 0.6099
## timetime4 2.968e-14 9.760e-01 8.100e+01 0.000 1.0000
## drugb:timetime2 5.900e+00 1.380e+00 8.100e+01 4.274 5.20e-05 ***
## drugp:timetime2 -1.200e+00 1.380e+00 8.100e+01 -0.869 0.3872
## drugb:timetime3 6.200e+00 1.380e+00 8.100e+01 4.492 2.32e-05 ***
## drugp:timetime3 -2.300e+00 1.380e+00 8.100e+01 -1.666 0.0995 .
## drugb:timetime4 -9.000e-01 1.380e+00 8.100e+01 -0.652 0.5162
## drugp:timetime4 -3.500e+00 1.380e+00 8.100e+01 -2.536 0.0131 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) drugb drugp timtm2 timtm3 timtm4 drgb:2 drgp:2 drgb:3
## drugb -0.707
## drugp -0.707 0.500
## timetime2 -0.358 0.253 0.253
## timetime3 -0.358 0.253 0.253 0.500
## timetime4 -0.358 0.253 0.253 0.500 0.500
## drugb:tmtm2 0.253 -0.358 -0.179 -0.707 -0.354 -0.354
## drugp:tmtm2 0.253 -0.179 -0.358 -0.707 -0.354 -0.354 0.500
## drugb:tmtm3 0.253 -0.358 -0.179 -0.354 -0.707 -0.354 0.500 0.250
## drugp:tmtm3 0.253 -0.179 -0.358 -0.354 -0.707 -0.354 0.250 0.500 0.500
## drugb:tmtm4 0.253 -0.358 -0.179 -0.354 -0.354 -0.707 0.500 0.250 0.500
## drugp:tmtm4 0.253 -0.179 -0.358 -0.354 -0.354 -0.707 0.250 0.500 0.250
## drgp:3 drgb:4
## drugb
## drugp
## timetime2
## timetime3
## timetime4
## drugb:tmtm2
## drugp:tmtm2
## drugb:tmtm3
## drugp:tmtm3
## drugb:tmtm4 0.250
## drugp:tmtm4 0.500 0.500
## convergence code: 0
## Model is nearly unidentifiable: large eigenvalue ratio
## - Rescale variables?
anova(myfit2)
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: large eigenvalue ratio
## - Rescale variables?
## Analysis of Variance Table of type III with Satterthwaite
## approximation for degrees of freedom
## Sum Sq Mean Sq NumDF DenDF F.value Pr(>F)
## drug 192.89 96.443 2 27 20.247 4.249e-06 ***
## time 222.29 74.097 3 81 15.556 4.444e-08 ***
## drug:time 320.13 53.356 6 81 11.201 4.539e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#same result if using d2.long data
myfit3<-lmer(rate~drug*time+(1|subject),data=d2.long)
summary(myfit3)
## Linear mixed model fit by REML t-tests use Satterthwaite approximations
## to degrees of freedom [lmerMod]
## Formula: rate ~ drug * time + (1 | subject)
## Data: d2.long
##
## REML criterion at convergence: 571.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.39109 -0.52260 -0.05669 0.50612 2.41993
##
## Random effects:
## Groups Name Variance Std.Dev.
## subject (Intercept) 13.864 3.723
## Residual 4.763 2.182
## Number of obs: 120, groups: subject, 30
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 8.290e+01 1.365e+00 4.057e+01 60.741 < 2e-16 ***
## drugb -1.000e+01 1.930e+00 4.057e+01 -5.181 6.41e-06 ***
## drugp -9.100e+00 1.930e+00 4.057e+01 -4.715 2.85e-05 ***
## timetime2 2.000e-01 9.760e-01 8.100e+01 0.205 0.8382
## timetime3 5.000e-01 9.760e-01 8.100e+01 0.512 0.6099
## timetime4 1.057e-14 9.760e-01 8.100e+01 0.000 1.0000
## drugb:timetime2 5.900e+00 1.380e+00 8.100e+01 4.274 5.20e-05 ***
## drugp:timetime2 -1.200e+00 1.380e+00 8.100e+01 -0.869 0.3872
## drugb:timetime3 6.200e+00 1.380e+00 8.100e+01 4.492 2.32e-05 ***
## drugp:timetime3 -2.300e+00 1.380e+00 8.100e+01 -1.666 0.0995 .
## drugb:timetime4 -9.000e-01 1.380e+00 8.100e+01 -0.652 0.5162
## drugp:timetime4 -3.500e+00 1.380e+00 8.100e+01 -2.536 0.0131 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) drugb drugp timtm2 timtm3 timtm4 drgb:2 drgp:2 drgb:3
## drugb -0.707
## drugp -0.707 0.500
## timetime2 -0.358 0.253 0.253
## timetime3 -0.358 0.253 0.253 0.500
## timetime4 -0.358 0.253 0.253 0.500 0.500
## drugb:tmtm2 0.253 -0.358 -0.179 -0.707 -0.354 -0.354
## drugp:tmtm2 0.253 -0.179 -0.358 -0.707 -0.354 -0.354 0.500
## drugb:tmtm3 0.253 -0.358 -0.179 -0.354 -0.707 -0.354 0.500 0.250
## drugp:tmtm3 0.253 -0.179 -0.358 -0.354 -0.707 -0.354 0.250 0.500 0.500
## drugb:tmtm4 0.253 -0.358 -0.179 -0.354 -0.354 -0.707 0.500 0.250 0.500
## drugp:tmtm4 0.253 -0.179 -0.358 -0.354 -0.354 -0.707 0.250 0.500 0.250
## drgp:3 drgb:4
## drugb
## drugp
## timetime2
## timetime3
## timetime4
## drugb:tmtm2
## drugp:tmtm2
## drugb:tmtm3
## drugp:tmtm3
## drugb:tmtm4 0.250
## drugp:tmtm4 0.500 0.500
anova(myfit3)
## Analysis of Variance Table of type III with Satterthwaite
## approximation for degrees of freedom
## Sum Sq Mean Sq NumDF DenDF F.value Pr(>F)
## drug 192.89 96.443 2 27 20.247 4.249e-06 ***
## time 222.29 74.097 3 81 15.556 4.444e-08 ***
## drug:time 320.13 53.356 6 81 11.201 4.539e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#however, if within each group p, a and b, subjects are listed as 1-10, 1-10, 1-10 respectively
#you will need to add the nested structure, otherwise, R will consider subject 1 from group p, a and b as the
#same subject
#d3 is constructed as "subjects are listed as 1-10, 1-10, 1-10 respectively within the three groups"
d3<-read.table("C:/jenn/teaching/stat579/data/splitd3.txt",header=TRUE)
d3.long <- melt(d3,
# id.vars: ID variables
# all variables to keep but not split apart on
id.vars=c("subject","drug"),
# measure.vars: The source columns
# (if unspecified then all other variables are measure.vars)
measure.vars = c("time1", "time2", "time3", "time4"),
# variable.name: Name of the destination column identifying each
# original column that the measurement came from
variable.name = "time",
# value.name: column name for values in table
value.name = "rate"
)
nrow(d3)
## [1] 30
d3
## drug subject time1 time2 time3 time4
## 1 p 1 80 77 73 69
## 2 p 2 64 66 68 71
## 3 p 3 75 73 73 69
## 4 p 4 72 70 74 73
## 5 p 5 74 74 71 67
## 6 p 6 71 71 72 70
## 7 p 7 76 78 74 71
## 8 p 8 73 68 64 64
## 9 p 9 76 73 74 76
## 10 p 10 77 78 77 73
## 11 a 1 81 81 82 82
## 12 a 2 82 83 80 81
## 13 a 3 81 77 80 80
## 14 a 4 84 86 85 85
## 15 a 5 88 90 88 86
## 16 a 6 83 82 86 85
## 17 a 7 85 83 87 86
## 18 a 8 81 85 86 85
## 19 a 9 87 89 87 82
## 20 a 10 77 75 73 77
## 21 b 1 76 83 85 79
## 22 b 2 75 81 85 73
## 23 b 3 75 82 80 77
## 24 b 4 68 73 72 69
## 25 b 5 78 87 86 77
## 26 b 6 81 85 81 74
## 27 b 7 67 73 75 66
## 28 b 8 68 73 73 66
## 29 b 9 68 75 79 69
## 30 b 10 73 78 80 70
d3.long[1:60,]
## subject drug time rate
## 1 1 p time1 80
## 2 2 p time1 64
## 3 3 p time1 75
## 4 4 p time1 72
## 5 5 p time1 74
## 6 6 p time1 71
## 7 7 p time1 76
## 8 8 p time1 73
## 9 9 p time1 76
## 10 10 p time1 77
## 11 1 a time1 81
## 12 2 a time1 82
## 13 3 a time1 81
## 14 4 a time1 84
## 15 5 a time1 88
## 16 6 a time1 83
## 17 7 a time1 85
## 18 8 a time1 81
## 19 9 a time1 87
## 20 10 a time1 77
## 21 1 b time1 76
## 22 2 b time1 75
## 23 3 b time1 75
## 24 4 b time1 68
## 25 5 b time1 78
## 26 6 b time1 81
## 27 7 b time1 67
## 28 8 b time1 68
## 29 9 b time1 68
## 30 10 b time1 73
## 31 1 p time2 77
## 32 2 p time2 66
## 33 3 p time2 73
## 34 4 p time2 70
## 35 5 p time2 74
## 36 6 p time2 71
## 37 7 p time2 78
## 38 8 p time2 68
## 39 9 p time2 73
## 40 10 p time2 78
## 41 1 a time2 81
## 42 2 a time2 83
## 43 3 a time2 77
## 44 4 a time2 86
## 45 5 a time2 90
## 46 6 a time2 82
## 47 7 a time2 83
## 48 8 a time2 85
## 49 9 a time2 89
## 50 10 a time2 75
## 51 1 b time2 83
## 52 2 b time2 81
## 53 3 b time2 82
## 54 4 b time2 73
## 55 5 b time2 87
## 56 6 b time2 85
## 57 7 b time2 73
## 58 8 b time2 73
## 59 9 b time2 75
## 60 10 b time2 78
#in this case, without nested structure, R analyze as a completely randomized block design
myfit4<-lmer(rate~drug*time+(1|subject),data=d3.long)
summary(myfit4)
## Linear mixed model fit by REML t-tests use Satterthwaite approximations
## to degrees of freedom [lmerMod]
## Formula: rate ~ drug * time + (1 | subject)
## Data: d3.long
##
## REML criterion at convergence: 644.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.3605 -0.6893 0.1336 0.7202 1.7950
##
## Random effects:
## Groups Name Variance Std.Dev.
## subject (Intercept) 2.391 1.546
## Residual 16.236 4.029
## Number of obs: 120, groups: subject, 10
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 8.290e+01 1.365e+00 9.143e+01 60.741 < 2e-16 ***
## drugb -1.000e+01 1.802e+00 9.900e+01 -5.549 2.40e-07 ***
## drugp -9.100e+00 1.802e+00 9.900e+01 -5.050 2.02e-06 ***
## timetime2 2.000e-01 1.802e+00 9.900e+01 0.111 0.9119
## timetime3 5.000e-01 1.802e+00 9.900e+01 0.277 0.7820
## timetime4 -5.256e-14 1.802e+00 9.900e+01 0.000 1.0000
## drugb:timetime2 5.900e+00 2.548e+00 9.900e+01 2.315 0.0227 *
## drugp:timetime2 -1.200e+00 2.548e+00 9.900e+01 -0.471 0.6388
## drugb:timetime3 6.200e+00 2.548e+00 9.900e+01 2.433 0.0168 *
## drugp:timetime3 -2.300e+00 2.548e+00 9.900e+01 -0.903 0.3690
## drugb:timetime4 -9.000e-01 2.548e+00 9.900e+01 -0.353 0.7247
## drugp:timetime4 -3.500e+00 2.548e+00 9.900e+01 -1.373 0.1727
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) drugb drugp timtm2 timtm3 timtm4 drgb:2 drgp:2 drgb:3
## drugb -0.660
## drugp -0.660 0.500
## timetime2 -0.660 0.500 0.500
## timetime3 -0.660 0.500 0.500 0.500
## timetime4 -0.660 0.500 0.500 0.500 0.500
## drugb:tmtm2 0.467 -0.707 -0.354 -0.707 -0.354 -0.354
## drugp:tmtm2 0.467 -0.354 -0.707 -0.707 -0.354 -0.354 0.500
## drugb:tmtm3 0.467 -0.707 -0.354 -0.354 -0.707 -0.354 0.500 0.250
## drugp:tmtm3 0.467 -0.354 -0.707 -0.354 -0.707 -0.354 0.250 0.500 0.500
## drugb:tmtm4 0.467 -0.707 -0.354 -0.354 -0.354 -0.707 0.500 0.250 0.500
## drugp:tmtm4 0.467 -0.354 -0.707 -0.354 -0.354 -0.707 0.250 0.500 0.250
## drgp:3 drgb:4
## drugb
## drugp
## timetime2
## timetime3
## timetime4
## drugb:tmtm2
## drugp:tmtm2
## drugb:tmtm3
## drugp:tmtm3
## drugb:tmtm4 0.250
## drugp:tmtm4 0.500 0.500
anova(myfit4)
## Analysis of Variance Table of type III with Satterthwaite
## approximation for degrees of freedom
## Sum Sq Mean Sq NumDF DenDF F.value Pr(>F)
## drug 2438.47 1219.23 2 99 75.095 < 2.2e-16 ***
## time 222.29 74.10 3 99 4.564 0.004886 **
## drug:time 320.13 53.36 6 99 3.286 0.005444 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#adding nested structure
myfit5<-lmer(rate~drug*time+(1|subject/drug),data=d3.long) #subject nested in drug
summary(myfit5)
## Linear mixed model fit by REML t-tests use Satterthwaite approximations
## to degrees of freedom [lmerMod]
## Formula: rate ~ drug * time + (1 | subject/drug)
## Data: d3.long
##
## REML criterion at convergence: 571.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.39109 -0.52260 -0.05669 0.50612 2.41993
##
## Random effects:
## Groups Name Variance Std.Dev.
## drug:subject (Intercept) 13.864 3.723
## subject (Intercept) 0.000 0.000
## Residual 4.763 2.182
## Number of obs: 120, groups: drug:subject, 30; subject, 10
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 8.290e+01 1.365e+00 4.057e+01 60.741 < 2e-16 ***
## drugb -1.000e+01 1.930e+00 4.057e+01 -5.181 6.41e-06 ***
## drugp -9.100e+00 1.930e+00 4.057e+01 -4.715 2.85e-05 ***
## timetime2 2.000e-01 9.760e-01 8.100e+01 0.205 0.8382
## timetime3 5.000e-01 9.760e-01 8.100e+01 0.512 0.6099
## timetime4 -7.512e-14 9.760e-01 8.100e+01 0.000 1.0000
## drugb:timetime2 5.900e+00 1.380e+00 8.100e+01 4.274 5.20e-05 ***
## drugp:timetime2 -1.200e+00 1.380e+00 8.100e+01 -0.869 0.3872
## drugb:timetime3 6.200e+00 1.380e+00 8.100e+01 4.492 2.32e-05 ***
## drugp:timetime3 -2.300e+00 1.380e+00 8.100e+01 -1.666 0.0995 .
## drugb:timetime4 -9.000e-01 1.380e+00 8.100e+01 -0.652 0.5162
## drugp:timetime4 -3.500e+00 1.380e+00 8.100e+01 -2.536 0.0131 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) drugb drugp timtm2 timtm3 timtm4 drgb:2 drgp:2 drgb:3
## drugb -0.707
## drugp -0.707 0.500
## timetime2 -0.358 0.253 0.253
## timetime3 -0.358 0.253 0.253 0.500
## timetime4 -0.358 0.253 0.253 0.500 0.500
## drugb:tmtm2 0.253 -0.358 -0.179 -0.707 -0.354 -0.354
## drugp:tmtm2 0.253 -0.179 -0.358 -0.707 -0.354 -0.354 0.500
## drugb:tmtm3 0.253 -0.358 -0.179 -0.354 -0.707 -0.354 0.500 0.250
## drugp:tmtm3 0.253 -0.179 -0.358 -0.354 -0.707 -0.354 0.250 0.500 0.500
## drugb:tmtm4 0.253 -0.358 -0.179 -0.354 -0.354 -0.707 0.500 0.250 0.500
## drugp:tmtm4 0.253 -0.179 -0.358 -0.354 -0.354 -0.707 0.250 0.500 0.250
## drgp:3 drgb:4
## drugb
## drugp
## timetime2
## timetime3
## timetime4
## drugb:tmtm2
## drugp:tmtm2
## drugb:tmtm3
## drugp:tmtm3
## drugb:tmtm4 0.250
## drugp:tmtm4 0.500 0.500
anova(myfit5)
## Analysis of Variance Table of type III with Satterthwaite
## approximation for degrees of freedom
## Sum Sq Mean Sq NumDF DenDF F.value Pr(>F)
## drug 192.89 96.443 2 27 20.247 4.249e-06 ***
## time 222.29 74.097 3 81 15.556 4.444e-08 ***
## drug:time 320.13 53.356 6 81 11.201 4.539e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##wrong degrees of freedom from nlme package again, note that the degrees of
#freedom for testing drug effect is 18 instead of 27
myfit6<-lme(rate~drug*time,random=~1|subject/drug,data=d3.long)
summary(myfit6)
## Linear mixed-effects model fit by REML
## Data: d3.long
## AIC BIC logLik
## 601.2025 641.4345 -285.6013
##
## Random effects:
## Formula: ~1 | subject
## (Intercept)
## StdDev: 0.0004930058
##
## Formula: ~1 | drug %in% subject
## (Intercept) Residual
## StdDev: 3.723383 2.182492
##
## Fixed effects: rate ~ drug * time
## Value Std.Error DF t-value p-value
## (Intercept) 82.9 1.3648023 81 60.74140 0.0000
## drugb -10.0 1.9301219 18 -5.18102 0.0001
## drugp -9.1 1.9301219 18 -4.71473 0.0002
## timetime2 0.2 0.9760401 81 0.20491 0.8382
## timetime3 0.5 0.9760401 81 0.51227 0.6099
## timetime4 0.0 0.9760401 81 0.00000 1.0000
## drugb:timetime2 5.9 1.3803292 81 4.27434 0.0001
## drugp:timetime2 -1.2 1.3803292 81 -0.86936 0.3872
## drugb:timetime3 6.2 1.3803292 81 4.49168 0.0000
## drugp:timetime3 -2.3 1.3803292 81 -1.66627 0.0995
## drugb:timetime4 -0.9 1.3803292 81 -0.65202 0.5162
## drugp:timetime4 -3.5 1.3803292 81 -2.53563 0.0131
## Correlation:
## (Intr) drugb drugp timtm2 timtm3 timtm4 drgb:2 drgp:2
## drugb -0.707
## drugp -0.707 0.500
## timetime2 -0.358 0.253 0.253
## timetime3 -0.358 0.253 0.253 0.500
## timetime4 -0.358 0.253 0.253 0.500 0.500
## drugb:timetime2 0.253 -0.358 -0.179 -0.707 -0.354 -0.354
## drugp:timetime2 0.253 -0.179 -0.358 -0.707 -0.354 -0.354 0.500
## drugb:timetime3 0.253 -0.358 -0.179 -0.354 -0.707 -0.354 0.500 0.250
## drugp:timetime3 0.253 -0.179 -0.358 -0.354 -0.707 -0.354 0.250 0.500
## drugb:timetime4 0.253 -0.358 -0.179 -0.354 -0.354 -0.707 0.500 0.250
## drugp:timetime4 0.253 -0.179 -0.358 -0.354 -0.354 -0.707 0.250 0.500
## drgb:3 drgp:3 drgb:4
## drugb
## drugp
## timetime2
## timetime3
## timetime4
## drugb:timetime2
## drugp:timetime2
## drugb:timetime3
## drugp:timetime3 0.500
## drugb:timetime4 0.500 0.250
## drugp:timetime4 0.250 0.500 0.500
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -2.39108657 -0.52260081 -0.05669221 0.50611907 2.41992750
##
## Number of Observations: 120
## Number of Groups:
## subject drug %in% subject
## 10 30
anova(myfit6)
## numDF denDF F-value p-value
## (Intercept) 1 81 11833.060 <.0001
## drug 2 18 20.247 <.0001
## time 3 81 15.556 <.0001
## drug:time 6 81 11.201 <.0001
#We could check of if the random effect is important or not, by the step
#function of lmerTest: (usually, people would prefer to include the random effect
#in the model whether they are signnificant or not)
mystep <- step(myfit) #subject is significant, need to keep
mystep$rand.table
## Chi.sq Chi.DF elim.num p.value
## subject 78.7765 1 kept 0
mystep$anova.table
## Sum Sq Mean Sq NumDF DenDF F.value elim.num Pr(>F)
## drug 192.8851 96.44257 2 27.00002 20.24713 kept 4.249203e-06
## time 222.2917 74.09722 3 81.00001 15.55595 kept 4.444219e-08
## drug:time 320.1333 53.35556 6 81.00001 11.20145 kept 4.539026e-09
mystep$diffs.lsmeans.table #mutlitple comparisons
## Estimate Standard Error DF t-value
## drug a - b 7.2000 1.7352 27.0 4.15
## drug a - p 10.8500 1.7352 27.0 6.25
## drug b - p 3.6500 1.7352 27.0 2.10
## time time1 - time2 -1.7667 0.5635 81.0 -3.14
## time time1 - time3 -1.8000 0.5635 81.0 -3.19
## time time1 - time4 1.4667 0.5635 81.0 2.60
## time time2 - time3 -0.0333 0.5635 81.0 -0.06
## time time2 - time4 3.2333 0.5635 81.0 5.74
## time time3 - time4 3.2667 0.5635 81.0 5.80
## drug:time a time1 - b time1 10.0000 1.9301 40.6 5.18
## drug:time a time1 - p time1 9.1000 1.9301 40.6 4.71
## drug:time a time1 - a time2 -0.2000 0.9760 81.0 -0.20
## drug:time a time1 - b time2 3.9000 1.9301 40.6 2.02
## drug:time a time1 - p time2 10.1000 1.9301 40.6 5.23
## drug:time a time1 - a time3 -0.5000 0.9760 81.0 -0.51
## drug:time a time1 - b time3 3.3000 1.9301 40.6 1.71
## drug:time a time1 - p time3 10.9000 1.9301 40.6 5.65
## drug:time a time1 - a time4 0.0000 0.9760 81.0 0.00
## drug:time a time1 - b time4 10.9000 1.9301 40.6 5.65
## drug:time a time1 - p time4 12.6000 1.9301 40.6 6.53
## drug:time b time1 - p time1 -0.9000 1.9301 40.6 -0.47
## drug:time b time1 - a time2 -10.2000 1.9301 40.6 -5.28
## drug:time b time1 - b time2 -6.1000 0.9760 81.0 -6.25
## drug:time b time1 - p time2 0.1000 1.9301 40.6 0.05
## drug:time b time1 - a time3 -10.5000 1.9301 40.6 -5.44
## drug:time b time1 - b time3 -6.7000 0.9760 81.0 -6.86
## drug:time b time1 - p time3 0.9000 1.9301 40.6 0.47
## drug:time b time1 - a time4 -10.0000 1.9301 40.6 -5.18
## drug:time b time1 - b time4 0.9000 0.9760 81.0 0.92
## drug:time b time1 - p time4 2.6000 1.9301 40.6 1.35
## drug:time p time1 - a time2 -9.3000 1.9301 40.6 -4.82
## drug:time p time1 - b time2 -5.2000 1.9301 40.6 -2.69
## drug:time p time1 - p time2 1.0000 0.9760 81.0 1.02
## drug:time p time1 - a time3 -9.6000 1.9301 40.6 -4.97
## drug:time p time1 - b time3 -5.8000 1.9301 40.6 -3.00
## drug:time p time1 - p time3 1.8000 0.9760 81.0 1.84
## drug:time p time1 - a time4 -9.1000 1.9301 40.6 -4.71
## drug:time p time1 - b time4 1.8000 1.9301 40.6 0.93
## drug:time p time1 - p time4 3.5000 0.9760 81.0 3.59
## drug:time a time2 - b time2 4.1000 1.9301 40.6 2.12
## drug:time a time2 - p time2 10.3000 1.9301 40.6 5.34
## drug:time a time2 - a time3 -0.3000 0.9760 81.0 -0.31
## drug:time a time2 - b time3 3.5000 1.9301 40.6 1.81
## drug:time a time2 - p time3 11.1000 1.9301 40.6 5.75
## drug:time a time2 - a time4 0.2000 0.9760 81.0 0.20
## drug:time a time2 - b time4 11.1000 1.9301 40.6 5.75
## drug:time a time2 - p time4 12.8000 1.9301 40.6 6.63
## drug:time b time2 - p time2 6.2000 1.9301 40.6 3.21
## drug:time b time2 - a time3 -4.4000 1.9301 40.6 -2.28
## drug:time b time2 - b time3 -0.6000 0.9760 81.0 -0.61
## drug:time b time2 - p time3 7.0000 1.9301 40.6 3.63
## drug:time b time2 - a time4 -3.9000 1.9301 40.6 -2.02
## drug:time b time2 - b time4 7.0000 0.9760 81.0 7.17
## drug:time b time2 - p time4 8.7000 1.9301 40.6 4.51
## drug:time p time2 - a time3 -10.6000 1.9301 40.6 -5.49
## drug:time p time2 - b time3 -6.8000 1.9301 40.6 -3.52
## drug:time p time2 - p time3 0.8000 0.9760 81.0 0.82
## drug:time p time2 - a time4 -10.1000 1.9301 40.6 -5.23
## drug:time p time2 - b time4 0.8000 1.9301 40.6 0.41
## drug:time p time2 - p time4 2.5000 0.9760 81.0 2.56
## drug:time a time3 - b time3 3.8000 1.9301 40.6 1.97
## drug:time a time3 - p time3 11.4000 1.9301 40.6 5.91
## drug:time a time3 - a time4 0.5000 0.9760 81.0 0.51
## drug:time a time3 - b time4 11.4000 1.9301 40.6 5.91
## drug:time a time3 - p time4 13.1000 1.9301 40.6 6.79
## drug:time b time3 - p time3 7.6000 1.9301 40.6 3.94
## drug:time b time3 - a time4 -3.3000 1.9301 40.6 -1.71
## drug:time b time3 - b time4 7.6000 0.9760 81.0 7.79
## drug:time b time3 - p time4 9.3000 1.9301 40.6 4.82
## drug:time p time3 - a time4 -10.9000 1.9301 40.6 -5.65
## drug:time p time3 - b time4 0.0000 1.9301 40.6 0.00
## drug:time p time3 - p time4 1.7000 0.9760 81.0 1.74
## drug:time a time4 - b time4 10.9000 1.9301 40.6 5.65
## drug:time a time4 - p time4 12.6000 1.9301 40.6 6.53
## drug:time b time4 - p time4 1.7000 1.9301 40.6 0.88
## Lower CI Upper CI p-value
## drug a - b 3.6397 10.7603 0.0003
## drug a - p 7.2897 14.4103 0.0000
## drug b - p 0.0897 7.2103 0.0449
## time time1 - time2 -2.8879 -0.6454 0.0024
## time time1 - time3 -2.9212 -0.6788 0.0020
## time time1 - time4 0.3454 2.5879 0.0110
## time time2 - time3 -1.1546 1.0879 0.9530
## time time2 - time4 2.1121 4.3546 0.0000
## time time3 - time4 2.1454 4.3879 0.0000
## drug:time a time1 - b time1 6.1008 13.8992 0.0000
## drug:time a time1 - p time1 5.2008 12.9992 0.0000
## drug:time a time1 - a time2 -2.1420 1.7420 0.8382
## drug:time a time1 - b time2 0.0008 7.7992 0.0500
## drug:time a time1 - p time2 6.2008 13.9992 0.0000
## drug:time a time1 - a time3 -2.4420 1.4420 0.6099
## drug:time a time1 - b time3 -0.5992 7.1992 0.0950
## drug:time a time1 - p time3 7.0008 14.7992 0.0000
## drug:time a time1 - a time4 -1.9420 1.9420 1.0000
## drug:time a time1 - b time4 7.0008 14.7992 0.0000
## drug:time a time1 - p time4 8.7008 16.4992 0.0000
## drug:time b time1 - p time1 -4.7992 2.9992 0.6435
## drug:time b time1 - a time2 -14.0992 -6.3008 0.0000
## drug:time b time1 - b time2 -8.0420 -4.1580 0.0000
## drug:time b time1 - p time2 -3.7992 3.9992 0.9589
## drug:time b time1 - a time3 -14.3992 -6.6008 0.0000
## drug:time b time1 - b time3 -8.6420 -4.7580 0.0000
## drug:time b time1 - p time3 -2.9992 4.7992 0.6435
## drug:time b time1 - a time4 -13.8992 -6.1008 0.0000
## drug:time b time1 - b time4 -1.0420 2.8420 0.3592
## drug:time b time1 - p time4 -1.2992 6.4992 0.1854
## drug:time p time1 - a time2 -13.1992 -5.4008 0.0000
## drug:time p time1 - b time2 -9.0992 -1.3008 0.0102
## drug:time p time1 - p time2 -0.9420 2.9420 0.3086
## drug:time p time1 - a time3 -13.4992 -5.7008 0.0000
## drug:time p time1 - b time3 -9.6992 -1.9008 0.0045
## drug:time p time1 - p time3 -0.1420 3.7420 0.0688
## drug:time p time1 - a time4 -12.9992 -5.2008 0.0000
## drug:time p time1 - b time4 -2.0992 5.6992 0.3566
## drug:time p time1 - p time4 1.5580 5.4420 0.0006
## drug:time a time2 - b time2 0.2008 7.9992 0.0398
## drug:time a time2 - p time2 6.4008 14.1992 0.0000
## drug:time a time2 - a time3 -2.2420 1.6420 0.7594
## drug:time a time2 - b time3 -0.3992 7.3992 0.0772
## drug:time a time2 - p time3 7.2008 14.9992 0.0000
## drug:time a time2 - a time4 -1.7420 2.1420 0.8382
## drug:time a time2 - b time4 7.2008 14.9992 0.0000
## drug:time a time2 - p time4 8.9008 16.6992 0.0000
## drug:time b time2 - p time2 2.3008 10.0992 0.0026
## drug:time b time2 - a time3 -8.2992 -0.5008 0.0280
## drug:time b time2 - b time3 -2.5420 1.3420 0.5405
## drug:time b time2 - p time3 3.1008 10.8992 0.0008
## drug:time b time2 - a time4 -7.7992 -0.0008 0.0500
## drug:time b time2 - b time4 5.0580 8.9420 0.0000
## drug:time b time2 - p time4 4.8008 12.5992 0.0001
## drug:time p time2 - a time3 -14.4992 -6.7008 0.0000
## drug:time p time2 - b time3 -10.6992 -2.9008 0.0011
## drug:time p time2 - p time3 -1.1420 2.7420 0.4148
## drug:time p time2 - a time4 -13.9992 -6.2008 0.0000
## drug:time p time2 - b time4 -3.0992 4.6992 0.6807
## drug:time p time2 - p time4 0.5580 4.4420 0.0123
## drug:time a time3 - b time3 -0.0992 7.6992 0.0558
## drug:time a time3 - p time3 7.5008 15.2992 0.0000
## drug:time a time3 - a time4 -1.4420 2.4420 0.6099
## drug:time a time3 - b time4 7.5008 15.2992 0.0000
## drug:time a time3 - p time4 9.2008 16.9992 0.0000
## drug:time b time3 - p time3 3.7008 11.4992 0.0003
## drug:time b time3 - a time4 -7.1992 0.5992 0.0950
## drug:time b time3 - b time4 5.6580 9.5420 0.0000
## drug:time b time3 - p time4 5.4008 13.1992 0.0000
## drug:time p time3 - a time4 -14.7992 -7.0008 0.0000
## drug:time p time3 - b time4 -3.8992 3.8992 1.0000
## drug:time p time3 - p time4 -0.2420 3.6420 0.0854
## drug:time a time4 - b time4 7.0008 14.7992 0.0000
## drug:time a time4 - p time4 8.7008 16.4992 0.0000
## drug:time b time4 - p time4 -2.1992 5.5992 0.3836
##since interaction is significant, let's do multiple comparisons
lsmeans(myfit,pairwise~drug:time)
## $lsmeans
## drug time lsmean SE df lower.CL upper.CL
## a time1 82.9 1.364802 40.57 80.14285 85.65715
## b time1 72.9 1.364802 40.57 70.14285 75.65715
## p time1 73.8 1.364802 40.57 71.04285 76.55715
## a time2 83.1 1.364802 40.57 80.34285 85.85715
## b time2 79.0 1.364802 40.57 76.24285 81.75715
## p time2 72.8 1.364802 40.57 70.04285 75.55715
## a time3 83.4 1.364802 40.57 80.64285 86.15715
## b time3 79.6 1.364802 40.57 76.84285 82.35715
## p time3 72.0 1.364802 40.57 69.24285 74.75715
## a time4 82.9 1.364802 40.57 80.14285 85.65715
## b time4 72.0 1.364802 40.57 69.24285 74.75715
## p time4 70.3 1.364802 40.57 67.54285 73.05715
##
## Degrees-of-freedom method: satterthwaite
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## a,time1 - b,time1 1.000000e+01 1.9301219 40.57 5.181 0.0004
## a,time1 - p,time1 9.100000e+00 1.9301219 40.57 4.715 0.0015
## a,time1 - a,time2 -2.000000e-01 0.9760401 81.00 -0.205 1.0000
## a,time1 - b,time2 3.900000e+00 1.9301219 40.57 2.021 0.6775
## a,time1 - p,time2 1.010000e+01 1.9301219 40.57 5.233 0.0003
## a,time1 - a,time3 -5.000000e-01 0.9760401 81.00 -0.512 1.0000
## a,time1 - b,time3 3.300000e+00 1.9301219 40.57 1.710 0.8534
## a,time1 - p,time3 1.090000e+01 1.9301219 40.57 5.647 0.0001
## a,time1 - a,time4 -1.057053e-14 0.9760401 81.00 0.000 1.0000
## a,time1 - b,time4 1.090000e+01 1.9301219 40.57 5.647 0.0001
## a,time1 - p,time4 1.260000e+01 1.9301219 40.57 6.528 <.0001
## b,time1 - p,time1 -9.000000e-01 1.9301219 40.57 -0.466 1.0000
## b,time1 - a,time2 -1.020000e+01 1.9301219 40.57 -5.285 0.0003
## b,time1 - b,time2 -6.100000e+00 0.9760401 81.00 -6.250 <.0001
## b,time1 - p,time2 1.000000e-01 1.9301219 40.57 0.052 1.0000
## b,time1 - a,time3 -1.050000e+01 1.9301219 40.57 -5.440 0.0002
## b,time1 - b,time3 -6.700000e+00 0.9760401 81.00 -6.864 <.0001
## b,time1 - p,time3 9.000000e-01 1.9301219 40.57 0.466 1.0000
## b,time1 - a,time4 -1.000000e+01 1.9301219 40.57 -5.181 0.0004
## b,time1 - b,time4 9.000000e-01 0.9760401 81.00 0.922 0.9987
## b,time1 - p,time4 2.600000e+00 1.9301219 40.57 1.347 0.9670
## p,time1 - a,time2 -9.300000e+00 1.9301219 40.57 -4.818 0.0011
## p,time1 - b,time2 -5.200000e+00 1.9301219 40.57 -2.694 0.2654
## p,time1 - p,time2 1.000000e+00 0.9760401 81.00 1.025 0.9967
## p,time1 - a,time3 -9.600000e+00 1.9301219 40.57 -4.974 0.0007
## p,time1 - b,time3 -5.800000e+00 1.9301219 40.57 -3.005 0.1443
## p,time1 - p,time3 1.800000e+00 0.9760401 81.00 1.844 0.7886
## p,time1 - a,time4 -9.100000e+00 1.9301219 40.57 -4.715 0.0015
## p,time1 - b,time4 1.800000e+00 1.9301219 40.57 0.933 0.9983
## p,time1 - p,time4 3.500000e+00 0.9760401 81.00 3.586 0.0266
## a,time2 - b,time2 4.100000e+00 1.9301219 40.57 2.124 0.6095
## a,time2 - p,time2 1.030000e+01 1.9301219 40.57 5.336 0.0002
## a,time2 - a,time3 -3.000000e-01 0.9760401 81.00 -0.307 1.0000
## a,time2 - b,time3 3.500000e+00 1.9301219 40.57 1.813 0.8014
## a,time2 - p,time3 1.110000e+01 1.9301219 40.57 5.751 0.0001
## a,time2 - a,time4 2.000000e-01 0.9760401 81.00 0.205 1.0000
## a,time2 - b,time4 1.110000e+01 1.9301219 40.57 5.751 0.0001
## a,time2 - p,time4 1.280000e+01 1.9301219 40.57 6.632 <.0001
## b,time2 - p,time2 6.200000e+00 1.9301219 40.57 3.212 0.0914
## b,time2 - a,time3 -4.400000e+00 1.9301219 40.57 -2.280 0.5061
## b,time2 - b,time3 -6.000000e-01 0.9760401 81.00 -0.615 1.0000
## b,time2 - p,time3 7.000000e+00 1.9301219 40.57 3.627 0.0332
## b,time2 - a,time4 -3.900000e+00 1.9301219 40.57 -2.021 0.6775
## b,time2 - b,time4 7.000000e+00 0.9760401 81.00 7.172 <.0001
## b,time2 - p,time4 8.700000e+00 1.9301219 40.57 4.507 0.0028
## p,time2 - a,time3 -1.060000e+01 1.9301219 40.57 -5.492 0.0001
## p,time2 - b,time3 -6.800000e+00 1.9301219 40.57 -3.523 0.0432
## p,time2 - p,time3 8.000000e-01 0.9760401 81.00 0.820 0.9996
## p,time2 - a,time4 -1.010000e+01 1.9301219 40.57 -5.233 0.0003
## p,time2 - b,time4 8.000000e-01 1.9301219 40.57 0.414 1.0000
## p,time2 - p,time4 2.500000e+00 0.9760401 81.00 2.561 0.3188
## a,time3 - b,time3 3.800000e+00 1.9301219 40.57 1.969 0.7104
## a,time3 - p,time3 1.140000e+01 1.9301219 40.57 5.906 <.0001
## a,time3 - a,time4 5.000000e-01 0.9760401 81.00 0.512 1.0000
## a,time3 - b,time4 1.140000e+01 1.9301219 40.57 5.906 <.0001
## a,time3 - p,time4 1.310000e+01 1.9301219 40.57 6.787 <.0001
## b,time3 - p,time3 7.600000e+00 1.9301219 40.57 3.938 0.0145
## b,time3 - a,time4 -3.300000e+00 1.9301219 40.57 -1.710 0.8534
## b,time3 - b,time4 7.600000e+00 0.9760401 81.00 7.787 <.0001
## b,time3 - p,time4 9.300000e+00 1.9301219 40.57 4.818 0.0011
## p,time3 - a,time4 -1.090000e+01 1.9301219 40.57 -5.647 0.0001
## p,time3 - b,time4 6.547974e-14 1.9301219 40.57 0.000 1.0000
## p,time3 - p,time4 1.700000e+00 0.9760401 81.00 1.742 0.8432
## a,time4 - b,time4 1.090000e+01 1.9301219 40.57 5.647 0.0001
## a,time4 - p,time4 1.260000e+01 1.9301219 40.57 6.528 <.0001
## b,time4 - p,time4 1.700000e+00 1.9301219 40.57 0.881 0.9990
##
## P value adjustment: tukey method for comparing a family of 12 estimates
##diagnostics
fit.lmer<-predict(myfit)
resid.lmer<-resid(myfit)
par(mfrow=c(2,2))
plot(resid.lmer~fit.lmer,main="fitted values vs. residuals",xlab="fitted",ylab="residuals")
abline(0,0,lty=2)
qqnorm(resid.lmer)
qqline(resid.lmer)
hist(resid.lmer,main="histogram of residuals",xlab="residuals")
#random effects normality
par(mfrow=c(1,2))
![](data:image/png;base64,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)
alphahat<-ranef(myfit)
hist(alphahat$subject[,1])
abline(0,0,lty=2)
qqnorm(alphahat$subject[,1])
qqline(alphahat$subject[,1])
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)