Random coefficients modelsQ127

Q1

##Random intercepts, random slopes 

setwd('C:/Users/USER/Desktop/Multilevel Statistical/w7 exercise')
dta<-read.table('reading_piat.txt', header = T)
require(pacman)

## Loading required package: pacman

pacman::p_load(mlmRev, tidyverse, lme4)
str(dta)

## 'data.frame':    267 obs. of  5 variables:
##  $ ID   : int  1 1 1 2 2 2 3 3 3 4 ...
##  $ Wave : int  1 2 3 1 2 3 1 2 3 1 ...
##  $ Age_G: num  6.5 8.5 10.5 6.5 8.5 10.5 6.5 8.5 10.5 6.5 ...
##  $ Age  : num  6 8.33 10.33 6 8.5 ...
##  $ PIAT : int  18 35 59 18 25 28 18 23 32 18 ...

dta$ID <- factor(dta$ID)
dta$Age_G <- dta$Age_G-6.5

require(MASS)

## Loading required package: MASS

## 
## Attaching package: 'MASS'

## The following object is masked from 'package:dplyr':
## 
##     select

#lmplot
theme_set(theme_bw())
ggplot(dta, aes(Age_G, PIAT, group = ID)) +                             #every student
  stat_smooth(method = "rlm", se = F, lwd= .1) +
  stat_smooth(aes(group = 1), method = "lm", se = F, col="magenta") +   #all
  labs(x = "Age_G-6.5", y = "PIAT") 

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
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## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

# plot PIAT for a sample of indinidual student
ggplot(filter(dta, ID %in% levels(dta$ID)[sample(89, 25)]), 
       aes(Age_G, PIAT)) +
  geom_smooth(method = "rlm") +
  geom_point(cex = 0.7)+
  facet_wrap(~ ID, nrow = 5) +
  labs(x = "Age_G-6.5", y = "PIAT")

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps

# random intercepts, random slopes
summary(m1 <- lmer(PIAT ~ Age_G + (1+ Age_G | ID), data = dta))

## Linear mixed model fit by REML ['lmerMod']
## Formula: PIAT ~ Age_G + (1 + Age_G | ID)
##    Data: dta
## 
## REML criterion at convergence: 1819.8
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.6539 -0.5413 -0.1497  0.3854  3.2811 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr
##  ID       (Intercept) 11.427   3.380        
##           Age_G        4.486   2.118    0.22
##  Residual             27.043   5.200        
## Number of obs: 267, groups:  ID, 89
## 
## Fixed effects:
##             Estimate Std. Error t value
## (Intercept)  21.1629     0.6177   34.26
## Age_G         5.0309     0.2973   16.92
## 
## Correlation of Fixed Effects:
##       (Intr)
## Age_G -0.316

# residual plot
plot(m1, pch = 20, cex = 0.8, col = "steelblue", 
     xlab = "Fitted values", ylab = "Pearson residuals")

# ordinary regression for comparison
summary(m0 <- lm(PIAT ~ Age_G, data = dta))

## 
## Call:
## lm(formula = PIAT ~ Age_G, data = dta)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -20.287  -4.225  -1.286   5.713  24.775 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  21.1629     0.8355   25.33   <2e-16 ***
## Age_G         5.0309     0.3236   15.55   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 8.634 on 265 degrees of freedom
## Multiple R-squared:  0.477,  Adjusted R-squared:  0.4751 
## F-statistic: 241.7 on 1 and 265 DF,  p-value: < 2.2e-16

#anova
anova(m1,m0)

## refitting model(s) with ML (instead of REML)

## Data: dta
## Models:
## m0: PIAT ~ Age_G
## m1: PIAT ~ Age_G + (1 + Age_G | ID)
##    Df    AIC    BIC  logLik deviance Chisq Chi Df Pr(>Chisq)    
## m0  3 1912.9 1923.6 -953.43   1906.9                            
## m1  6 1832.0 1853.5 -909.97   1820.0 86.92      3  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#學生確實造成差異，應該量學生個別性
#Scoreij = 21.16(±3.38) + 5.031(±2.12) × (ageij - 6.5)

Q2

dta<-read.csv('visual_search.csv', header = T,sep =',')
require(pacman)
head(dta)

##   Participant      Dx Set.Size      RT
## 1        9129 Control        1  786.50
## 2        9051 Control        1  935.83
## 3        9126 Control        1  750.83
## 4       9171* Control        1 1129.50
## 5        9176 Control        1 1211.33
## 6        9167 Control        1 1178.83

str(dta)

## 'data.frame':    132 obs. of  4 variables:
##  $ Participant: Factor w/ 33 levels "0042","0044",..: 19 16 18 25 28 22 24 23 26 27 ...
##  $ Dx         : Factor w/ 2 levels "Aphasic","Control": 2 2 2 2 2 2 2 2 2 2 ...
##  $ Set.Size   : int  1 1 1 1 1 1 1 1 1 1 ...
##  $ RT         : num  786 936 751 1130 1211 ...

pacman::p_load(mlmRev, tidyverse, lme4, gridExtra)


theme_set(theme_bw())

#plot
ggplot(dta, aes(Set.Size, RT))+
  geom_point()+ 
  geom_line(aes(group = Participant), alpha = .5) +
  stat_smooth(aes(group = Dx),color = "gray", method = "lm") +
  facet_grid(. ~ Dx)+
  labs(x = "Set Size", y = "RT")

summary(mr <- lmer(RT~ Set.Size+Dx+Set.Size:Dx + (1 + Set.Size | Participant ), data = dta))

## Linear mixed model fit by REML ['lmerMod']
## Formula: RT ~ Set.Size + Dx + Set.Size:Dx + (1 + Set.Size | Participant)
##    Data: dta
## 
## REML criterion at convergence: 2186.1
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.7578 -0.3130 -0.0750  0.3117  6.1372 
## 
## Random effects:
##  Groups      Name        Variance Std.Dev. Corr
##  Participant (Intercept) 657552.9 810.90       
##              Set.Size       407.4  20.18   1.00
##  Residual                772433.1 878.88       
## Number of obs: 132, groups:  Participant, 33
## 
## Fixed effects:
##                    Estimate Std. Error t value
## (Intercept)         2078.75     270.98   7.671
## Set.Size              73.49      11.40   6.446
## DxControl          -1106.05     366.90  -3.015
## Set.Size:DxControl   -21.74      15.44  -1.408
## 
## Correlation of Fixed Effects:
##             (Intr) Set.Sz DxCntr
## Set.Size    -0.071              
## DxControl   -0.739  0.053       
## St.Sz:DxCnt  0.053 -0.739 -0.071

#plot 迴歸線+樣本平均與標準差
ggplot(dta, aes(Set.Size, RT, shape = Dx, linetype = Dx)) +
  stat_smooth(method = "lm",se = F,col = "gray") +
  stat_summary(fun.y = mean, geom = "point", position = position_dodge(width=.2)) +
  stat_summary(fun.data = mean_se, geom = "errorbar",position = position_dodge(width=.2), linetype = "solid", width = 0.5) +
  labs(x = "Set Size", y = "RT", linetype = "Group", shape = "Group") +
  theme(legend.justification = c(0, 1), legend.position = c(0, 1),
        legend.background = element_rect(fill = "white", color = "black"))

#resisuals
#pearson resisuals
plot(mr, resid(., type = "pearson") ~ fitted(.) | Dx,
     layout = c(3,1), aspect = 2, abline = 0, pch = 20, cex = .8,
     xlab = "Ftted values", ylab = "Pearson residuals")

Q7

pacman::p_load('scan')
dta <- Borckardt2014
str(Borckardt2014)

## 'data.frame':    21 obs. of  3 variables:
##  $ phase : Factor w/ 2 levels "A","B": 1 1 1 1 1 1 1 2 2 2 ...
##  $ values: num  7 9 8 7 7 8 8 3 4 2 ...
##  $ mt    : int  1 2 3 4 5 6 7 8 9 10 ...
##  - attr(*, "info")= chr "Example from Borckardt, J. J., & Nash, M. R. (2014). Simulation modelling analysis for small sets of single-sub"| __truncated__

# plot data
theme_set(theme_bw())
ggplot(Borckardt2014, aes(mt, values)) + geom_line()+       #折線圖
  geom_point(size = 1)+                     #折線圖上的點
  geom_vline(xintercept = 7, col="red")+    #設定參考線區分A和B組
  stat_smooth(method = "lm", se = F, linetype = "dashed")   #全體的迴歸線

theme_set(theme_bw())
ggplot(Borckardt2014, aes(mt, values))+
  geom_point(size = 1)+                     #折線圖上的點
  geom_vline(xintercept = 7, col="red")+    #設定參考線區分A和B組
  stat_smooth(method = "lm", se = F, linetype = "dashed")+  #全體的迴歸線
  stat_smooth(aes(group = phase), method = "lm", se = F)    #兩組各自的迴歸線

summary(m1 <- lm(values ~ mt+phase, data = dta))

## 
## Call:
## lm(formula = values ~ mt + phase, data = dta)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.93151 -0.91977  0.07436  1.06458  2.07241 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  7.722114   0.527293  14.645 1.92e-11 ***
## mt          -0.001957   0.072773  -0.027    0.979    
## phaseB      -4.765166   0.934791  -5.098 7.52e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.163 on 18 degrees of freedom
## Multiple R-squared:  0.8144, Adjusted R-squared:  0.7938 
## F-statistic: 39.49 on 2 and 18 DF,  p-value: 2.612e-07

summary(m0 <- lm(values ~ mt, data = dta))

## 
## Call:
## lm(formula = values ~ mt, data = dta)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.91342 -1.13420  0.00216  1.69697  2.52814 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  7.88095    0.80088   9.840 6.82e-09 ***
## mt          -0.30519    0.06378  -4.785 0.000129 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.77 on 19 degrees of freedom
## Multiple R-squared:  0.5465, Adjusted R-squared:  0.5226 
## F-statistic:  22.9 on 1 and 19 DF,  p-value: 0.0001288

anova(m0,m1)

## Analysis of Variance Table
## 
## Model 1: values ~ mt
## Model 2: values ~ mt + phase
##   Res.Df    RSS Df Sum of Sq      F   Pr(>F)    
## 1     19 59.517                                 
## 2     18 24.356  1    35.161 25.985 7.52e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1