---

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#Title: 0928 Homework2
#Name: Szu-Yu Chen
#Date: 4 Oct,2020


data(ergoStool, package="nlme")
dta_stool <- ergoStool
str(dta_stool)

## 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 TRUE

head(dta_stool)

##   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

#LMM outputs and 95% confidence intervals
 
summary(m0 <- nlme::lme(effort ~ Type, random = ~ 1 | Subject, data=dta_stool, method="REML") )

## Linear mixed-effects model fit by REML
##  Data: dta_stool 
##        AIC      BIC    logLik
##   133.1308 141.9252 -60.56539
## 
## Random effects:
##  Formula: ~1 | Subject
##         (Intercept) Residual
## StdDev:    1.332465 1.100295
## 
## Fixed effects: effort ~ Type 
##                Value Std.Error DF   t-value p-value
## (Intercept) 8.555556 0.5760123 24 14.853079  0.0000
## TypeT2      3.888889 0.5186838 24  7.497610  0.0000
## TypeT3      2.222222 0.5186838 24  4.284348  0.0003
## TypeT4      0.666667 0.5186838 24  1.285304  0.2110
##  Correlation: 
##        (Intr) TypeT2 TypeT3
## TypeT2 -0.45               
## TypeT3 -0.45   0.50        
## TypeT4 -0.45   0.50   0.50 
## 
## Standardized Within-Group Residuals:
##         Min          Q1         Med          Q3         Max 
## -1.80200345 -0.64316591  0.05783115  0.70099706  1.63142054 
## 
## Number of Observations: 36
## Number of Groups: 9

faraway::sumary(m1 <-lme4::lmer(effort ~ Type + (1 | Subject), data=dta_stool) )

## Fixed Effects:
##             coef.est coef.se
## (Intercept) 8.56     0.58   
## TypeT2      3.89     0.52   
## TypeT3      2.22     0.52   
## TypeT4      0.67     0.52   
## 
## Random Effects:
##  Groups   Name        Std.Dev.
##  Subject  (Intercept) 1.33    
##  Residual             1.10    
## ---
## number of obs: 36, groups: Subject, 9
## AIC = 133.1, DIC = 123.2
## deviance = 122.1

nlme::intervals(m0)

## Approximate 95% confidence intervals
## 
##  Fixed effects:
##                  lower      est.    upper
## (Intercept)  7.3667247 8.5555556 9.744386
## TypeT2       2.8183781 3.8888889 4.959400
## TypeT3       1.1517114 2.2222222 3.292733
## TypeT4      -0.4038442 0.6666667 1.737177
## attr(,"label")
## [1] "Fixed effects:"
## 
##  Random Effects:
##   Level: Subject 
##                    lower     est.    upper
## sd((Intercept)) 0.749509 1.332465 2.368835
## 
##  Within-group standard error:
##     lower      est.     upper 
## 0.8292494 1.1002946 1.4599324