Two data sets are generated for you to investigate how the estimate of grand mean depend on the intra-class correlation in a simple random-effects model.
Column 1: Score Column 2: School ID Column 3: Student ID
#載入套件
pacman::p_load(tidyverse, lme4, merTools, dplyr)
#載入資料
setwd("C:/Users/Username/Desktop/111-1/Multilevel Analysis/HomeWork/0924/Q4")
demo1 <- read.table("demo1.txt", header = T)
demo2 <- read.table("demo2.txt", header = T)
#查看資料
head(demo1)## Score School Pupil
## 1 11 S1 P1
## 2 13 S1 P2
## 3 51 S2 P3
## 4 53 S2 P4
## 5 55 S2 P5
## 6 91 S3 P6head(demo2)## Score School Pupil
## 1 11 S1 P1
## 2 51 S1 P2
## 3 13 S2 P3
## 4 55 S2 P4
## 5 91 S2 P5
## 6 51 S3 P6Demo 1展示了學校的變異數為1679，標準差為40.976；Demo 2學校的變異數為104.2，標準差為10.21。
#Model 1
summary(m1 <- lmer(Score ~ 1 + (1 | School), data=demo1))## Linear mixed model fit by REML ['lmerMod']
## Formula: Score ~ 1 + (1 | School)
## Data: demo1
##
## REML criterion at convergence: 51.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.3280 -0.4745 0.0000 0.4608 1.3553
##
## Random effects:
## Groups Name Variance Std.Dev.
## School (Intercept) 1679 40.976
## Residual 5 2.236
## Number of obs: 9, groups: School, 3
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 53.01 23.67 2.24#Model 2
summary(m2 <- lmer(Score ~ 1 + (1 | School), data=demo2))## Linear mixed model fit by REML ['lmerMod']
## Formula: Score ~ 1 + (1 | School)
## Data: demo2
##
## REML criterion at convergence: 80.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.36734 -0.34286 -0.02776 1.07153 1.13999
##
## Random effects:
## Groups Name Variance Std.Dev.
## School (Intercept) 104.2 10.21
## Residual 967.8 31.11
## Number of obs: 9, groups: School, 3
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 56.36 12.01 4.692