M7 Analysis V1.2
Russell Chan
6th June 2021
##Set working directory
setwd("C:/Users/Russell Chan/OneDrive - Universiteit Twente/2020_MSCA_IF/4_2021_Mod_7/Data Analysis/Scripts")##Packages that are required for the analysis
library(readxl)
library(haven)
library(tidyverse)
library(lme4)
library(effects)
library(lattice)
library(car)
library(ggplot2)
library(knitr)
library(reshape2)
library(dplyr)
library(forcats)
library(DHARMa)
library(Hmisc)
library(phia)
library(lsmeans)
library(emmeans)
library(multcomp)
library(nlme)
library(gplots)
library(scales)
library(Rmisc)##Import dataset from the directory
d.MSL <- read_excel("C:\\Users\\Russell Chan\\OneDrive - Universiteit Twente\\2020_MSCA_IF\\4_2021_Mod_7\\Data Analysis\\M7_Triallvl_2105231_Final.xlsx")##Create factors for analysis
#Subject is a factor to account for intraclass variance in linear models
d.MSL$Subject <- factor(d.MSL$Subject)
#Block is our function of time
d.MSL$Block <- factor(d.MSL$Block)
#Accuracy is a factor to know if it determines RT
d.MSL$Trial.ACC.Num <- factor(d.MSL$Trial.ACC.Num)###Building models
#First model: To simply understand if RT changes as a function of block (i.e. learning)
m.MSL.RT <- lmer(AvgTrial.RT ~ Block + (1|Subject), data = d.MSL)
Anova(m.MSL.RT)summary(m.MSL.RT)## Linear mixed model fit by REML ['lmerMod']
## Formula: AvgTrial.RT ~ Block + (1 | Subject)
## Data: d.MSL
##
## REML criterion at convergence: 36672.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.058 -0.200 -0.043 0.086 43.416
##
## Random effects:
## Groups Name Variance Std.Dev.
## Subject (Intercept) 23182 152.3
## Residual 255177 505.2
## Number of obs: 2400, groups: Subject, 10
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 603.52 53.38 11.305
## Block2 -299.48 32.61 -9.184
## Block3 -348.79 32.61 -10.697
## Block4 -365.19 32.61 -11.200
## Block5 -373.81 32.61 -11.464
##
## Correlation of Fixed Effects:
## (Intr) Block2 Block3 Block4
## Block2 -0.305
## Block3 -0.305 0.500
## Block4 -0.305 0.500 0.500
## Block5 -0.305 0.500 0.500 0.500#Plotting of quick interactions1
emmip(m.MSL.RT, ~Block)
#The results of the model reveal that indeed AvgTrial.RT (Which is the average of the 6 steps). As block progresses. RT is getting faster.
#Second model: To understand if Trial.RT is different between accurate and inaccurate trials.
m.MSL.ACC <- lmer(AvgTrial.RT ~ Trial.ACC.Num + (1|Subject), data = d.MSL)
Anova(m.MSL.ACC)summary(m.MSL.ACC)## Linear mixed model fit by REML ['lmerMod']
## Formula: AvgTrial.RT ~ Trial.ACC.Num + (1 | Subject)
## Data: d.MSL
##
## REML criterion at convergence: 36751.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.020 -0.210 -0.071 0.088 43.063
##
## Random effects:
## Groups Name Variance Std.Dev.
## Subject (Intercept) 19361 139.1
## Residual 260713 510.6
## Number of obs: 2400, groups: Subject, 10
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 541.05 48.96 11.05
## Trial.ACC.Num1 -289.87 25.30 -11.46
##
## Correlation of Fixed Effects:
## (Intr)
## Trl.ACC.Nm1 -0.383#Plotting of quick interactions2
emmip(m.MSL.ACC, ~Trial.ACC.Num)
#The results of the model reveal that indeed AvgTrial.RT is different between accurate and inaccurate.
#Third model: To understand if Trial.RT as a function of accuracy and block (learning) is different and changing.
m.MSL.RTACC <- lmer(AvgTrial.RT ~ Block * Trial.ACC.Num + (1|Subject), data = d.MSL)
Anova(m.MSL.RTACC)summary(m.MSL.RTACC)## Linear mixed model fit by REML ['lmerMod']
## Formula: AvgTrial.RT ~ Block * Trial.ACC.Num + (1 | Subject)
## Data: d.MSL
##
## REML criterion at convergence: 36546.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.234 -0.177 -0.030 0.092 43.706
##
## Random effects:
## Groups Name Variance Std.Dev.
## Subject (Intercept) 20217 142.2
## Residual 247714 497.7
## Number of obs: 2400, groups: Subject, 10
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 775.85 55.09 14.084
## Block2 -377.79 53.96 -7.001
## Block3 -461.22 64.16 -7.189
## Block4 -451.78 62.60 -7.217
## Block5 -363.23 68.08 -5.335
## Trial.ACC.Num1 -358.10 46.32 -7.731
## Block2:Trial.ACC.Num1 228.03 68.78 3.315
## Block3:Trial.ACC.Num1 285.67 76.49 3.735
## Block4:Trial.ACC.Num1 253.64 75.21 3.373
## Block5:Trial.ACC.Num1 144.47 79.91 1.808
##
## Correlation of Fixed Effects:
## (Intr) Block2 Block3 Block4 Block5 T.ACC. B2:T.A B3:T.A B4:T.A
## Block2 -0.330
## Block3 -0.276 0.310
## Block4 -0.289 0.306 0.265
## Block5 -0.270 0.270 0.228 0.237
## Trl.ACC.Nm1 -0.405 0.387 0.322 0.343 0.328
## B2:T.ACC.N1 0.261 -0.788 -0.248 -0.244 -0.214 -0.645
## B3:T.ACC.N1 0.235 -0.262 -0.841 -0.225 -0.194 -0.580 0.414
## B4:T.ACC.N1 0.244 -0.254 -0.220 -0.835 -0.201 -0.603 0.412 0.376
## B5:T.ACC.N1 0.235 -0.227 -0.191 -0.202 -0.857 -0.581 0.377 0.340 0.353#Plotting of quick interactions3
emmip(m.MSL.RTACC, Block ~Trial.ACC.Num)
#The results of the model reveal that indeed AvgTrial.RT modulated by accuracy and that there is a significant interaction with blocks. We will know the direction of the change only when we plot it later.
#Fourth model: To understand if CoM Velocity is changing as learning occurs.
m.MSL.COMVE <- lmer(COM.X.VE ~ Block + (1|Subject), data = d.MSL)## boundary (singular) fit: see ?isSingularAnova(m.MSL.COMVE)summary(m.MSL.COMVE)## Linear mixed model fit by REML ['lmerMod']
## Formula: COM.X.VE ~ Block + (1 | Subject)
## Data: d.MSL
##
## REML criterion at convergence: -8615
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.6418 -0.6246 0.0012 0.6528 3.6028
##
## Random effects:
## Groups Name Variance Std.Dev.
## Subject (Intercept) 7.660e-20 2.768e-10
## Residual 1.584e-03 3.980e-02
## Number of obs: 2400, groups: Subject, 10
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.010226 0.001817 5.629
## Block2 0.007319 0.002569 2.849
## Block3 0.012244 0.002569 4.766
## Block4 0.015556 0.002569 6.055
## Block5 0.024984 0.002569 9.725
##
## Correlation of Fixed Effects:
## (Intr) Block2 Block3 Block4
## Block2 -0.707
## Block3 -0.707 0.500
## Block4 -0.707 0.500 0.500
## Block5 -0.707 0.500 0.500 0.500
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular#Plotting of quick interactions5
emmip(m.MSL.COMVE, ~Block)
#4.5 model: To understand if CoM Velocity is changing with Accuracy.
m.MSL.COMVE.ACC <- lmer(COM.X.VE ~ Trial.ACC.Num + (1|Subject), data = d.MSL)
Anova(m.MSL.COMVE.ACC)summary(m.MSL.COMVE.ACC)## Linear mixed model fit by REML ['lmerMod']
## Formula: COM.X.VE ~ Trial.ACC.Num + (1 | Subject)
## Data: d.MSL
##
## REML criterion at convergence: -8554.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.5342 -0.6688 -0.0168 0.6439 3.7863
##
## Random effects:
## Groups Name Variance Std.Dev.
## Subject (Intercept) 1.953e-06 0.001398
## Residual 1.642e-03 0.040521
## Number of obs: 2400, groups: Subject, 10
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.017308 0.001702 10.168
## Trial.ACC.Num1 0.006658 0.001915 3.476
##
## Correlation of Fixed Effects:
## (Intr)
## Trl.ACC.Nm1 -0.835#Plotting of quick interactions Model 4.5
emmip(m.MSL.COMVE.ACC, ~Trial.ACC.Num)
#The results support that COM.X Velocity is indeed changing with accuracy. Accurate trials are slower than inaccurate trials. Perhaps some impulsitivity there.
#Fifth model: To understand The interaction if RT predicts CoM.X Velocity changes is changing as learning occurs.
m.MSL.COMVE.RT.Inter <- lmer(AvgTrial.RT ~ Block * COM.X.VE + (1|Subject), data = d.MSL)
Anova(m.MSL.COMVE.RT.Inter)summary(m.MSL.COMVE.RT.Inter)## Linear mixed model fit by REML ['lmerMod']
## Formula: AvgTrial.RT ~ Block * COM.X.VE + (1 | Subject)
## Data: d.MSL
##
## REML criterion at convergence: 36598.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.091 -0.196 -0.044 0.087 43.370
##
## Random effects:
## Groups Name Variance Std.Dev.
## Subject (Intercept) 23163 152.2
## Residual 255555 505.5
## Number of obs: 2400, groups: Subject, 10
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 613.24 54.06 11.343
## Block2 -311.03 35.75 -8.701
## Block3 -359.14 35.90 -10.003
## Block4 -370.00 36.11 -10.246
## Block5 -386.23 38.32 -10.079
## COM.X.VE -950.89 842.36 -1.129
## Block2:COM.X.VE 1055.01 1077.21 0.979
## Block3:COM.X.VE 979.09 1003.26 0.976
## Block4:COM.X.VE 760.37 978.81 0.777
## Block5:COM.X.VE 1027.41 987.30 1.041
##
## Correlation of Fixed Effects:
## (Intr) Block2 Block3 Block4 Block5 COM.X. B2:COM B3:COM B4:COM
## Block2 -0.314
## Block3 -0.312 0.473
## Block4 -0.311 0.470 0.467
## Block5 -0.293 0.443 0.441 0.439
## COM.X.VE -0.159 0.241 0.240 0.239 0.224
## B2:COM.X.VE 0.125 -0.394 -0.188 -0.186 -0.175 -0.782
## B3:COM.X.VE 0.134 -0.203 -0.387 -0.200 -0.188 -0.839 0.657
## B4:COM.X.VE 0.137 -0.207 -0.206 -0.386 -0.194 -0.861 0.673 0.722
## B5:COM.X.VE 0.136 -0.205 -0.204 -0.204 -0.439 -0.853 0.667 0.716 0.734#Plotting of quick interactions5
emmip(m.MSL.COMVE.RT.Inter, Block~COM.X.VE)## Suggestion: Add 'at = list(COM.X.VE = ...)' to call to see > 1 value per group.## geom_path: Each group consists of only one observation. Do you need to adjust
## the group aesthetic?
#Not significant result. Significance only between block and RT but not the interactions of the velocity and Trial RT within the blocks.
#Sixth model: To understand The interaction if RT predicts CoM.X Velocity changes that is modulated by blocks (learning).
m.MSL.COMVE.RT <- lmer(AvgTrial.RT ~ COM.X.VE + (1|Subject), data = d.MSL)
Anova(m.MSL.COMVE.RT)summary(m.MSL.COMVE.RT)## Linear mixed model fit by REML ['lmerMod']
## Formula: AvgTrial.RT ~ COM.X.VE + (1 | Subject)
## Data: d.MSL
##
## REML criterion at convergence: 36867.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -0.677 -0.240 -0.105 0.080 42.395
##
## Random effects:
## Groups Name Variance Std.Dev.
## Subject (Intercept) 23182 152.3
## Residual 274085 523.5
## Number of obs: 2400, groups: Subject, 10
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 341.21 49.67 6.870
## COM.X.VE -681.11 263.51 -2.585
##
## Correlation of Fixed Effects:
## (Intr)
## COM.X.VE -0.118#Plotting of quick interactions6
emmip(m.MSL.COMVE.RT, ~COM.X.VE)## Suggestion: Add 'at = list(COM.X.VE = ...)' to call to see > 1 value per group.
## geom_path: Each group consists of only one observation. Do you need to adjust
## the group aesthetic?
#When block is removed however, there is a relationship with RT and COM. Scatter plot here will show the linear relationship.###Effects and plots of the models
#We now we need prepare the data to plot the effects and not the raw numbers. Because after statistical testing the numbers are changed and the raw values are not representative of the models after factors were specified.
#Effects Model 1
ae.m.MSL.RT <- allEffects(m.MSL.RT)
ae.m.df.RT <- as.data.frame(ae.m.MSL.RT[[1]])
#The plot of RT~Block
RT <- ggplot(ae.m.df.RT, aes(x=Block, y=fit)) +
geom_errorbar(aes(ymin=lower, ymax=upper), width=.1) +
geom_line() +
geom_point() +
ylab("RT (ms)") +
xlab("Block") +
ggtitle("RT~Block") +
theme_classic()
print(RT)## geom_path: Each group consists of only one observation. Do you need to adjust
## the group aesthetic?
##Block determines RT. Difference is predicated on the difference in the 1st block.
#Effects Model 2
ae.m.MSL.ACC <- allEffects(m.MSL.ACC)
ae.m.df.ACC <- as.data.frame(ae.m.MSL.ACC[[1]])
#The plot of RT~ACC
ACC<-ggplot(ae.m.df.ACC, aes(x=Trial.ACC.Num,y=fit))+
geom_errorbar(aes(ymin=lower, ymax=upper), width=.1) +
geom_point() +
geom_line()+
ylab("RT (ms)")+
xlab("ACC")+
ggtitle("RT~ACC")+
theme_classic()
print(ACC)## geom_path: Each group consists of only one observation. Do you need to adjust
## the group aesthetic?
##Clear difference between accurate and inaccurate. Accurate significantly faster.
#Effects Model 3
ae.m.MSL.RTACC <- allEffects(m.MSL.RTACC)
ae.m.df.RTACC <- as.data.frame(ae.m.MSL.RTACC[[1]])
#The plot of RT~Block*ACC
RTACC<-ggplot(ae.m.df.RTACC, aes(x=Block,y=fit, group=Trial.ACC.Num))+
geom_ribbon(aes(ymin=lower, ymax=upper, fill=Trial.ACC.Num), alpha=0.2) +
geom_line(aes(size=1, color=Trial.ACC.Num)) +
geom_point(aes(color=Trial.ACC.Num, shape=Trial.ACC.Num, size=2))+
ylab("RT (ms)")+
xlab("Block")+
ggtitle("RT~ACC*Block")+
theme_classic()
print(RTACC)
##Differences in accurate and inaccurate trials. Again predicated on the 1st block. In general, the RT is decreasing per block too, even for inaccurate trials.
#Effects Model 4
ae.m.MSL.COMVE <- allEffects(m.MSL.COMVE)
ae.m.df.COMVE <- as.data.frame(ae.m.MSL.COMVE[[1]])
#The plot of COMVelocity~Block
COMVE <- ggplot(ae.m.df.COMVE, aes(x=Block, y=fit)) +
geom_errorbar(aes(ymin=lower, ymax=upper), width=.1) +
geom_line() +
geom_point() +
ylab("COM Velocity (m)") +
xlab("Block") +
ggtitle("COM Velocity~Block") +
theme_classic()
print(COMVE)## geom_path: Each group consists of only one observation. Do you need to adjust
## the group aesthetic?
##The COM is moving faster overtime. There are differences in 1st vs 3rd, 1st vs 4th and 1st vs 5th (largest increase in velocity).
#Effects Model 4.5
ae.m.MSL.COMVE.ACC <- allEffects(m.MSL.COMVE.ACC)
ae.m.df.COMVE.ACC <- as.data.frame(ae.m.MSL.COMVE.ACC[[1]])
#The plot of RT~ACC
COMVE.ACC<-ggplot(ae.m.df.COMVE.ACC, aes(x=Trial.ACC.Num,y=fit))+
geom_errorbar(aes(ymin=lower, ymax=upper), width=.1) +
geom_point() +
geom_line()+
ylab("COM X Velocity(m/s)")+
xlab("ACC")+
ggtitle("COM X Velocity~ACC")+
theme_classic()
print(COMVE.ACC)## geom_path: Each group consists of only one observation. Do you need to adjust
## the group aesthetic?
##The COM is faster for inaccurate trials but more variable compared to accurate trials which are slower but less variable. This suggests that there is a level of certainty with the motion in accurate trials since they don't fluctuate as much.
#Effects Model 5
ae.m.COMVE.RT.Inter <- allEffects(m.MSL.COMVE.RT.Inter)
ae.m.df.COMVE.RT.Inter <- as.data.frame(ae.m.COMVE.RT.Inter[[1]])
#The plot of RT ~ Block * COM.X.VE
RTCOMVE.inter<-ggplot(ae.m.df.COMVE.RT.Inter, aes(x=COM.X.VE,y=fit, color=Block))+
geom_ribbon(aes(ymin=lower, ymax=upper, fill=Block), alpha=0.2) +
geom_line() +
geom_point()+
ylab("RT (ms)")+
xlab("COM Velocity (m/s)")+
ggtitle("RT~Block*COMVE")+
theme_classic() +
facet_wrap(~Block)
print(RTCOMVE.inter)
##Fast and slow COM have the same reaction times by block 3 to 5. So COM when understood from a block perspective has no differences. Even in the 1st block.
#Effects Model 6 - So now we remove the issue of block and just check how Trial RT predicts COM Velocity
ae.m.COMVE.RT <- allEffects(m.MSL.COMVE.RT)
ae.m.df.COMVE.RT <- as.data.frame(ae.m.COMVE.RT[[1]])
#The plot of RT ~ COMVelocity
RTCOMVE <- ggplot(ae.m.df.COMVE.RT, aes(x=COM.X.VE, y=fit)) +
geom_errorbar(aes(ymin=lower, ymax=upper), width=0.075) +
geom_line() +
geom_point() +
ylab("RT (ms)") +
xlab("COM Velocity (m/s)") +
ggtitle("RT~COM Velocity") +
theme_classic()
print(RTCOMVE)
##This is just a clear and significant linear relationship in that the fastest RT is also predicting the fastest COM Velocities.#Posthocs (Tukey tests for sanity checks. Not really needed.)
#Summary of posthocs
summary(glht(m.MSL.RT, linfct = mcp(Block = "Tukey")), test = adjusted("holm"))##
## Simultaneous Tests for General Linear Hypotheses
##
## Multiple Comparisons of Means: Tukey Contrasts
##
##
## Fit: lmer(formula = AvgTrial.RT ~ Block + (1 | Subject), data = d.MSL)
##
## Linear Hypotheses:
## Estimate Std. Error z value Pr(>|z|)
## 2 - 1 == 0 -299.48 32.61 -9.184 <2e-16 ***
## 3 - 1 == 0 -348.79 32.61 -10.697 <2e-16 ***
## 4 - 1 == 0 -365.19 32.61 -11.200 <2e-16 ***
## 5 - 1 == 0 -373.81 32.61 -11.464 <2e-16 ***
## 3 - 2 == 0 -49.30 32.61 -1.512 0.522
## 4 - 2 == 0 -65.71 32.61 -2.015 0.219
## 5 - 2 == 0 -74.33 32.61 -2.280 0.136
## 4 - 3 == 0 -16.41 32.61 -0.503 1.000
## 5 - 3 == 0 -25.03 32.61 -0.768 1.000
## 5 - 4 == 0 -8.62 32.61 -0.264 1.000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- holm method)summary(glht(m.MSL.ACC, linfct = mcp(Trial.ACC.Num = "Tukey")), test = adjusted("holm"))##
## Simultaneous Tests for General Linear Hypotheses
##
## Multiple Comparisons of Means: Tukey Contrasts
##
##
## Fit: lmer(formula = AvgTrial.RT ~ Trial.ACC.Num + (1 | Subject), data = d.MSL)
##
## Linear Hypotheses:
## Estimate Std. Error z value Pr(>|z|)
## 1 - 0 == 0 -289.9 25.3 -11.46 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- holm method)summary(glht(m.MSL.RTACC, linfct = mcp(Block = "Tukey")), test = adjusted("holm"))## Warning in mcp2matrix(model, linfct = linfct): covariate interactions found --
## default contrast might be inappropriate##
## Simultaneous Tests for General Linear Hypotheses
##
## Multiple Comparisons of Means: Tukey Contrasts
##
##
## Fit: lmer(formula = AvgTrial.RT ~ Block * Trial.ACC.Num + (1 | Subject),
## data = d.MSL)
##
## Linear Hypotheses:
## Estimate Std. Error z value Pr(>|z|)
## 2 - 1 == 0 -377.786 53.960 -7.001 2.03e-11 ***
## 3 - 1 == 0 -461.216 64.157 -7.189 5.88e-12 ***
## 4 - 1 == 0 -451.782 62.602 -7.217 5.32e-12 ***
## 5 - 1 == 0 -363.227 68.082 -5.335 6.68e-07 ***
## 3 - 2 == 0 -83.429 69.844 -1.195 1
## 4 - 2 == 0 -73.996 69.000 -1.072 1
## 5 - 2 == 0 14.559 74.609 0.195 1
## 4 - 3 == 0 9.434 76.877 0.123 1
## 5 - 3 == 0 97.988 82.238 1.192 1
## 5 - 4 == 0 88.555 80.856 1.095 1
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- holm method)summary(glht(m.MSL.COMVE.ACC, linfct = mcp(Trial.ACC.Num = "Tukey")), test = adjusted("holm"))##
## Simultaneous Tests for General Linear Hypotheses
##
## Multiple Comparisons of Means: Tukey Contrasts
##
##
## Fit: lmer(formula = COM.X.VE ~ Trial.ACC.Num + (1 | Subject), data = d.MSL)
##
## Linear Hypotheses:
## Estimate Std. Error z value Pr(>|z|)
## 1 - 0 == 0 0.006658 0.001915 3.476 0.000509 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- holm method)summary(glht(m.MSL.COMVE, linfct = mcp(Block = "Tukey")), test = adjusted("holm"))##
## Simultaneous Tests for General Linear Hypotheses
##
## Multiple Comparisons of Means: Tukey Contrasts
##
##
## Fit: lmer(formula = COM.X.VE ~ Block + (1 | Subject), data = d.MSL)
##
## Linear Hypotheses:
## Estimate Std. Error z value Pr(>|z|)
## 2 - 1 == 0 0.007319 0.002569 2.849 0.01316 *
## 3 - 1 == 0 0.012244 0.002569 4.766 1.13e-05 ***
## 4 - 1 == 0 0.015556 0.002569 6.055 1.12e-08 ***
## 5 - 1 == 0 0.024984 0.002569 9.725 < 2e-16 ***
## 3 - 2 == 0 0.004925 0.002569 1.917 0.11049
## 4 - 2 == 0 0.008237 0.002569 3.206 0.00538 **
## 5 - 2 == 0 0.017665 0.002569 6.876 5.53e-11 ***
## 4 - 3 == 0 0.003312 0.002569 1.289 0.19728
## 5 - 3 == 0 0.012740 0.002569 4.959 4.95e-06 ***
## 5 - 4 == 0 0.009428 0.002569 3.670 0.00121 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- holm method)summary(glht(m.MSL.COMVE.RT.Inter, linfct = mcp(Block = "Tukey")), test = adjusted("holm"))## Warning in mcp2matrix(model, linfct = linfct): covariate interactions found --
## default contrast might be inappropriate##
## Simultaneous Tests for General Linear Hypotheses
##
## Multiple Comparisons of Means: Tukey Contrasts
##
##
## Fit: lmer(formula = AvgTrial.RT ~ Block * COM.X.VE + (1 | Subject),
## data = d.MSL)
##
## Linear Hypotheses:
## Estimate Std. Error z value Pr(>|z|)
## 2 - 1 == 0 -311.03 35.75 -8.701 <2e-16 ***
## 3 - 1 == 0 -359.14 35.90 -10.003 <2e-16 ***
## 4 - 1 == 0 -370.00 36.11 -10.246 <2e-16 ***
## 5 - 1 == 0 -386.23 38.32 -10.079 <2e-16 ***
## 3 - 2 == 0 -48.11 36.78 -1.308 0.764
## 4 - 2 == 0 -58.97 37.00 -1.594 0.555
## 5 - 2 == 0 -75.20 39.16 -1.920 0.329
## 4 - 3 == 0 -10.86 37.16 -0.292 1.000
## 5 - 3 == 0 -27.09 39.31 -0.689 1.000
## 5 - 4 == 0 -16.23 39.48 -0.411 1.000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- holm method)