Nested Designs - Chicano

1 in class Exercise2

1.1 load data

dta <- read.csv('Chicano.csv', stringsAsFactors = TRUE)
str(dta)

## 'data.frame':    24 obs. of  4 variables:
##  $ Pupil: Factor w/ 24 levels "P01","P02","P03",..: 1 2 3 4 5 6 7 8 9 10 ...
##  $ Class: Factor w/ 6 levels "C1","C2","C3",..: 1 1 1 1 2 2 2 2 3 3 ...
##  $ Trt  : Factor w/ 2 levels "C","T": 2 2 2 2 2 2 2 2 2 2 ...
##  $ Score: int  5 2 10 11 10 15 11 8 7 12 ...

pacman::p_load(tidyverse, VCA, lme4, nlme)

1.2 varPlot of Score and two treatment conditions

VCA::varPlot(Score ~ Trt/Class/Pupil, 
             Data=dta,
             YLabel=list(text="Score", 
                         side=2, 
                         cex=1),
             MeanLine=list(var=c("Trt", "Class"),
                           col=c("yellow", "purple"), 
                           lwd=c(1, 2)))

##黃色線=兩種Trt(實驗和控制)的平均成績
##紫色線=各班平均
#各個點=觀察值

1.3 Anova

summary(m1 <- aov(Score ~ Trt + Error(Class), data=dta))

## 
## Error: Class
##           Df Sum Sq Mean Sq F value Pr(>F)  
## Trt        1    216     216   9.818 0.0351 *
## Residuals  4     88      22                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Error: Within
##           Df Sum Sq Mean Sq F value Pr(>F)
## Residuals 18    198      11

##Trt這變項對於Score 有顯著差異

1.4 Fixed Effects and random effect

##沒有做去掉截距這指令-1顯示如下
faraway::sumary(m2 <- lmer(Score ~ Trt + (1 | Class), data=dta))

## Fixed Effects:
##             coef.est coef.se
## (Intercept) 4.00     1.35   
## TrtT        6.00     1.91   
## 
## Random Effects:
##  Groups   Name        Std.Dev.
##  Class    (Intercept) 1.66    
##  Residual             3.32    
## ---
## number of obs: 24, groups: Class, 6
## AIC = 130.9, DIC = 131.8
## deviance = 127.4

1.5 Confidence Intervals by bootstrapping

confint(m2, method="boot")

## Computing bootstrap confidence intervals ...

## 
## 136 message(s): boundary (singular) fit: see ?isSingular
## 1 warning(s): Model failed to converge with max|grad| = 0.00416971 (tol = 0.002, component 1)

##                2.5 %   97.5 %
## .sig01      0.000000 3.663767
## .sigma      2.297173 4.277030
## (Intercept) 1.669229 6.787090
## TrtT        1.640800 9.573697