#Problem An experimenter wishes to compare 4 particular type of stools. Each of nine individuals randomly selected from a subject pool is asked to test the stools by recording the effort required to arise from each of 4 types of stools.
#install packages
#install.packages("nlme")library(nlme)#load data ergoStool{nlme}
data(ergoStool, package="nlme")
dta<-ergoStool#exam data #show structure of data
str(dta)## Classes 'nffGroupedData', 'nfGroupedData', 'groupedData' and 'data.frame': 36 obs. of 3 variables:
## $ effort : num 12 15 12 10 10 14 13 12 7 14 ...
## $ Type : Factor w/ 4 levels "T1","T2","T3",..: 1 2 3 4 1 2 3 4 1 2 ...
## $ Subject: Ord.factor w/ 9 levels "8"<"5"<"4"<"9"<..: 8 8 8 8 9 9 9 9 6 6 ...
## - attr(*, "formula")=Class 'formula' language effort ~ Type | Subject
## .. ..- attr(*, ".Environment")=<environment: R_GlobalEnv>
## - attr(*, "labels")=List of 2
## ..$ x: chr "Type of stool"
## ..$ y: chr "Effort required to arise"
## - attr(*, "units")=List of 1
## ..$ y: chr "(Borg scale)"
## - attr(*, "FUN")=function (x)
## ..- attr(*, "source")= chr "function (x) mean(x, na.rm = TRUE)"
## - attr(*, "order.groups")= logi TRUEhead(dta)## Grouped Data: effort ~ Type | Subject
## effort Type Subject
## 1 12 T1 1
## 2 15 T2 1
## 3 12 T3 1
## 4 10 T4 1
## 5 10 T1 2
## 6 14 T2 2#各種類型的平均數
aggregate(dta[,1], list(dta$Type), mean)## Group.1 x
## 1 T1 8.555556
## 2 T2 12.444444
## 3 T3 10.777778
## 4 T4 9.222222#每位受試者的平均數
aggregate(dta[,1], list(dta$Subject), mean)## Group.1 x
## 1 8 8.25
## 2 5 8.50
## 3 4 9.25
## 4 9 10.00
## 5 6 10.25
## 6 3 10.75
## 7 7 10.75
## 8 1 12.25
## 9 2 12.25pacman::p_load(tidyverse, lme4)#Linear mixed-effects model fit by REML (PPT 第21頁)
lmer(effort ~ Type + (1 | Subject) - 1, data=dta)## Linear mixed model fit by REML ['lmerMod']
## Formula: effort ~ Type + (1 | Subject) - 1
## Data: dta
## REML criterion at convergence: 121.1308
## Random effects:
## Groups Name Std.Dev.
## Subject (Intercept) 1.332
## Residual 1.100
## Number of obs: 36, groups: Subject, 9
## Fixed Effects:
## TypeT1 TypeT2 TypeT3 TypeT4
## 8.556 12.444 10.778 9.222m1<-lmer(effort ~ Type + (1 | Subject) - 1, data=dta)summary(lmer(effort ~ Type + (1 | Subject) - 1, data=dta))## Linear mixed model fit by REML ['lmerMod']
## Formula: effort ~ Type + (1 | Subject) - 1
## Data: dta
##
## REML criterion at convergence: 121.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.80200 -0.64317 0.05783 0.70100 1.63142
##
## Random effects:
## Groups Name Variance Std.Dev.
## Subject (Intercept) 1.775 1.332
## Residual 1.211 1.100
## Number of obs: 36, groups: Subject, 9
##
## Fixed effects:
## Estimate Std. Error t value
## TypeT1 8.556 0.576 14.85
## TypeT2 12.444 0.576 21.60
## TypeT3 10.778 0.576 18.71
## TypeT4 9.222 0.576 16.01
##
## Correlation of Fixed Effects:
## TypeT1 TypeT2 TypeT3
## TypeT2 0.595
## TypeT3 0.595 0.595
## TypeT4 0.595 0.595 0.595#The End