RHI data analysis

Sung-en Chien

2016年12月12日

This presentation is to analyze the data in the manuscript “Identifying a role for executive function in the rubber hand illusion” with an hierarchical regression.

Why analyze the data with hierarchical regression

present separated results of regression in previous manuscript
- onset time - switch cost
- onset time - mind wandering
- onset time - shift attention aptitude

comments from JEPHP reviewers in data analysis

The analyses of scores of the standard 9 Questionnaire were not present.
How to show the link between the RHI and exevutive function
- ask switiching
- mind wandering
- attentional control

suggestions from reviewer 3

Conduct two hierarchical regressions
- one with the time of onset of illusion as dependent variable and
- the other with the RHI questionnaire scores as the dependent variable
allow us to establish executive function actually affects the strength of the illusion itself or just how quickly participants respond after experiencing the illusion.

how to decide the structure of hierarchical regression

possibile explanation
- Higher cognitive functions enable individuals to switch away from internal mind wandering thoughts and back to the external task-related stimuli.

order of adding predictors for updating the models

select the model with best R2 and relatvie less predictors

hierarchical regression - onset time

# settings
setwd("~/Dropbox/NTU exp/RHI/RHI_ANYI/Exp8_ACS&TS&MW") # switch directory to the file directory
library(xlsx)
# load and set data
data <- read.xlsx(file = "SwitchingRHI_n36.xlsx", sheetIndex = 3, header = TRUE)
mw.model <- lm(data$OnsetTime ~ data$Mind.Wandering, data=data)
mw.shift.model <- lm(data$OnsetTime ~ data$Mind.Wandering + data$Shift.Attention, data=data)
mw.shift.ts.model <- lm(data$OnsetTime ~ data$Mind.Wandering + data$Shift.Attention + 
                            data$Switch.Cost, data=data)
mw.shift.ts.focus.model <- lm(data$OnsetTime ~ data$Mind.Wandering + data$Shift.Attention + 
                            data$Switch.Cost+data$Focus.Attention, data=data)

summary(mw.model) # R square = 0.3859

## 
## Call:
## lm(formula = data$OnsetTime ~ data$Mind.Wandering, data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -100.10  -57.35  -14.98   48.14  127.68 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          -111.84      18.06  -6.194 4.83e-07 ***
## data$Mind.Wandering    98.68      36.98   2.668   0.0116 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 64.41 on 34 degrees of freedom
## Multiple R-squared:  0.1731, Adjusted R-squared:  0.1488 
## F-statistic:  7.12 on 1 and 34 DF,  p-value: 0.0116

summary(mw.shift.model) # R square = 0.3859

## 
## Call:
## lm(formula = data$OnsetTime ~ data$Mind.Wandering + data$Shift.Attention, 
##     data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -99.813 -53.434   0.479  37.229 104.579 
## 
## Coefficients:
##                      Estimate Std. Error t value Pr(>|t|)  
## (Intercept)             51.09      70.38   0.726    0.473  
## data$Mind.Wandering     59.75      38.32   1.559    0.128  
## data$Shift.Attention   -59.72      25.04  -2.385    0.023 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 60.38 on 33 degrees of freedom
## Multiple R-squared:  0.2947, Adjusted R-squared:  0.252 
## F-statistic: 6.895 on 2 and 33 DF,  p-value: 0.003147

summary(mw.shift.ts.model) # R square = 0.3859

## 
## Call:
## lm(formula = data$OnsetTime ~ data$Mind.Wandering + data$Shift.Attention + 
##     data$Switch.Cost, data = data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -112.877  -30.397   -2.512   35.169  119.799 
## 
## Coefficients:
##                      Estimate Std. Error t value Pr(>|t|)  
## (Intercept)             1.347     70.489   0.019   0.9849  
## data$Mind.Wandering    53.193     36.435   1.460   0.1541  
## data$Shift.Attention  -56.831     23.765  -2.391   0.0228 *
## data$Switch.Cost       99.999     45.886   2.179   0.0368 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 57.22 on 32 degrees of freedom
## Multiple R-squared:  0.3859, Adjusted R-squared:  0.3283 
## F-statistic: 6.702 on 3 and 32 DF,  p-value: 0.001227

summary(mw.shift.ts.focus.model)

## 
## Call:
## lm(formula = data$OnsetTime ~ data$Mind.Wandering + data$Shift.Attention + 
##     data$Switch.Cost + data$Focus.Attention, data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -115.68  -26.48  -11.11   33.55  125.90 
## 
## Coefficients:
##                      Estimate Std. Error t value Pr(>|t|)   
## (Intercept)            -79.48      78.97  -1.007   0.3220   
## data$Mind.Wandering     55.98      34.92   1.603   0.1191   
## data$Shift.Attention   -64.04      23.05  -2.778   0.0092 **
## data$Switch.Cost        89.60      44.26   2.024   0.0516 . 
## data$Focus.Attention    37.91      19.22   1.973   0.0575 . 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 54.8 on 31 degrees of freedom
## Multiple R-squared:  0.4544, Adjusted R-squared:  0.384 
## F-statistic: 6.454 on 4 and 31 DF,  p-value: 0.0006721

anova(mw.model, mw.shift.model, mw.shift.ts.model, mw.shift.ts.focus.model)

## Analysis of Variance Table
## 
## Model 1: data$OnsetTime ~ data$Mind.Wandering
## Model 2: data$OnsetTime ~ data$Mind.Wandering + data$Shift.Attention
## Model 3: data$OnsetTime ~ data$Mind.Wandering + data$Shift.Attention + 
##     data$Switch.Cost
## Model 4: data$OnsetTime ~ data$Mind.Wandering + data$Shift.Attention + 
##     data$Switch.Cost + data$Focus.Attention
##   Res.Df    RSS Df Sum of Sq      F  Pr(>F)  
## 1     34 141072                              
## 2     33 120329  1     20743 6.9076 0.01323 *
## 3     32 104778  1     15550 5.1783 0.02993 *
## 4     31  93093  1     11685 3.8912 0.05752 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

results on set time

chose the 3rd model
- Task switch and shift attention are both related to the onset time of RHI.

possible explanation

Shift attention from internal thoughts to external stimuli could help participants to experience the RHI.
Shift attention, switch cost: faster onset time

hierarchical regression - RHI quesionaire scores

mw.model2 <-  lm(data$Ques.RHI ~ data$Mind.Wandering , data=data)
mw.shift.model2 <- lm(data$Ques.RHI ~ data$Mind.Wandering + data$Shift.Attention , data=data)
mw.shift.ts.model2 <- lm(data$Ques.RHI ~ data$Mind.Wandering + data$Shift.Attention
                         +data$Switch.Cost, data=data)
mw.shift.ts.focus.model2 <- lm(data$Ques.RHI ~ data$Mind.Wandering + data$Shift.Attention
                         +data$Switch.Cost+data$Focus.Attention, data=data)

summary(mw.model2) # mind wandering is negatively related to RHI , R suare =0.1217

## 
## Call:
## lm(formula = data$Ques.RHI ~ data$Mind.Wandering, data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.4827 -1.0193  0.2091  1.0258  3.9465 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)           3.2358     0.4694   6.894 6.09e-08 ***
## data$Mind.Wandering  -2.0864     0.9613  -2.170    0.037 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.674 on 34 degrees of freedom
## Multiple R-squared:  0.1217, Adjusted R-squared:  0.09586 
## F-statistic: 4.711 on 1 and 34 DF,  p-value: 0.03705

summary(mw.shift.model2) # R sqare =0.1705

## 
## Call:
## lm(formula = data$Ques.RHI ~ data$Mind.Wandering + data$Shift.Attention, 
##     data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.2364 -1.3156  0.0329  1.0337  3.9419 
## 
## Coefficients:
##                      Estimate Std. Error t value Pr(>|t|)
## (Intercept)            0.6330     1.9250   0.329    0.744
## data$Mind.Wandering   -1.4646     1.0481  -1.397    0.172
## data$Shift.Attention   0.9541     0.6849   1.393    0.173
## 
## Residual standard error: 1.652 on 33 degrees of freedom
## Multiple R-squared:  0.1705, Adjusted R-squared:  0.1202 
## F-statistic: 3.391 on 2 and 33 DF,  p-value: 0.04578

summary(mw.shift.ts.model2) # R sqared = 0.2029

## 
## Call:
## lm(formula = data$Ques.RHI ~ data$Mind.Wandering + data$Shift.Attention + 
##     data$Switch.Cost, data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.6100 -1.0424  0.0756  0.8746  4.1383 
## 
## Coefficients:
##                      Estimate Std. Error t value Pr(>|t|)
## (Intercept)            1.3810     2.0255   0.682    0.500
## data$Mind.Wandering   -1.3660     1.0469  -1.305    0.201
## data$Shift.Attention   0.9106     0.6829   1.333    0.192
## data$Switch.Cost      -1.5036     1.3185  -1.140    0.263
## 
## Residual standard error: 1.644 on 32 degrees of freedom
## Multiple R-squared:  0.2029, Adjusted R-squared:  0.1281 
## F-statistic: 2.715 on 3 and 32 DF,  p-value: 0.06112

summary(mw.shift.ts.focus.model2) #R sqared = 0.2987

## 
## Call:
## lm(formula = data$Ques.RHI ~ data$Mind.Wandering + data$Shift.Attention + 
##     data$Switch.Cost + data$Focus.Attention, data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.7666 -0.8308 -0.0165  0.7380  4.2218 
## 
## Coefficients:
##                      Estimate Std. Error t value Pr(>|t|)  
## (Intercept)            3.7923     2.2580   1.679   0.1031  
## data$Mind.Wandering   -1.4491     0.9985  -1.451   0.1568  
## data$Shift.Attention   1.1257     0.6591   1.708   0.0977 .
## data$Switch.Cost      -1.1933     1.2655  -0.943   0.3530  
## data$Focus.Attention  -1.1309     0.5495  -2.058   0.0481 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.567 on 31 degrees of freedom
## Multiple R-squared:  0.2987, Adjusted R-squared:  0.2082 
## F-statistic: 3.301 on 4 and 31 DF,  p-value: 0.02302

anova(mw.model2,mw.shift.model2,mw.shift.ts.model2,mw.shift.ts.focus.model2)

## Analysis of Variance Table
## 
## Model 1: data$Ques.RHI ~ data$Mind.Wandering
## Model 2: data$Ques.RHI ~ data$Mind.Wandering + data$Shift.Attention
## Model 3: data$Ques.RHI ~ data$Mind.Wandering + data$Shift.Attention + 
##     data$Switch.Cost
## Model 4: data$Ques.RHI ~ data$Mind.Wandering + data$Shift.Attention + 
##     data$Switch.Cost + data$Focus.Attention
##   Res.Df    RSS Df Sum of Sq      F  Pr(>F)  
## 1     34 95.321                              
## 2     33 90.027  1    5.2936 2.1560 0.15208  
## 3     32 86.511  1    3.5159 1.4320 0.24051  
## 4     31 76.113  1   10.3983 4.2351 0.04809 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

results - RHI

chose the 4th model
- Focus attention is significant related to the strength of RHI.

possible explanation

Strength of RHI might be dependent on how participants attended to the external stimuli.
catch the external stimuli, strong RHI

RHI - onset time

RHIcor <- lm(data$Ques.RHI ~ data$OnsetTime, data=data) # fit linear model
plot(data$OnsetTime, data$Ques.RHI, xlab = "onset time", ylab = "RHI", xlim=c(-200,100), ylim = c(-3,7))
abline(RHIcor, col = "black")

cor(data$OnsetTime, data$Ques.RHI)

## [1] -0.7312217

discussion

task switch, shift attentoin
- contribute to how quick a participant could experience RHI.
focus attention (engagement)
- contribute to the strength of RHI
people with high cognitive function might have better performance on all kinds of cognitive functions
- therefore RHI scores are highly related to onset time