new analyses
noah castelo
November 19, 2016
options(rpubs.upload.method = "internal")
options(RCurlOptions = list(verbose = FALSE, capath = system.file("CurlSSL", "cacert.pem", package = "RCurl"), ssl.verifypeer = FALSE))
setwd("~/Documents/Dropbox/Research/Eric")
combined2<-read.csv("old and new data.csv", header=T, sep=",")
combined2$bd<-combined2$beta*((1/(1+combined2$delta))^(2/52))*1.5
combined2$bd<-combined2$bd-mean(combined2$bd)
combined2$beta<-combined2$beta-mean(combined2$beta)
combined2$delta<-combined2$delta-mean(combined2$delta)
#re-coding education as numeric
table(combined2$education)##
## 9th, 10th or 11th grade
## 5
## Associate degree (for example: AA, AS)
## 112
## Bachelor's degree (for example: BA, AB, BS)
## 423
## Doctorate degree (for example: PhD, EdD)
## 12
## High school diploma or the equivalent (for example: GED)
## 101
## Master's degree (for example: MA, MS, MEng, MEd, MSW, MBA)
## 92
## Professional degree (for example: MD, DDS, DVM, LLB, JD)
## 14
## Some college, and currently enrolled
## 98
## Some college, but not currently enrolled
## 231combined2$edu[combined2$education=="9th, 10th or 11th grade"]<-1
combined2$edu[combined2$education=="High school diploma or the equivalent (for example: GED)"]<-2
combined2$edu[combined2$education=="Associate degree (for example: AA, AS)"]<-3
combined2$edu[combined2$education=="Some college, but not currently enrolled"]<-4
combined2$edu[combined2$education=="Some college, and currently enrolled"]<-5
combined2$edu[combined2$education=="Bachelor's degree (for example: BA, AB, BS)"]<-6
combined2$edu[combined2$education=="Professional degree (for example: MD, DDS, DVM, LLB, JD)"]<-6
combined2$edu[combined2$education=="Master's degree (for example: MA, MS, MEng, MEd, MSW, MBA)"]<-7
combined2$edu[combined2$education=="Doctorate degree (for example: PhD, EdD)"]<-8
combined2$edu<-as.numeric(combined2$edu)
combined2$edu[combined2$education=="9th, 10th or 11th grade"]<-1
combined2$edu[combined2$education=="High school diploma or the equivalent (for example: GED)"]<-2
combined2$edu[combined2$education=="Associate degree (for example: AA, AS)"]<-3
combined2$edu[combined2$education=="Some college, but not currently enrolled"]<-4
combined2$edu[combined2$education=="Some college, and currently enrolled"]<-5
combined2$edu[combined2$education=="Bachelor's degree (for example: BA, AB, BS)"]<-6
combined2$edu[combined2$education=="Professional degree (for example: MD, DDS, DVM, LLB, JD)"]<-6
combined2$edu[combined2$education=="Master's degree (for example: MA, MS, MEng, MEd, MSW, MBA)"]<-7
combined2$edu[combined2$education=="Doctorate degree (for example: PhD, EdD)"]<-8
table(combined2$edu)##
## 1 2 3 4 5 6 7 8
## 5 101 112 231 98 437 92 12#centering
summary(combined2$edu)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.000 4.000 5.000 4.889 6.000 8.000combined2$eduCentered<-combined2$edu - 4.889
summary(combined2$eduCentered)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -3.889000 -0.889000 0.111000 -0.000213 1.111000 3.111000#re-coding income as numeric
table(combined2$income)##
## $10,000 to $19,999 $100,000 to $124,999 $125,000 to $149,999
## 106 69 36
## $150,000 to $199,999 $20,000 to $29,999 $200,000 or more
## 24 133 12
## $30,000 to $39,999 $40,000 to $49,999 $50,000 to $59,999
## 147 132 102
## $60,000 to $69,999 $70,000 to $79,999 $80,000 to $89,999
## 86 65 53
## $90,000 to $99,999 Less than $10,000
## 41 82combined2$inc[combined2$income=="Less than $10,000"]<-1
combined2$inc[combined2$income=="$10,000 to $19,999"]<-2
combined2$inc[combined2$income=="$20,000 to $29,999"]<-3
combined2$inc[combined2$income=="$30,000 to $39,999"]<-4
combined2$inc[combined2$income=="$40,000 to $49,999"]<-5
combined2$inc[combined2$income=="$50,000 to $59,999"]<-6
combined2$inc[combined2$income=="$60,000 to $69,999"]<-7
combined2$inc[combined2$income=="$70,000 to $79,999"]<-8
combined2$inc[combined2$income=="$80,000 to $89,999"]<-9
combined2$inc[combined2$income=="$90,000 to $99,999"]<-10
combined2$inc[combined2$income=="$100,000 to $124,999"]<-11
combined2$inc[combined2$income=="$150,000 to $199,999"]<-12
combined2$inc[combined2$income=="200,000 or more"]<-13
combined2$inc<-as.numeric(combined2$inc)
combined2$inc[combined2$income=="Less than $10,000"]<-1
combined2$inc[combined2$income=="$10,000 to $19,999"]<-2
combined2$inc[combined2$income=="$20,000 to $29,999"]<-3
combined2$inc[combined2$income=="$30,000 to $39,999"]<-4
combined2$inc[combined2$income=="$40,000 to $49,999"]<-5
combined2$inc[combined2$income=="$50,000 to $59,999"]<-6
combined2$inc[combined2$income=="$60,000 to $69,999"]<-7
combined2$inc[combined2$income=="$70,000 to $79,999"]<-8
combined2$inc[combined2$income=="$80,000 to $89,999"]<-9
combined2$inc[combined2$income=="$90,000 to $99,999"]<-10
combined2$inc[combined2$income=="$100,000 to $124,999"]<-11
combined2$inc[combined2$income=="$150,000 to $199,999"]<-12
combined2$inc[combined2$income=="200,000 or more"]<-13
table(combined2$inc)##
## 1 2 3 4 5 6 7 8 9 10 11 12
## 82 106 169 147 132 114 86 65 53 41 69 24#centering
combined2$incCentered<-combined2$inc - mean(combined2$inc)
summary(combined2$incCentered)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -4.3210 -2.3210 -0.3208 0.0000 1.6790 6.6790summary(aov(SS~cond + eduCentered + eduCentered*cond, data=combined2))## Df Sum Sq Mean Sq F value Pr(>F)
## cond 2 1.77 0.887 3.632 0.0268 *
## eduCentered 1 4.74 4.741 19.401 1.16e-05 ***
## cond:eduCentered 2 0.92 0.459 1.879 0.1533
## Residuals 1082 264.39 0.244
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(aov(SS~cond + incCentered + incCentered*cond, data=combined2))## Df Sum Sq Mean Sq F value Pr(>F)
## cond 2 1.77 0.8875 3.586 0.02804 *
## incCentered 1 1.93 1.9326 7.809 0.00529 **
## cond:incCentered 2 0.34 0.1681 0.679 0.50713
## Residuals 1082 267.78 0.2475
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(aov(SS~cond + gender + gender*cond, data=combined2))## Df Sum Sq Mean Sq F value Pr(>F)
## cond 2 1.32 0.6584 2.634 0.0723 .
## gender 2 0.38 0.1904 0.762 0.4671
## cond:gender 3 0.36 0.1211 0.485 0.6930
## Residuals 909 227.18 0.2499
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 171 observations deleted due to missingnesssummary(aov(SS~cond + age + age*cond, data=combined2))## Df Sum Sq Mean Sq F value Pr(>F)
## cond 2 1.77 0.8875 3.560 0.0288 *
## age 1 0.22 0.2166 0.869 0.3515
## cond:age 2 0.09 0.0441 0.177 0.8380
## Residuals 1082 269.74 0.2493
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(aov(SS ~ cond*age*bd, data=combined2))## Df Sum Sq Mean Sq F value Pr(>F)
## cond 2 1.77 0.887 3.850 0.021584 *
## age 1 0.22 0.217 0.939 0.332659
## bd 1 17.17 17.166 74.461 < 2e-16 ***
## cond:age 2 0.03 0.014 0.059 0.942807
## cond:bd 2 3.84 1.922 8.337 0.000255 ***
## age:bd 1 0.18 0.178 0.772 0.379899
## cond:age:bd 2 0.55 0.276 1.196 0.302688
## Residuals 1076 248.06 0.231
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(aov(SS ~ cond*eduCentered*bd, data=combined2))## Df Sum Sq Mean Sq F value Pr(>F)
## cond 2 1.77 0.887 3.893 0.020671 *
## eduCentered 1 4.74 4.741 20.795 5.70e-06 ***
## bd 1 14.64 14.641 64.224 2.87e-15 ***
## cond:eduCentered 2 1.00 0.499 2.191 0.112327
## cond:bd 2 3.32 1.661 7.287 0.000718 ***
## eduCentered:bd 1 0.70 0.705 3.091 0.079009 .
## cond:eduCentered:bd 2 0.35 0.174 0.762 0.466916
## Residuals 1076 245.29 0.228
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(aov(SS ~ cond*incCentered*bd, data=combined2))## Df Sum Sq Mean Sq F value Pr(>F)
## cond 2 1.77 0.887 3.882 0.020901 *
## incCentered 1 1.93 1.933 8.453 0.003719 **
## bd 1 16.34 16.339 71.470 < 2e-16 ***
## cond:incCentered 2 0.28 0.140 0.614 0.541450
## cond:bd 2 3.97 1.983 8.675 0.000183 ***
## incCentered:bd 1 0.60 0.599 2.621 0.105761
## cond:incCentered:bd 2 0.93 0.467 2.044 0.130018
## Residuals 1076 245.99 0.229
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(aov(SS ~ cond*gender*bd, data=combined2))## Df Sum Sq Mean Sq F value Pr(>F)
## cond 2 1.32 0.658 2.850 0.0583 .
## gender 2 0.38 0.190 0.824 0.4388
## bd 1 13.32 13.319 57.660 7.78e-14 ***
## cond:gender 3 0.33 0.111 0.479 0.6972
## cond:bd 2 4.70 2.349 10.168 4.30e-05 ***
## gender:bd 2 0.48 0.242 1.047 0.3514
## cond:gender:bd 2 0.36 0.178 0.770 0.4632
## Residuals 902 208.35 0.231
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 171 observations deleted due to missingness1. Re-run 3-factor model with factors re-ordered.
We can start with eric’s suggested changes to the 3-factor model. It doesn’t appear to reveal the significant differences we were hoping for.
library(gdata)
combined2$cond <- reorder(combined2$cond, new.order = c(2, 3, 1))
summary(glm(SS ~ cond, data = combined2, family = binomial))##
## Call:
## glm(formula = SS ~ cond, family = binomial, data = combined2)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.247 -1.111 -1.099 1.246 1.257
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.15928 0.11545 -1.380 0.1677
## condSS 0.32043 0.15312 2.093 0.0364 *
## condLL -0.02683 0.15404 -0.174 0.8617
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1507.6 on 1087 degrees of freedom
## Residual deviance: 1500.5 on 1085 degrees of freedom
## AIC: 1506.5
##
## Number of Fisher Scoring iterations: 32. Run nested model, including mean centering beta-delta
library(lme4)
library(pbkrtest)
library(car)
library(lmerTest)
library(afex)
nest.reg2 <- glm(SS ~ bd * cond, contrasts = list(cond = contr.sum), family = "binomial",
data = combined2)
table(combined2$cond)##
## no SS LL
## 302 398 388# what does the cond=contr.sum mean slope would be value of bd is there an
# relationship between reaction time and bd among impatient people in the LL
# condition?
nest.reg2 <- glmer(SS ~ bd + (bd | cond), family = "binomial", data = combined2)
coef(nest.reg2)## $cond
## (Intercept) bd
## no -0.004256083 -3.160553
## SS 0.199603270 -5.156105
## LL -0.208312298 -1.163075
##
## attr(,"class")
## [1] "coef.mer"fixef(nest.reg2)## (Intercept) bd
## -0.0005440959 -3.1968893801summary(nest.reg2)## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: SS ~ bd + (bd | cond)
## Data: combined2
##
## AIC BIC logLik deviance df.resid
## 1417.5 1442.4 -703.7 1407.5 1083
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -8.6901 -0.8643 -0.4522 1.0719 2.3340
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## cond (Intercept) 0.03157 0.1777
## bd 3.02469 1.7392 -1.00
## Number of obs: 1088, groups: cond, 3
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.0005441 0.1216153 -0.004 0.996
## bd -3.1968894 1.0773377 -2.967 0.003 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr)
## bd -0.822anova(nest.reg2)## Analysis of Variance Table
## Df Sum Sq Mean Sq F value
## bd 1 8.859 8.859 8.859confint(nest.reg2)## 2.5 % 97.5 %
## .sig01 0.04707627 0.5983397
## .sig02 -1.00415322 -0.3124030
## .sig03 0.75869989 5.4468863
## (Intercept) -0.33216967 0.3356995
## bd -6.27249659 -0.27628773. Re-running basic analyses.
Next we can look at the basic analysis (not nested) that we’ve been using all along, first without excluding outliers.
prop.test(table(combined2$cond, combined2$SS))##
## 3-sample test for equality of proportions without continuity
## correction
##
## data: table(combined2$cond, combined2$SS)
## X-squared = 7.1045, df = 2, p-value = 0.02866
## alternative hypothesis: two.sided
## sample estimates:
## prop 1 prop 2 prop 3
## 0.5397351 0.4597990 0.5463918SScontrol<-subset(combined2, cond!="LL")
SScontrol<-droplevels(SScontrol)
SScontrol$bd<-SScontrol$bd - mean(SScontrol$bd)
prop.test(table(SScontrol$cond, SScontrol$SS))##
## 2-sample test for equality of proportions with continuity
## correction
##
## data: table(SScontrol$cond, SScontrol$SS)
## X-squared = 4.0753, df = 1, p-value = 0.04351
## alternative hypothesis: two.sided
## 95 percent confidence interval:
## 0.002476825 0.157395383
## sample estimates:
## prop 1 prop 2
## 0.5397351 0.4597990LLcontrol<-subset(combined2, cond!="SS")
LLcontrol<-droplevels(LLcontrol)
LLcontrol$bd<-LLcontrol$bd - mean(LLcontrol$bd)
summary(glm(SS ~ cond * bd, data=SScontrol, family="binomial"))##
## Call:
## glm(formula = SS ~ cond * bd, family = "binomial", data = SScontrol)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.9784 -1.0328 0.1508 1.1515 1.9788
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.07956 0.12384 -0.642 0.5206
## condSS 0.29031 0.16669 1.742 0.0816 .
## bd -3.27059 0.72535 -4.509 6.51e-06 ***
## condSS:bd -2.15098 1.09581 -1.963 0.0497 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 970.31 on 699 degrees of freedom
## Residual deviance: 868.13 on 696 degrees of freedom
## AIC: 876.13
##
## Number of Fisher Scoring iterations: 5f1<-(glm(SS~cond*bd, data=SScontrol, family="binomial"))
library(visreg)
col<-c("black", "blue")
col2<-c("gray80", "cornflowerblue")
col3<-adjustcolor(col2, alpha=.7)
visreg(f1, "bd", by="cond", line=list(col=col), fill=list(col=col3), overlay=TRUE, partial=FALSE, scale="response", xlab="Present Value of LL", ylab="Percent Choosing SS")
LL/control
summary(glm(SS~cond*bd, data=LLcontrol,family="binomial"))##
## Call:
## glm(formula = SS ~ cond * bd, family = "binomial", data = LLcontrol)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.9784 -1.0523 -0.8936 1.2478 1.9788
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.06415 0.12462 -0.515 0.60672
## condLL -0.13867 0.16163 -0.858 0.39093
## bd -3.27059 0.72534 -4.509 6.51e-06 ***
## condLL:bd 2.25580 0.85101 2.651 0.00803 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 951.32 on 689 degrees of freedom
## Residual deviance: 916.60 on 686 degrees of freedom
## AIC: 924.6
##
## Number of Fisher Scoring iterations: 4f2<-(glm(SS~cond*bd, data=LLcontrol,family="binomial"))
col<-c("red", "black")
col2<-c("indianred1" , "gray80")
col3<-adjustcolor(col2, alpha=.45)
visreg(f2, "bd", by="cond", line=list(col=col), fill=list(col=col3), overlay=TRUE, partial=FALSE, xlab="Present value of LL", scale="response", ylab="P (choosing SS)")
And all 3 conditions together…
f3<-(glm(SS~cond*bd, data=combined2,family="binomial"))
visreg(f3, "bd", by="cond", overlay=TRUE, partial=FALSE, xlab="Present value of LL", scale="response", ylab="P (choosing SS)")
4. Removing outliers.
Let’s check if removing outliers changes things (any bd scores > 4 SDs from mean). The SS / control condition interaction becomes non-significant.
mean(combined2$bd)+(4*(sd(combined2$bd)))## [1] 0.9223074mean(combined2$bd)-(4*(sd(combined2$bd)))## [1] -0.9223074combined2<-subset(combined2, bd>=-0.9223074)
combined2<-subset(combined2, bd<=0.9223074)
SScontrol<-subset(combined2, cond!="LL")
SScontrol<-droplevels(SScontrol)
SScontrol$bd<-SScontrol$bd - mean(SScontrol$bd)
prop.test(table(SScontrol$cond, SScontrol$SS))##
## 2-sample test for equality of proportions with continuity
## correction
##
## data: table(SScontrol$cond, SScontrol$SS)
## X-squared = 3.9721, df = 1, p-value = 0.04626
## alternative hypothesis: two.sided
## 95 percent confidence interval:
## 0.001500071 0.157122484
## sample estimates:
## prop 1 prop 2
## 0.5402685 0.4609572SSLL<-subset(combined2, cond!="no")
SSLL<-droplevels(SSLL)
prop.test(table(SSLL$cond, SSLL$SS))##
## 2-sample test for equality of proportions with continuity
## correction
##
## data: table(SSLL$cond, SSLL$SS)
## X-squared = 5.7698, df = 1, p-value = 0.0163
## alternative hypothesis: two.sided
## 95 percent confidence interval:
## -0.160946 -0.016098
## sample estimates:
## prop 1 prop 2
## 0.4609572 0.5494792LLcontrol<-subset(combined2, cond!="SS")
LLcontrol<-droplevels(LLcontrol)
LLcontrol$bd<-LLcontrol$bd - mean(LLcontrol$bd)
prop.test(table(LLcontrol$cond, LLcontrol$SS))##
## 2-sample test for equality of proportions with continuity
## correction
##
## data: table(LLcontrol$cond, LLcontrol$SS)
## X-squared = 0.026273, df = 1, p-value = 0.8712
## alternative hypothesis: two.sided
## 95 percent confidence interval:
## -0.08754485 0.06912343
## sample estimates:
## prop 1 prop 2
## 0.5402685 0.5494792summary(glm(SS ~ cond * bd, data=SScontrol, family="binomial"))##
## Call:
## glm(formula = SS ~ cond * bd, family = "binomial", data = SScontrol)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.5539 -1.0252 0.1643 1.1261 2.3117
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.02411 0.12934 -0.186 0.852
## condSS 0.18616 0.16998 1.095 0.273
## bd -4.96633 0.90701 -5.476 4.36e-08 ***
## condSS:bd -0.45480 1.22373 -0.372 0.710
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 963.4 on 694 degrees of freedom
## Residual deviance: 847.7 on 691 degrees of freedom
## AIC: 855.7
##
## Number of Fisher Scoring iterations: 4f1<-(glm(SS~cond*bd, data=SScontrol, family="binomial"))
library(visreg)
col<-c("black", "blue")
col2<-c("gray80", "cornflowerblue")
col3<-adjustcolor(col2, alpha=.7)
visreg(f1, "bd", by="cond", line=list(col=col), fill=list(col=col3), overlay=TRUE, partial=FALSE, scale="response", xlab="Present Value of LL", ylab="Percent Choosing SS")
while the LL/no default interaction increaes in significance
summary(glm(SS~cond*bd, data=LLcontrol,family="binomial"))##
## Call:
## glm(formula = SS ~ cond * bd, family = "binomial", data = LLcontrol)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.5539 -1.0498 -0.8975 1.2496 2.3117
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.02151 0.12947 -0.166 0.868035
## condLL -0.19606 0.16579 -1.183 0.236989
## bd -4.96633 0.90701 -5.476 4.36e-08 ***
## condLL:bd 3.98993 1.03030 3.873 0.000108 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 939.81 on 681 degrees of freedom
## Residual deviance: 891.53 on 678 degrees of freedom
## AIC: 899.53
##
## Number of Fisher Scoring iterations: 4f2<-(glm(SS~cond*bd, data=LLcontrol,family="binomial"))
col<-c("red", "black")
col2<-c("indianred1" , "gray80")
col3<-adjustcolor(col2, alpha=.45)
visreg(f2, "bd", by="cond", line=list(col=col), fill=list(col=col3), overlay=TRUE, partial=FALSE, xlab="Present value of LL", scale="response", ylab="P (choosing SS)")
And looking at all 3 conditions together again, with 9 outliers excluded:
f3<-(glm(SS~cond*bd, data=combined2,family="binomial"))
visreg(f3, "bd", by="cond", overlay=TRUE, partial=FALSE, xlab="Present value of LL", scale="response", ylab="P (choosing SS)")
5. Using Delta instead of beta-delta.
Here we use delta instead of bd, and see a significant interaction, in the expected direction. People with a high discount rate are nudged towards the SS option - people with a low discount rate are not.
summary(glm(SS ~ cond * delta, data=SScontrol, family="binomial"))##
## Call:
## glm(formula = SS ~ cond * delta, family = "binomial", data = SScontrol)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.2392 -0.9865 0.2961 1.1243 1.8112
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.1101 0.1244 -0.885 0.3763
## condSS 0.4144 0.1706 2.430 0.0151 *
## delta 302.1355 56.2254 5.374 7.72e-08 ***
## condSS:delta 167.9677 85.1230 1.973 0.0485 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 963.40 on 694 degrees of freedom
## Residual deviance: 848.74 on 691 degrees of freedom
## AIC: 856.74
##
## Number of Fisher Scoring iterations: 4f1<-(glm(SS~cond*delta, data=SScontrol, family="binomial"))
library(visreg)
col<-c("black", "blue")
col2<-c("gray80", "cornflowerblue")
col3<-adjustcolor(col2, alpha=.7)
visreg(f1, "delta", by="cond", line=list(col=col), fill=list(col=col3), overlay=TRUE, partial=FALSE, scale="response", xlab="Delta", ylab="Percent Choosing SS")
LL condition - here we see a marginal interaction, in the same counter-intuitive direction as when we use bd. People with high discount rate are nudged AWAY from the SS option; people with low discount rate are nudged TOWARDS it.
summary(glm(SS~cond*delta, data=LLcontrol,family="binomial"))##
## Call:
## glm(formula = SS ~ cond * delta, family = "binomial", data = LLcontrol)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.1403 -1.0052 -0.8889 1.2012 1.8112
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.1101 0.1244 -0.885 0.3763
## condLL -0.1018 0.1628 -0.625 0.5318
## delta 302.1355 56.2254 5.374 7.72e-08 ***
## condLL:delta -131.5859 70.3829 -1.870 0.0615 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 939.81 on 681 degrees of freedom
## Residual deviance: 887.98 on 678 degrees of freedom
## AIC: 895.98
##
## Number of Fisher Scoring iterations: 4f2<-(glm(SS~cond*delta, data=LLcontrol,family="binomial"))
col<-c("red", "black")
col2<-c("indianred1" , "gray80")
col3<-adjustcolor(col2, alpha=.45)
visreg(f2, "delta", by="cond", line=list(col=col), fill=list(col=col3), overlay=TRUE, partial=FALSE, xlab="Delta", scale="response", ylab="P (choosing SS)")
6. Using beta instead.
summary(glm(SS ~ cond * beta, data=SScontrol, family="binomial"))##
## Call:
## glm(formula = SS ~ cond * beta, family = "binomial", data = SScontrol)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.5534 -1.0252 0.1644 1.1265 2.3110
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.05641 0.13389 0.421 0.673
## condSS 0.19353 0.17515 1.105 0.269
## beta -7.44694 1.36035 -5.474 4.39e-08 ***
## condSS:beta -0.68341 1.83550 -0.372 0.710
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 963.40 on 694 degrees of freedom
## Residual deviance: 847.77 on 691 degrees of freedom
## AIC: 855.77
##
## Number of Fisher Scoring iterations: 4f1<-(glm(SS~cond*beta, data=SScontrol, family="binomial"))
library(visreg)
col<-c("black", "blue")
col2<-c("gray80", "cornflowerblue")
col3<-adjustcolor(col2, alpha=.7)
visreg(f1, "beta", by="cond", line=list(col=col), fill=list(col=col3), overlay=TRUE, partial=FALSE, scale="response", xlab="Beta", ylab="Percent Choosing SS")
LL condition
summary(glm(SS~cond*beta, data=LLcontrol,family="binomial"))##
## Call:
## glm(formula = SS ~ cond * beta, family = "binomial", data = LLcontrol)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.5534 -1.0499 -0.8974 1.2496 2.3110
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.05641 0.13389 0.421 0.673499
## condLL -0.25865 0.16900 -1.530 0.125911
## beta -7.44694 1.36035 -5.474 4.39e-08 ***
## condLL:beta 5.98327 1.54536 3.872 0.000108 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 939.81 on 681 degrees of freedom
## Residual deviance: 891.56 on 678 degrees of freedom
## AIC: 899.56
##
## Number of Fisher Scoring iterations: 4f2<-(glm(SS~cond*beta, data=LLcontrol,family="binomial"))
col<-c("red", "black")
col2<-c("indianred1" , "gray80")
col3<-adjustcolor(col2, alpha=.45)
visreg(f2, "beta", by="cond", line=list(col=col), fill=list(col=col3), overlay=TRUE, partial=FALSE, xlab="Beta", scale="response", ylab="P (choosing SS)")
7. Effect of completion times.
First we can exclude people who were VERY slow - 30 mins or more…this doesn’t change the lack of default effects
combined4<-subset(combined2, interviewtime<2000)
summary(glm(SS~cond*bd, data=combined4, family=binomial))##
## Call:
## glm(formula = SS ~ cond * bd, family = binomial, data = combined4)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.6181 -1.1044 -0.3407 1.2083 2.3117
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.05648 0.13390 0.422 0.673
## condSS 0.26963 0.18709 1.441 0.150
## condLL -0.14457 0.17763 -0.814 0.416
## bd -4.96633 0.90702 -5.475 4.36e-08 ***
## condSS:bd -0.96072 1.33281 -0.721 0.471
## condLL:bd 4.47702 1.04749 4.274 1.92e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1258.7 on 907 degrees of freedom
## Residual deviance: 1148.6 on 902 degrees of freedom
## AIC: 1160.6
##
## Number of Fisher Scoring iterations: 5Now we can look at completion times as a covariate (the time it took people to choose on the default page, without mean-centering so that we can see actual times). Let’s start by checking for a 3 way interaction between bd, cond, and interview time:
summary(glm(SS~cond*bd*interviewtime, data=combined2, family="binomial"))##
## Call:
## glm(formula = SS ~ cond * bd * interviewtime, family = "binomial",
## data = combined2)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.480 -1.097 -0.236 1.212 2.203
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.0748006 0.2024628 0.369 0.71179
## condSS 0.6681462 0.3016874 2.215 0.02678 *
## condLL -0.2230693 0.2841749 -0.785 0.43247
## bd -3.9717065 1.5495428 -2.563 0.01037 *
## interviewtime -0.0005065 0.0067546 -0.075 0.94023
## condSS:bd -7.2864066 2.6570515 -2.742 0.00610 **
## condLL:bd 5.3937463 1.9657086 2.744 0.00607 **
## condSS:interviewtime -0.0128580 0.0085153 -1.510 0.13105
## condLL:interviewtime 0.0022399 0.0082771 0.271 0.78668
## bd:interviewtime -0.0429422 0.0579180 -0.741 0.45843
## condSS:bd:interviewtime 0.2201237 0.0807103 2.727 0.00638 **
## condLL:bd:interviewtime -0.0174593 0.0678091 -0.257 0.79681
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1260.1 on 908 degrees of freedom
## Residual deviance: 1134.5 on 897 degrees of freedom
## (170 observations deleted due to missingness)
## AIC: 1158.5
##
## Number of Fisher Scoring iterations: 6One way to break down the significant 3 way interaction above is by checking whether the cond*bd interaction depends on reaction time. We can separate the sample into fast, medium, and slow responders (dividing the data into thirds. Alternate splits based on quartiles also follow).
summary(combined4$interviewtime)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.71 17.39 24.37 30.54 33.66 500.30library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:gdata':
##
## combine, first, last## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unioncombined4$thirds<-ntile(combined4$interviewtime, 3)
fast<-subset(combined4, thirds==3)
summary(fast$interviewtime)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 30.09 33.76 40.12 52.74 51.50 500.30med<-subset(combined4, thirds==2)
summary(med$interviewtime)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 19.76 22.02 24.37 24.56 26.83 30.09slow<-subset(combined4,thirds==1)
summary(slow$interviewtime)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.71 12.07 14.93 14.38 17.38 19.70summary(lm(SS ~ cond * bd, data=fast))##
## Call:
## lm(formula = SS ~ cond * bd, data = fast)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.8187 -0.4616 -0.1979 0.5218 0.7305
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.54439 0.06398 8.509 8.91e-16 ***
## condSS -0.01876 0.07971 -0.235 0.81410
## condLL -0.07315 0.07698 -0.950 0.34277
## bd -1.05796 0.33179 -3.189 0.00158 **
## condSS:bd 0.49173 0.41650 1.181 0.23870
## condLL:bd 0.94271 0.37731 2.499 0.01301 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4917 on 296 degrees of freedom
## Multiple R-squared: 0.05203, Adjusted R-squared: 0.03602
## F-statistic: 3.249 on 5 and 296 DF, p-value: 0.007149summary(lm(SS ~ cond * bd, data=med))##
## Call:
## lm(formula = SS ~ cond * bd, data = med)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.8282 -0.4575 -0.1840 0.4819 0.8459
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.41451 0.05388 7.693 2.14e-13 ***
## condSS 0.13417 0.06902 1.944 0.0528 .
## condLL 0.10560 0.07122 1.483 0.1392
## bd -1.00303 0.29608 -3.388 0.0008 ***
## condSS:bd -0.05978 0.36399 -0.164 0.8697
## condLL:bd 0.86259 0.37458 2.303 0.0220 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4703 on 297 degrees of freedom
## Multiple R-squared: 0.1326, Adjusted R-squared: 0.118
## F-statistic: 9.082 on 5 and 297 DF, p-value: 4.739e-08summary(lm(SS ~ cond * bd, data=slow))##
## Call:
## lm(formula = SS ~ cond * bd, data = slow)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.04074 -0.42283 -0.07357 0.51884 0.91628
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.52043 0.03804 13.681 < 2e-16 ***
## condSS 0.05536 0.06243 0.887 0.3759
## condLL -0.10059 0.07218 -1.394 0.1645
## bd -0.81628 0.17999 -4.535 8.36e-06 ***
## condSS:bd -0.32504 0.28319 -1.148 0.2520
## condLL:bd 0.74295 0.32764 2.268 0.0241 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4663 on 297 degrees of freedom
## Multiple R-squared: 0.1475, Adjusted R-squared: 0.1332
## F-statistic: 10.28 on 5 and 297 DF, p-value: 4.206e-09SScontrolM<-subset(med, cond!="LL")
summary(lm(SS~cond*bd, data=SScontrolM))##
## Call:
## lm(formula = SS ~ cond * bd, data = SScontrolM)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.8282 -0.4014 -0.1932 0.4307 0.8459
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.41451 0.05183 7.998 1.06e-13 ***
## condSS 0.13417 0.06638 2.021 0.044621 *
## bd -1.00303 0.28478 -3.522 0.000532 ***
## condSS:bd -0.05978 0.35010 -0.171 0.864592
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4523 on 197 degrees of freedom
## Multiple R-squared: 0.1962, Adjusted R-squared: 0.184
## F-statistic: 16.03 on 3 and 197 DF, p-value: 2.297e-09LLcontrolM<-subset(med, cond!="SS")
summary(lm(SS~cond*bd, data=LLcontrolM))##
## Call:
## lm(formula = SS ~ cond * bd, data = LLcontrolM)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.8282 -0.5006 -0.2772 0.4891 0.8459
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.41451 0.05526 7.502 2.79e-12 ***
## condLL 0.10560 0.07304 1.446 0.14997
## bd -1.00303 0.30362 -3.304 0.00115 **
## condLL:bd 0.86259 0.38413 2.246 0.02595 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4823 on 180 degrees of freedom
## Multiple R-squared: 0.08112, Adjusted R-squared: 0.0658
## F-statistic: 5.297 on 3 and 180 DF, p-value: 0.0016n1<-lm(SS~cond*bd, data=LLcontrolM)
library(visreg)
visreg(n1, "bd", by="cond", line=list(col=col), fill=list(col=col3), overlay=TRUE, partial=FALSE, xlab="Present value of LL", scale="response", ylab="P (choosing SS)")
SScontrolS<-subset(slow, cond!="LL")
summary(lm(SS~cond*bd, data=SScontrolS))##
## Call:
## lm(formula = SS ~ cond * bd, data = SScontrolS)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.04074 -0.42897 0.02014 0.46884 0.91628
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.52043 0.03732 13.946 < 2e-16 ***
## condSS 0.05536 0.06124 0.904 0.367
## bd -0.81628 0.17656 -4.623 6.19e-06 ***
## condSS:bd -0.32504 0.27780 -1.170 0.243
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4574 on 239 degrees of freedom
## Multiple R-squared: 0.1757, Adjusted R-squared: 0.1654
## F-statistic: 16.98 on 3 and 239 DF, p-value: 4.947e-10LLcontrolS<-subset(slow, cond!="SS")
summary(lm(SS~cond*bd, data=LLcontrolS))##
## Call:
## lm(formula = SS ~ cond * bd, data = LLcontrolS)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.0407 -0.4152 -0.2501 0.5470 0.9163
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.52043 0.03924 13.262 < 2e-16 ***
## condLL -0.10059 0.07447 -1.351 0.178
## bd -0.81628 0.18567 -4.396 1.75e-05 ***
## condLL:bd 0.74295 0.33799 2.198 0.029 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.481 on 210 degrees of freedom
## Multiple R-squared: 0.08892, Adjusted R-squared: 0.07591
## F-statistic: 6.832 on 3 and 210 DF, p-value: 0.0002051fast<-subset(combined2, interviewtime<= 17.39)
slow<-subset(combined2, interviewtime>33.73 & interviewtime<2000)
summary(glm(SS~bd*cond, data=fast, family=binomial))##
## Call:
## glm(formula = SS ~ bd * cond, family = binomial, data = fast)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.25786 -1.04619 0.00243 1.17360 1.95772
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.1737 0.1933 0.898 0.36908
## bd -3.5988 1.1397 -3.158 0.00159 **
## condSS 1.2807 0.6983 1.834 0.06665 .
## condLL -0.6914 0.3813 -1.813 0.06976 .
## bd:condSS -11.9786 6.0350 -1.985 0.04716 *
## bd:condLL 4.2548 1.8994 2.240 0.02509 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 316.06 on 227 degrees of freedom
## Residual deviance: 270.55 on 222 degrees of freedom
## AIC: 282.55
##
## Number of Fisher Scoring iterations: 7Note that we DO see marginal default effects here!
Plotting the 2 way interaction between SS condition and bd among fast responders, we see the same pattern as in the data overall:
SSconf<-subset(fast, cond!="LL")
SSconf<-droplevels(SSconf)
f1<-(glm(SS~cond*bd, data=SSconf,family="binomial"))
col<-c("red", "black")
col2<-c("indianred1" , "gray80")
col3<-adjustcolor(col2, alpha=.45)
visreg(f1, "bd", by="cond", line=list(col=col), fill=list(col=col3), overlay=TRUE, partial=FALSE, xlab="Present Value of LL", scale="response", ylab="P (choosing SS)")
And there was an interaction between LL condition and bd among fast responders so we can plot that too - the LL condition here only has 42 people however.
LLconf<-subset(fast, cond!="SS")
LLconf<-droplevels(LLconf)
f1<-(glm(SS~cond*bd, data=LLconf,family="binomial"))
col<-c("red", "black")
col2<-c("indianred1" , "gray80")
col3<-adjustcolor(col2, alpha=.45)
visreg(f1, "bd", by="cond", line=list(col=col), fill=list(col=col3), overlay=TRUE, partial=FALSE, xlab="Present Value of LL", scale="response", ylab="P (choosing SS)")
However, the default effects among fast responders are not robust to alternative definitions of “fast” - i.e. if we take only people who are a few seconds faster than the first quartile, we no longer see the effects:
fast<-subset(combined2, interviewtime<= 14.39)
summary(glm(SS~bd*cond, data=fast, family=binomial))##
## Call:
## glm(formula = SS ~ bd * cond, family = binomial, data = fast)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.8780 -1.0722 0.1185 1.0394 2.1299
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.3992 0.2494 1.600 0.10956
## bd -4.7818 1.7279 -2.767 0.00565 **
## condSS 1.0817 0.8116 1.333 0.18261
## condLL -1.0466 0.5791 -1.807 0.07072 .
## bd:condSS -8.5882 6.6177 -1.298 0.19437
## bd:condLL 5.9257 2.7627 2.145 0.03196 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 187.09 on 135 degrees of freedom
## Residual deviance: 154.38 on 130 degrees of freedom
## AIC: 166.38
##
## Number of Fisher Scoring iterations: 7Next let’s look at slow responders.
summary(glm(SS~bd*cond, data=slow, family=binomial))##
## Call:
## glm(formula = SS ~ bd * cond, family = binomial, data = slow)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.90784 -1.08575 -0.02704 1.18098 1.61243
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.5078 0.3681 1.379 0.168
## bd -6.0262 2.6319 -2.290 0.022 *
## condSS -0.5142 0.4368 -1.177 0.239
## condLL -0.5668 0.4199 -1.350 0.177
## bd:condSS 3.5554 3.0129 1.180 0.238
## bd:condLL 4.1117 2.8193 1.458 0.145
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 313.3 on 225 degrees of freedom
## Residual deviance: 297.6 on 220 degrees of freedom
## AIC: 309.6
##
## Number of Fisher Scoring iterations: 4No default effects or interactions there.
As another approach, we can also break down the significant 3 way interaction between condition, beta-delta, and completion time, by looking for 2 way interactions between beta-delta and completion times in each of the conditions individually. First, we see no 2-way interaction in the no default condition:
no<-subset(combined2, cond=="no")
summary(glm(SS~bd*interviewtime, data=no, family="binomial"))##
## Call:
## glm(formula = SS ~ bd * interviewtime, family = "binomial", data = no)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.4797 -0.9953 -0.6797 1.1360 2.2026
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.0748006 0.2024501 0.369 0.7118
## bd -3.9717067 1.5493198 -2.564 0.0104 *
## interviewtime -0.0005065 0.0067534 -0.075 0.9402
## bd:interviewtime -0.0429422 0.0579007 -0.742 0.4583
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 411.18 on 297 degrees of freedom
## Residual deviance: 365.83 on 294 degrees of freedom
## AIC: 373.83
##
## Number of Fisher Scoring iterations: 4But we do see a 2-way in the SS default condition
SS<-subset(combined2, cond=="SS")
summary(glm(SS~bd*interviewtime, data=SS, family="binomial"))##
## Call:
## glm(formula = SS ~ bd * interviewtime, family = "binomial", data = SS)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.4244 -1.0412 0.2888 1.0638 1.8046
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.742947 0.223659 3.322 0.000894 ***
## bd -11.258113 2.158409 -5.216 1.83e-07 ***
## interviewtime -0.013365 0.005185 -2.577 0.009952 **
## bd:interviewtime 0.177181 0.056210 3.152 0.001621 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 434.01 on 314 degrees of freedom
## Residual deviance: 364.55 on 311 degrees of freedom
## (82 observations deleted due to missingness)
## AIC: 372.55
##
## Number of Fisher Scoring iterations: 5We can break this down further by checking whether the effect of beta-delta on choice of SS depends on reaction time. It does indeed - beta-delta only seems to have a significant effect on choice when people choose relatively quickly - here, in the first quartile of reaction time. people in the 3rd quartile of reaction time don’t show this expected effect (it’s marginally significant).
fast<-subset(SS, interviewtime<= 19.02)
slow<-subset(SS, interviewtime>33.54)
summary(glm(SS~bd, data=fast, family="binomial"))##
## Call:
## glm(formula = SS ~ bd, family = "binomial", data = fast)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.6649 -0.9409 0.1139 0.8010 1.8712
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.7132 0.3365 2.119 0.034080 *
## bd -9.9466 2.7544 -3.611 0.000305 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 108.490 on 78 degrees of freedom
## Residual deviance: 76.948 on 77 degrees of freedom
## AIC: 80.948
##
## Number of Fisher Scoring iterations: 6summary(glm(SS~bd, data=slow, family="binomial"))##
## Call:
## glm(formula = SS ~ bd, family = "binomial", data = slow)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.7671 -1.0953 -0.8303 1.2441 1.4060
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.02094 0.23379 0.09 0.9286
## bd -2.52071 1.48288 -1.70 0.0892 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 109.50 on 78 degrees of freedom
## Residual deviance: 105.94 on 77 degrees of freedom
## AIC: 109.94
##
## Number of Fisher Scoring iterations: 4And in the LL condition? The is no sigificant interaction between beta-delta and completion time.
LL<-subset(combined2, cond=="LL")
summary(glm(SS~bd*interviewtime, data=LL, family="binomial"))##
## Call:
## glm(formula = SS ~ bd * interviewtime, family = "binomial", data = LL)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.445 -1.136 -0.976 1.221 1.487
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.148269 0.199410 -0.744 0.4572
## bd 1.422040 1.209515 1.176 0.2397
## interviewtime 0.001733 0.004784 0.362 0.7171
## bd:interviewtime -0.060402 0.035264 -1.713 0.0867 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 409.68 on 295 degrees of freedom
## Residual deviance: 404.13 on 292 degrees of freedom
## (88 observations deleted due to missingness)
## AIC: 412.13
##
## Number of Fisher Scoring iterations: 6We can also treat completion time as a DV:
summary(lm(interviewtime~cond*bd, data=combined2))##
## Call:
## lm(formula = interviewtime ~ cond * bd, data = combined2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -36.28 -14.61 -8.00 1.24 2243.10
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 25.0414 4.8134 5.202 2.43e-07 ***
## condSS 7.2103 6.6521 1.084 0.2787
## condLL 16.7555 6.7528 2.481 0.0133 *
## bd 0.9544 24.0867 0.040 0.9684
## condSS:bd 6.1261 32.8465 0.187 0.8521
## condLL:bd 11.5569 32.0873 0.360 0.7188
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 81.48 on 903 degrees of freedom
## (170 observations deleted due to missingness)
## Multiple R-squared: 0.007419, Adjusted R-squared: 0.001923
## F-statistic: 1.35 on 5 and 903 DF, p-value: 0.2411Less patient people are not faster in their completion time
summary(lm(interviewtime~bd, data=combined2))##
## Call:
## lm(formula = interviewtime ~ bd, data = combined2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -30.26 -15.75 -8.58 1.40 2252.59
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 32.948 2.713 12.146 <2e-16 ***
## bd 4.994 12.933 0.386 0.699
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 81.6 on 907 degrees of freedom
## (170 observations deleted due to missingness)
## Multiple R-squared: 0.0001644, Adjusted R-squared: -0.000938
## F-statistic: 0.1491 on 1 and 907 DF, p-value: 0.6995Reaction time does not correlate with attention check failure.
combined2$attn[combined2$reader == "reader" | combined2$reader == "Reader"|combined2$reader == "READER"|combined2$reader== " reader"|combined2$reader== "reader " | combined2$reader== "readers"]<-1
combined2$attn[combined2$reader != "reader"]<-0
table(combined2$attn)##
## 0 1
## 291 788cor.test(combined2$attn, combined2$interviewtime)##
## Pearson's product-moment correlation
##
## data: combined2$attn and combined2$interviewtime
## t = 1.427, df = 907, p-value = 0.1539
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.01774857 0.11200848
## sample estimates:
## cor
## 0.04732962And attention check failure doesn’t interact with default condition or bd.
summary(glm(SS~bd*cond*attn, data=combined2, family=binomial))##
## Call:
## glm(formula = SS ~ bd * cond * attn, family = binomial, data = combined2)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.4880 -1.0420 -0.5422 1.2268 2.1744
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.17267 0.29443 0.586 0.55757
## bd -7.92819 2.46984 -3.210 0.00133 **
## condSS 0.07361 0.36841 0.200 0.84162
## condLL -0.25019 0.35071 -0.713 0.47560
## attn -0.14415 0.33127 -0.435 0.66346
## bd:condSS 2.13205 2.94342 0.724 0.46885
## bd:condLL 7.09958 2.60234 2.728 0.00637 **
## bd:attn 3.64086 2.65709 1.370 0.17061
## condSS:attn 0.14689 0.41960 0.350 0.72628
## condLL:attn -0.03095 0.40153 -0.077 0.93855
## bd:condSS:attn -3.12908 3.24641 -0.964 0.33512
## bd:condLL:attn -3.82449 2.84714 -1.343 0.17918
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1494.9 on 1078 degrees of freedom
## Residual deviance: 1369.3 on 1067 degrees of freedom
## AIC: 1393.3
##
## Number of Fisher Scoring iterations: 5Is there a relationship between reaction time and beta delta among impatient people in the LL condition?
LL<-subset(LLcontrol, cond=="LL")
LLimp<-subset(LL, bd< -0.1)
cor.test(LLimp$bd, LLimp$interviewtime)##
## Pearson's product-moment correlation
##
## data: LLimp$bd and LLimp$interviewtime
## t = 0.28708, df = 61, p-value = 0.775
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2129708 0.2819316
## sample estimates:
## cor
## 0.036732488. Reactance data.
Next we can look at the reactance data. Beta-delta doesn’t seem to predict reactance in either the LL or the SS conditions.
debrief<-read.csv("debrief data from ls.csv", header=T, sep=",")
combined3<-merge(debrief, combined2, by="mturkID")
combined3<-combined3[!duplicated(combined3$mturkID),]
combined3$rep[combined3$Wave==4]<-1
combined3$rep[combined3$Wave!=4]<-0
react<-read.csv("reactance data.csv", header=T, sep=",")
react$serial.y<-react$serial
react<-merge(react, combined3, by="serial.y")
react$reactance<-(react$hong8+react$hong9+react$hong11+react$hong13)/4
react$reactance<-react$reactance-mean(react$reactance)
summary(lm(reactance~cond*bd, data=react))##
## Call:
## lm(formula = reactance ~ cond * bd, data = react)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.26155 -0.40261 -0.07246 0.38586 2.15111
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.012244 0.046259 -0.265 0.7914
## condSS 0.040178 0.063393 0.634 0.5265
## condLL 0.003027 0.065066 0.047 0.9629
## bd -0.325190 0.245544 -1.324 0.1859
## condSS:bd 0.500902 0.312513 1.603 0.1095
## condLL:bd 0.550672 0.328357 1.677 0.0941 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6356 on 600 degrees of freedom
## Multiple R-squared: 0.007243, Adjusted R-squared: -0.00103
## F-statistic: 0.8755 on 5 and 600 DF, p-value: 0.4971LL<-subset(react, cond=="LL")
summary(lm(reactance~bd, data=LL))##
## Call:
## lm(formula = reactance ~ bd, data = LL)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.13292 -0.36268 -0.07573 0.38909 1.92276
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.009217 0.044328 -0.208 0.836
## bd 0.225481 0.211199 1.068 0.287
##
## Residual standard error: 0.6157 on 192 degrees of freedom
## Multiple R-squared: 0.005902, Adjusted R-squared: 0.0007239
## F-statistic: 1.14 on 1 and 192 DF, p-value: 0.287SS<-subset(react, cond=="SS")
summary(lm(reactance~bd, data=SS))##
## Call:
## lm(formula = reactance ~ bd, data = SS)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.1544 -0.3836 -0.1052 0.3654 2.1328
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.02793 0.04248 0.658 0.512
## bd 0.17571 0.18946 0.927 0.355
##
## Residual standard error: 0.6229 on 213 degrees of freedom
## Multiple R-squared: 0.004022, Adjusted R-squared: -0.0006542
## F-statistic: 0.8601 on 1 and 213 DF, p-value: 0.3548And reactance only predicts choice in the SS condition
summary(glm(SS~reactance, data=LL, family="binomial"))##
## Call:
## glm(formula = SS ~ reactance, family = "binomial", data = LL)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.082 -1.035 -1.000 1.314 1.430
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.3553 0.1460 -2.434 0.0149 *
## reactance -0.1163 0.2385 -0.487 0.6260
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 262.95 on 193 degrees of freedom
## Residual deviance: 262.71 on 192 degrees of freedom
## AIC: 266.71
##
## Number of Fisher Scoring iterations: 4summary(glm(SS~reactance, data=SS, family="binomial"))##
## Call:
## glm(formula = SS ~ reactance, family = "binomial", data = SS)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.4354 -1.2218 0.9397 1.1337 1.6150
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.05979 0.13804 0.433 0.6649
## reactance -0.48497 0.22852 -2.122 0.0338 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 297.94 on 214 degrees of freedom
## Residual deviance: 293.25 on 213 degrees of freedom
## AIC: 297.25
##
## Number of Fisher Scoring iterations: 4Reactance does not correlate wtih familiarity with default studies.
react$defaultstudies.x<-as.numeric(react$defaultstudies.x)
cor.test(react$defaultstudies.x, react$reactance)##
## Pearson's product-moment correlation
##
## data: react$defaultstudies.x and react$reactance
## t = 0.10728, df = 604, p-value = 0.9146
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.07530774 0.08398293
## sample estimates:
## cor
## 0.004365283Does reactance predict or correlate with anything among patient people?
summary(react$bd)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -0.80880 -0.06133 0.08501 0.01732 0.13430 0.53790react$bd<-react$bd-mean(react$bd)
patient<-subset(react, bd>0)
summary(lm(reactance~cond, data=patient))##
## Call:
## lm(formula = reactance ~ cond, data = patient)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.12195 -0.49457 -0.08991 0.37805 1.87805
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.09619 0.05173 -1.860 0.0637 .
## condSS 0.12739 0.07535 1.691 0.0918 .
## condLL 0.09535 0.07691 1.240 0.2159
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6077 on 372 degrees of freedom
## Multiple R-squared: 0.008333, Adjusted R-squared: 0.003001
## F-statistic: 1.563 on 2 and 372 DF, p-value: 0.2109cor.test(patient$reactance, patient$SS)##
## Pearson's product-moment correlation
##
## data: patient$reactance and patient$SS
## t = -0.10718, df = 373, p-value = 0.9147
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.1067604 0.0957755
## sample estimates:
## cor
## -0.005549373cor.test(patient$reactance, patient$bd)##
## Pearson's product-moment correlation
##
## data: patient$reactance and patient$bd
## t = 1.1209, df = 373, p-value = 0.2631
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.04358638 0.15828272
## sample estimates:
## cor
## 0.057940429. Default channels.
We can also check whether any of the “default channels” are affected by default condition, beta-delta, or their interaction. First, direct implied endorsement:
SScontrol<-subset(react, cond!="LL")
SScontrol<-droplevels(SScontrol)
LLcontrol<-subset(react, cond!="SS")
LLcontrol<-droplevels(LLcontrol)
summary(lm(directIE~bd*cond, data=SScontrol))##
## Call:
## lm(formula = directIE ~ bd * cond, data = SScontrol)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.8643 -0.5211 -0.3856 0.4491 3.6452
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.43003 0.06287 22.744 <2e-16 ***
## bd -0.65064 0.33871 -1.921 0.0554 .
## condSS 0.10942 0.08690 1.259 0.2087
## bd:condSS 0.38516 0.43109 0.893 0.3721
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8767 on 408 degrees of freedom
## Multiple R-squared: 0.01656, Adjusted R-squared: 0.009329
## F-statistic: 2.29 on 3 and 408 DF, p-value: 0.07781summary(lm(directIE~bd*cond, data=LLcontrol))##
## Call:
## lm(formula = directIE ~ bd * cond, data = LLcontrol)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.8643 -0.6134 -0.3818 0.3808 3.6452
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.43003 0.06337 22.566 <2e-16 ***
## bd -0.65064 0.34138 -1.906 0.0574 .
## condLL 0.19860 0.08967 2.215 0.0274 *
## bd:condLL 0.52075 0.45651 1.141 0.2547
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8836 on 387 degrees of freedom
## Multiple R-squared: 0.0239, Adjusted R-squared: 0.01633
## F-statistic: 3.159 on 3 and 387 DF, p-value: 0.02472summary(aov(SS ~ directIE * cond, data=react))## Df Sum Sq Mean Sq F value Pr(>F)
## directIE 1 1.98 1.9802 8.148 0.00446 **
## cond 2 1.22 0.6087 2.505 0.08256 .
## directIE:cond 2 1.09 0.5452 2.243 0.10701
## Residuals 600 145.82 0.2430
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(aov(SS ~ indirectIE * cond, data=react))## Df Sum Sq Mean Sq F value Pr(>F)
## indirectIE 1 1.43 1.4306 5.824 0.0161 *
## cond 2 1.07 0.5333 2.171 0.1149
## indirectIE:cond 2 0.25 0.1232 0.502 0.6058
## Residuals 600 147.37 0.2456
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(aov(SS ~ ease * cond , data=react))## Df Sum Sq Mean Sq F value Pr(>F)
## ease 1 9.50 9.504 41.005 3.07e-10 ***
## cond 2 1.15 0.575 2.481 0.0845 .
## ease:cond 2 0.38 0.192 0.830 0.4367
## Residuals 600 139.07 0.232
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(aov(SS ~ refdep * cond , data=react))## Df Sum Sq Mean Sq F value Pr(>F)
## refdep 1 6.30 6.304 27.744 1.93e-07 ***
## cond 2 0.92 0.460 2.024 0.133
## refdep:cond 2 6.57 3.283 14.450 7.43e-07 ***
## Residuals 600 136.32 0.227
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1table(react$refdep)##
## 1 2 3 4 5
## 368 96 67 42 33lowRD<-subset(react, refdep==1)
hiRD<-subset(react, refdep>1)
summary(aov(SS ~ cond, data=lowRD))## Df Sum Sq Mean Sq F value Pr(>F)
## cond 2 0.11 0.05304 0.222 0.801
## Residuals 365 87.33 0.23925summary(aov(SS ~ cond, data=hiRD))## Df Sum Sq Mean Sq F value Pr(>F)
## cond 2 4.14 2.070 8.884 0.000191 ***
## Residuals 235 54.75 0.233
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(aov(SS ~ directIE * cond * bd, data=react))## Df Sum Sq Mean Sq F value Pr(>F)
## directIE 1 1.98 1.980 9.480 0.00217 **
## cond 2 1.22 0.609 2.914 0.05502 .
## bd 1 19.02 19.023 91.069 < 2e-16 ***
## directIE:cond 2 1.28 0.641 3.071 0.04713 *
## directIE:bd 1 1.56 1.560 7.469 0.00646 **
## cond:bd 2 0.59 0.293 1.404 0.24639
## directIE:cond:bd 2 0.39 0.194 0.927 0.39619
## Residuals 594 124.08 0.209
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(aov(SS ~ indirectIE * cond * bd, data=react))## Df Sum Sq Mean Sq F value Pr(>F)
## indirectIE 1 1.43 1.431 6.699 0.00988 **
## cond 2 1.07 0.533 2.497 0.08319 .
## bd 1 19.33 19.334 90.531 < 2e-16 ***
## indirectIE:cond 2 0.40 0.200 0.938 0.39193
## indirectIE:bd 1 0.29 0.292 1.367 0.24279
## cond:bd 2 0.69 0.346 1.622 0.19834
## indirectIE:cond:bd 2 0.04 0.021 0.100 0.90514
## Residuals 594 126.85 0.214
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(aov(SS ~ ease * cond * bd, data=react))## Df Sum Sq Mean Sq F value Pr(>F)
## ease 1 9.50 9.504 46.372 2.4e-11 ***
## cond 2 1.15 0.575 2.806 0.0613 .
## bd 1 15.95 15.949 77.816 < 2e-16 ***
## ease:cond 2 0.56 0.282 1.374 0.2538
## ease:bd 1 0.35 0.347 1.692 0.1938
## cond:bd 2 0.71 0.355 1.733 0.1777
## ease:cond:bd 2 0.14 0.070 0.340 0.7119
## Residuals 594 121.75 0.205
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(aov(SS ~ refdep * cond * bd, data=react))## Df Sum Sq Mean Sq F value Pr(>F)
## refdep 1 6.30 6.304 31.540 3e-08 ***
## cond 2 0.92 0.460 2.301 0.101093
## bd 1 17.26 17.257 86.342 < 2e-16 ***
## refdep:cond 2 3.68 1.840 9.207 0.000115 ***
## refdep:bd 1 2.16 2.163 10.822 0.001062 **
## cond:bd 2 0.49 0.247 1.234 0.291809
## refdep:cond:bd 2 0.58 0.289 1.445 0.236537
## Residuals 594 118.72 0.200
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(aov(SS ~ cond*bd, data=lowRD))## Df Sum Sq Mean Sq F value Pr(>F)
## cond 2 0.11 0.053 0.261 0.770
## bd 1 12.98 12.979 63.883 1.79e-14 ***
## cond:bd 2 0.80 0.400 1.967 0.141
## Residuals 362 73.55 0.203
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(aov(SS ~ cond*bd, data=hiRD))## Df Sum Sq Mean Sq F value Pr(>F)
## cond 2 4.14 2.070 9.613 9.75e-05 ***
## bd 1 4.33 4.335 20.131 1.14e-05 ***
## cond:bd 2 0.46 0.232 1.077 0.342
## Residuals 232 49.96 0.215
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1veryhiRD<-subset(react, refdep>2)
summary(aov(SS ~ cond*bd, data=veryhiRD))## Df Sum Sq Mean Sq F value Pr(>F)
## cond 2 7.658 3.829 22.601 3.35e-09 ***
## bd 1 0.978 0.978 5.773 0.0176 *
## cond:bd 2 0.718 0.359 2.120 0.1240
## Residuals 136 23.040 0.169
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Then indirect IE:
summary(lm(indirectIE~bd*cond, data=SScontrol))##
## Call:
## lm(formula = indirectIE ~ bd * cond, data = SScontrol)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.9902 -0.6830 -0.5273 0.3859 3.3303
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.57849 0.07352 21.469 <2e-16 ***
## bd -0.70967 0.39608 -1.792 0.0739 .
## condSS 0.12369 0.10161 1.217 0.2242
## bd:condSS 0.44050 0.50411 0.874 0.3827
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.025 on 408 degrees of freedom
## Multiple R-squared: 0.01442, Adjusted R-squared: 0.007175
## F-statistic: 1.99 on 3 and 408 DF, p-value: 0.1149summary(lm(indirectIE~bd*cond, data=LLcontrol))##
## Call:
## lm(formula = indirectIE ~ bd * cond, data = LLcontrol)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.9902 -0.6181 -0.5063 0.3993 3.3670
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.57849 0.06427 24.560 <2e-16 ***
## bd -0.70967 0.34623 -2.050 0.0411 *
## condLL 0.04020 0.09094 0.442 0.6587
## bd:condLL 0.78401 0.46300 1.693 0.0912 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8962 on 387 degrees of freedom
## Multiple R-squared: 0.01182, Adjusted R-squared: 0.004161
## F-statistic: 1.543 on 3 and 387 DF, p-value: 0.2029Only effects of beta-delta so far. Ease?
summary(lm(ease~bd*cond, data=SScontrol))##
## Call:
## lm(formula = ease ~ bd * cond, data = SScontrol)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.1339 -1.0656 -0.3200 0.9715 3.0324
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.22091 0.09444 23.516 < 2e-16 ***
## bd -1.32174 0.50876 -2.598 0.00972 **
## condSS -0.10806 0.13052 -0.828 0.40821
## bd:condSS 0.08579 0.64752 0.132 0.89466
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.317 on 408 degrees of freedom
## Multiple R-squared: 0.0388, Adjusted R-squared: 0.03173
## F-statistic: 5.49 on 3 and 408 DF, p-value: 0.001049summary(lm(ease~bd*cond, data=LLcontrol))##
## Call:
## lm(formula = ease ~ bd * cond, data = LLcontrol)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.9877 -1.0664 -0.2654 0.9185 3.3121
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.22091 0.09438 23.532 < 2e-16 ***
## bd -1.32174 0.50843 -2.600 0.00969 **
## condLL -0.17060 0.13355 -1.277 0.20221
## bd:condLL 0.61714 0.67990 0.908 0.36460
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.316 on 387 degrees of freedom
## Multiple R-squared: 0.02598, Adjusted R-squared: 0.01843
## F-statistic: 3.441 on 3 and 387 DF, p-value: 0.01694Still only effects of beta-delta. Reference dependence measure mentions “the option that I was assigned,” so it doesn’t make sense to look at that measure in the no default control condition.
summary(lm(refdep~bd, data=SS)) ##
## Call:
## lm(formula = refdep ~ bd, data = SS)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.1082 -0.7803 -0.6839 0.6242 3.3049
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.93397 0.08663 22.325 < 2e-16 ***
## bd -1.81004 0.38637 -4.685 4.99e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.27 on 213 degrees of freedom
## Multiple R-squared: 0.09341, Adjusted R-squared: 0.08916
## F-statistic: 21.95 on 1 and 213 DF, p-value: 4.994e-06summary(lm(refdep~bd, data=LL))##
## Call:
## lm(formula = refdep ~ bd, data = LL)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.0853 -0.8999 -0.7846 0.2398 3.1521
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.86471 0.09064 20.573 <2e-16 ***
## bd 0.41307 0.43185 0.957 0.34
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.259 on 192 degrees of freedom
## Multiple R-squared: 0.004743, Adjusted R-squared: -0.0004409
## F-statistic: 0.9149 on 1 and 192 DF, p-value: 0.3410. Wave / Replication.
Let’s check if wave # interacts with anything:
combined2$rep[combined2$Wave==4]<-1
combined2$rep[combined2$Wave!=4]<-0
SScontrol<-subset(combined2, cond!="LL")
SScontrol<-droplevels(SScontrol)
LLcontrol<-subset(combined2, cond!="SS")
LLcontrol<-droplevels(LLcontrol)
summary(glm(SS ~ cond * bd*rep, data=combined2, family="binomial"))##
## Call:
## glm(formula = SS ~ cond * bd * rep, family = "binomial", data = combined2)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.6315 -1.0574 -0.5146 1.1613 2.0404
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.11165 0.22557 0.495 0.62062
## condSS 0.24884 0.28057 0.887 0.37511
## condLL -0.12655 0.26904 -0.470 0.63808
## bd -3.21585 1.26537 -2.541 0.01104 *
## rep -0.05319 0.28270 -0.188 0.85077
## condSS:bd -2.57878 1.84555 -1.397 0.16233
## condLL:bd 4.03081 1.44031 2.799 0.00513 **
## condSS:rep -0.15443 0.36246 -0.426 0.67005
## condLL:rep -0.25965 0.35300 -0.736 0.46200
## bd:rep -2.95724 1.77857 -1.663 0.09637 .
## condSS:bd:rep 3.60552 2.45547 1.468 0.14201
## condLL:bd:rep -0.90584 2.07897 -0.436 0.66304
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1494.9 on 1078 degrees of freedom
## Residual deviance: 1351.7 on 1067 degrees of freedom
## AIC: 1375.7
##
## Number of Fisher Scoring iterations: 4So it does in the LL/no default conditions. In the “replication” wave, where we ran all 3 conditions at once, we don’t see a significant interaction between BD and condition. We do in the original wave. I think this should decrease our confidence in the results, and encourage a large scale replicaiton.
rep<-subset(combined2, Wave==4)
summary(glm(SS~bd*cond, data=rep, family="binomial"))##
## Call:
## glm(formula = SS ~ bd * cond, family = "binomial", data = rep)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.3979 -0.9583 -0.7840 1.1290 2.0404
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.05847 0.17040 0.343 0.7315
## bd -6.17309 1.24985 -4.939 7.85e-07 ***
## condSS 0.09441 0.22948 0.411 0.6808
## condLL -0.38621 0.22853 -1.690 0.0910 .
## bd:condSS 1.02674 1.61965 0.634 0.5261
## bd:condLL 3.12497 1.49921 2.084 0.0371 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 848.34 on 614 degrees of freedom
## Residual deviance: 749.14 on 609 degrees of freedom
## AIC: 761.14
##
## Number of Fisher Scoring iterations: 4not<-subset(combined2, Wave!=4)
summary(glm(SS~bd*cond, data=not, family="binomial"))##
## Call:
## glm(formula = SS ~ bd * cond, family = "binomial", data = not)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.6315 -1.1449 0.4483 1.1661 1.8927
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.1117 0.2256 0.495 0.62062
## bd -3.2159 1.2654 -2.541 0.01104 *
## condSS 0.2488 0.2806 0.887 0.37511
## condLL -0.1266 0.2690 -0.470 0.63808
## bd:condSS -2.5788 1.8456 -1.397 0.16233
## bd:condLL 4.0308 1.4403 2.799 0.00513 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 642.38 on 463 degrees of freedom
## Residual deviance: 602.61 on 458 degrees of freedom
## AIC: 614.61
##
## Number of Fisher Scoring iterations: 4#proportions choosing SS in the original and replication waves:
prop.test(table(rep$cond, rep$SS))##
## 3-sample test for equality of proportions without continuity
## correction
##
## data: table(rep$cond, rep$SS)
## X-squared = 4.8948, df = 2, p-value = 0.08652
## alternative hypothesis: two.sided
## sample estimates:
## prop 1 prop 2 prop 3
## 0.5560976 0.4837209 0.5897436prop.test(table(not$cond, not$SS))##
## 3-sample test for equality of proportions without continuity
## correction
##
## data: table(not$cond, not$SS)
## X-squared = 2.3655, df = 2, p-value = 0.3064
## alternative hypothesis: two.sided
## sample estimates:
## prop 1 prop 2 prop 3
## 0.5053763 0.4340659 0.507936511. Familiarity with default studies.
Check if familiarity with this kind of study varies with wave. It does - people are apparently more familiar with default studies in the original than in the replication.
table(combined3$defaultstudies)##
## 1 2 3 4 5
## 450 271 307 36 11mean(combined3$defaultstudies, na.rm=TRUE)## [1] 1.964651combined3$defaultstudies<-combined3$defaultstudies - 1.964651
summary(combined3$defaultstudies)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## -0.96470 -0.96470 0.03535 0.00000 1.03500 3.03500 4summary(glm(defaultstudies~rep, data=combined3))##
## Call:
## glm(formula = defaultstudies ~ rep, data = combined3)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.03905 -0.90879 -0.03905 0.96095 3.09121
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.07439 0.04483 1.659 0.0973 .
## rep -0.13025 0.05932 -2.196 0.0283 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.9265514)
##
## Null deviance: 998.66 on 1074 degrees of freedom
## Residual deviance: 994.19 on 1073 degrees of freedom
## (4 observations deleted due to missingness)
## AIC: 2972.7
##
## Number of Fisher Scoring iterations: 2rep<-subset(combined3, rep==1)
not<-subset(combined3, rep!=1)
t.test(rep$defaultstudies, not$defaultstudies)##
## Welch Two Sample t-test
##
## data: rep$defaultstudies and not$defaultstudies
## t = -2.1874, df = 976.56, p-value = 0.02895
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.24710565 -0.01339588
## sample estimates:
## mean of x mean of y
## -0.05585621 0.07439455And we can use familiarity with default studies (mean-centered) as a covariate, excluding outliers based on beta-delta (+/- 4 SDs from the mean). Note that bd is mean centered here too:
#no default effects overall, but we do see several 2 way interactions and a 3 way interaction
summary(glm(SS~cond*bd*defaultstudies, data=combined3, family=binomial))##
## Call:
## glm(formula = SS ~ cond * bd * defaultstudies, family = binomial,
## data = combined3)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.5888 -1.0517 -0.5589 1.1964 2.5763
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.11949 0.14345 0.833 0.40486
## condSS 0.12875 0.18267 0.705 0.48093
## condLL -0.31206 0.17719 -1.761 0.07821 .
## bd -5.44512 0.98172 -5.547 2.91e-08 ***
## defaultstudies 0.43399 0.16167 2.684 0.00726 **
## condSS:bd 0.03875 1.28216 0.030 0.97589
## condLL:bd 4.50850 1.10234 4.090 4.31e-05 ***
## condSS:defaultstudies -0.32155 0.19697 -1.632 0.10258
## condLL:defaultstudies -0.57438 0.19491 -2.947 0.00321 **
## bd:defaultstudies -1.69239 1.08746 -1.556 0.11964
## condSS:bd:defaultstudies 1.40874 1.40731 1.001 0.31682
## condLL:bd:defaultstudies 2.44884 1.22439 2.000 0.04550 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1489.5 on 1074 degrees of freedom
## Residual deviance: 1354.8 on 1063 degrees of freedom
## (4 observations deleted due to missingness)
## AIC: 1378.8
##
## Number of Fisher Scoring iterations: 5#breaking down the 3 way interaction by separating the sample by familiarity (familiar are those who say they've seen at least "something like this study", unfamiliar are people who report below that point. That's the midpoint of the scale - 3 before it was mean-centered.)
table(combined3$defaultstudies)##
## -0.964651 0.0353490000000001 1.035349
## 450 271 307
## 2.035349 3.035349
## 36 11familiar<-subset(combined3, defaultstudies>=1.035)
not<-subset(combined3, defaultstudies<1.035)
#among familiar people, there's a main effect of LL condition, not of SS, plus a main effect of bd and a 2 way interaction between bd and LL condition
summary(glm(SS~cond*bd, data=familiar, family=binomial))##
## Call:
## glm(formula = SS ~ cond * bd, family = binomial, data = familiar)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.8078 -1.0426 0.1997 1.1597 2.6434
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.7203 0.2998 2.403 0.016268 *
## condSS -0.2078 0.3640 -0.571 0.568139
## condLL -1.0075 0.3508 -2.872 0.004076 **
## bd -7.8195 2.1168 -3.694 0.000221 ***
## condSS:bd 1.2327 2.6759 0.461 0.645030
## condLL:bd 7.2295 2.3047 3.137 0.001708 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 489.83 on 353 degrees of freedom
## Residual deviance: 427.24 on 348 degrees of freedom
## AIC: 439.24
##
## Number of Fisher Scoring iterations: 5#plotting that 2 way interaction - LL default makes people less likely to choose SS, but only among relatively impatient people
LLfam<-subset(familiar, cond!="SS")
f6<-glm(SS~cond*bd, data=LLfam, family=binomial)
col<-c("black", "blue")
col2<-c("gray80", "cornflowerblue")
col3<-adjustcolor(col2, alpha=.7)
visreg(f6, "bd", by="cond", line=list(col=col), fill=list(col=col3), overlay=TRUE, partial=FALSE, scale="response", xlab="Present Value of LL", ylab="Percent Choosing SS")
And among people unfamiliar with default studies, there are no main default effects but there is one interaction, in the same pattern:
summary(glm(SS~cond*bd, data=not, family=binomial))##
## Call:
## glm(formula = SS ~ cond * bd, family = binomial, data = not)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.3685 -1.0545 -0.8169 1.2246 1.7275
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.160095 0.157065 -1.019 0.3081
## condSS 0.285898 0.207945 1.375 0.1692
## condLL 0.008997 0.201230 0.045 0.9643
## bd -4.147045 1.034004 -4.011 6.05e-05 ***
## condSS:bd -0.791866 1.409927 -0.562 0.5744
## condLL:bd 3.045944 1.189602 2.560 0.0105 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 996.45 on 720 degrees of freedom
## Residual deviance: 928.88 on 715 degrees of freedom
## AIC: 940.88
##
## Number of Fisher Scoring iterations: 4#plotting the pattern:
LLnot<-subset(not, cond!="SS")
f7<-glm(SS~cond*bd, data=LLnot, family=binomial)
col<-c("black", "blue")
col2<-c("gray80", "cornflowerblue")
col3<-adjustcolor(col2, alpha=.7)
visreg(f7, "bd", by="cond", line=list(col=col), fill=list(col=col3), overlay=TRUE, partial=FALSE, scale="response", xlab="Present Value of LL", ylab="Percent Choosing SS")
Finally, we can also just control for default studies as a covariate, without interacting it with the other factors. Here we see no default effects overall, but a similar interaction with LL.
summary(glm(SS~bd*cond + defaultstudies, data=combined3, family="binomial"))##
## Call:
## glm(formula = SS ~ bd * cond + defaultstudies, family = "binomial",
## data = combined3)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.5500 -1.0536 -0.5938 1.2233 2.2920
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.07048 0.13544 0.520 0.603
## bd -5.02482 0.91920 -5.467 4.59e-08 ***
## condSS 0.17838 0.17637 1.011 0.312
## condLL -0.26712 0.17032 -1.568 0.117
## defaultstudies 0.06387 0.06687 0.955 0.339
## bd:condSS -0.37989 1.23329 -0.308 0.758
## bd:condLL 4.10931 1.04324 3.939 8.18e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1489.5 on 1074 degrees of freedom
## Residual deviance: 1366.5 on 1068 degrees of freedom
## (4 observations deleted due to missingness)
## AIC: 1380.5
##
## Number of Fisher Scoring iterations: 4LLcontrol<-subset(combined3, cond!="SS")
f8<-glm(SS~cond*bd, data=LLcontrol, family=binomial)
col<-c("black", "blue")
col2<-c("gray80", "cornflowerblue")
col3<-adjustcolor(col2, alpha=.7)
visreg(f7, "bd", by="cond", line=list(col=col), fill=list(col=col3), overlay=TRUE, partial=FALSE, scale="response", xlab="Present Value of LL", ylab="Percent Choosing SS")
What does familiarity correlate with?
cor.test(combined3$defaultstudies, combined3$interviewtime)##
## Pearson's product-moment correlation
##
## data: combined3$defaultstudies and combined3$interviewtime
## t = -1.3369, df = 903, p-value = 0.1816
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.10929522 0.02078278
## sample estimates:
## cor
## -0.04444459cor.test(combined3$defaultstudies, combined3$bd)##
## Pearson's product-moment correlation
##
## data: combined3$defaultstudies and combined3$bd
## t = -1.1884, df = 1073, p-value = 0.2349
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.09583971 0.02358470
## sample estimates:
## cor
## -0.03625695SS<-subset(combined3, cond=="SS")
LL<-subset(combined3, cond=="LL")
cor.test(SS$defaultstudies, SS$interviewtime)##
## Pearson's product-moment correlation
##
## data: SS$defaultstudies and SS$interviewtime
## t = -1.5737, df = 313, p-value = 0.1166
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.19718021 0.02212162
## sample estimates:
## cor
## -0.08860292cor.test(SS$defaultstudies, SS$bd)##
## Pearson's product-moment correlation
##
## data: SS$defaultstudies and SS$bd
## t = -1.2776, df = 395, p-value = 0.2022
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.16155031 0.03449129
## sample estimates:
## cor
## -0.06414837cor.test(LL$defaultstudies, LL$interviewtime)##
## Pearson's product-moment correlation
##
## data: LL$defaultstudies and LL$interviewtime
## t = -0.74253, df = 293, p-value = 0.4584
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.15676023 0.07121212
## sample estimates:
## cor
## -0.04333818cor.test(LL$defaultstudies, LL$bd)##
## Pearson's product-moment correlation
##
## data: LL$defaultstudies and LL$bd
## t = -1.3669, df = 381, p-value = 0.1725
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.16888275 0.03056215
## sample estimates:
## cor
## -0.0698583812. Recoding the condition variable.
By default, GLM displays the effects of different levels of a factor relative to the level with the earliest letter in the alphabet. The factor levels are “SS” “LL” and “no.” Throughout this analysis we have re-ordered the factor levels so that the effects of SS and LL default conditions are shown relative to the no default condition.
Similarly, if we re-code the factor levels to be numbers instead of letters, GLM will show the effects of the factor levels relative to the lowest number. Since we’re interested in the effects of the SS and LL defaults relative to no default, we would want to code the no default condition as the lowest number. Doing so gives the same results as using letters.
summary(glm(SS~cond*bd, data=combined3, family="binomial"))##
## Call:
## glm(formula = SS ~ cond * bd, family = "binomial", data = combined3)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.5539 -1.0494 -0.6123 1.2303 2.3117
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.05648 0.13389 0.422 0.673172
## condSS 0.19354 0.17516 1.105 0.269194
## condLL -0.25871 0.16901 -1.531 0.125827
## bd -4.96633 0.90701 -5.476 4.36e-08 ***
## condSS:bd -0.45480 1.22373 -0.372 0.710156
## condLL:bd 3.98993 1.03030 3.873 0.000108 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1494.9 on 1078 degrees of freedom
## Residual deviance: 1372.2 on 1073 degrees of freedom
## AIC: 1384.2
##
## Number of Fisher Scoring iterations: 4combined3$cond2[combined3$cond=="no"]<-0
combined3$cond2[combined3$cond=="SS"]<-1
combined3$cond2[combined3$cond=="LL"]<-2
combined3$cond2<-as.factor(combined3$cond2)
summary(glm(SS~cond2*bd, data=combined3, family="binomial"))##
## Call:
## glm(formula = SS ~ cond2 * bd, family = "binomial", data = combined3)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.5539 -1.0494 -0.6123 1.2303 2.3117
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.05648 0.13389 0.422 0.673172
## cond21 0.19354 0.17516 1.105 0.269194
## cond22 -0.25871 0.16901 -1.531 0.125827
## bd -4.96633 0.90701 -5.476 4.36e-08 ***
## cond21:bd -0.45480 1.22373 -0.372 0.710156
## cond22:bd 3.98993 1.03030 3.873 0.000108 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1494.9 on 1078 degrees of freedom
## Residual deviance: 1372.2 on 1073 degrees of freedom
## AIC: 1384.2
##
## Number of Fisher Scoring iterations: 413. Test-retest measure.
Next we can look at the “test-retest reliability” measure - i.e. the difference in beta-delta scores between the original and the follow up measures. This measure doesn’t interact with condition
deep<-read.csv("deep_time8recontact.csv", header=T, sep=",")
ls<-read.csv("LS completes_july29recontacts.csv", header=T, sep=",")
r<-merge(deep, ls, by="serial")
r$mturkID<-r$"s643213.q8245.WorkerID"
r<-merge(r, combined2, by="mturkID")
r$bd1<-r$beta.y*((1/(1+r$delta.y))^(2/52))*1.5
r$bd2<-r$beta.x*((1/(1+r$delta.x))^(2/52))*1.5
r$diff<-abs(r$bd1 - r$bd2)
r$diffcen<-r$diff - mean(r$diff)
summary(glm(SS~diffcen*cond, data=r, family="binomial"))##
## Call:
## glm(formula = SS ~ diffcen * cond, family = "binomial", data = r)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.309 -1.100 -1.034 1.237 1.453
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.25458 0.14879 -1.711 0.0871 .
## diffcen -0.64830 0.76992 -0.842 0.3998
## condSS 0.34379 0.20012 1.718 0.0858 .
## condLL 0.03062 0.19901 0.154 0.8777
## diffcen:condSS 0.35380 1.03411 0.342 0.7323
## diffcen:condLL 1.08797 1.01996 1.067 0.2861
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 900.37 on 650 degrees of freedom
## Residual deviance: 895.51 on 645 degrees of freedom
## AIC: 907.51
##
## Number of Fisher Scoring iterations: 4However, there is a 3 way interaction between the original beta-delta measure, condition, and the test-retest measure.
summary(glm(SS~diffcen*cond*bd1, data=r, family="binomial"))##
## Call:
## glm(formula = SS ~ diffcen * cond * bd1, family = "binomial",
## data = r)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.9453 -0.9973 -0.5602 1.1417 2.7529
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.25066 0.21475 1.167 0.243111
## diffcen -4.73906 1.33751 -3.543 0.000395 ***
## condSS 0.09053 0.27833 0.325 0.744984
## condLL -0.45459 0.25550 -1.779 0.075208 .
## bd1 -8.79052 1.82281 -4.822 1.42e-06 ***
## diffcen:condSS 1.67915 1.68895 0.994 0.320127
## diffcen:condLL 3.85669 1.56795 2.460 0.013905 *
## diffcen:bd1 7.02432 4.63621 1.515 0.129747
## condSS:bd1 1.55049 2.30199 0.674 0.500601
## condLL:bd1 6.37274 1.99166 3.200 0.001376 **
## diffcen:condSS:bd1 -5.35078 6.11850 -0.875 0.381833
## diffcen:condLL:bd1 -9.74433 5.30036 -1.838 0.065999 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 900.37 on 650 degrees of freedom
## Residual deviance: 783.37 on 639 degrees of freedom
## AIC: 807.37
##
## Number of Fisher Scoring iterations: 5LLcontrol<-subset(r, cond!="SS")
LLcontrol<-droplevels(LLcontrol)
summary(glm(SS~diffcen*cond*bd1, data=LLcontrol, family="binomial")) #this is where the three way interaction shows up##
## Call:
## glm(formula = SS ~ diffcen * cond * bd1, family = "binomial",
## data = LLcontrol)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.9034 -0.9994 -0.7322 1.1958 2.7529
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.2507 0.2147 1.167 0.243111
## diffcen -4.7391 1.3375 -3.543 0.000395 ***
## condLL -0.4546 0.2555 -1.779 0.075208 .
## bd1 -8.7905 1.8228 -4.822 1.42e-06 ***
## diffcen:condLL 3.8567 1.5680 2.460 0.013905 *
## diffcen:bd1 7.0243 4.6362 1.515 0.129747
## condLL:bd1 6.3727 1.9917 3.200 0.001376 **
## diffcen:condLL:bd1 -9.7443 5.3004 -1.838 0.065999 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 586.76 on 426 degrees of freedom
## Residual deviance: 526.88 on 419 degrees of freedom
## AIC: 542.88
##
## Number of Fisher Scoring iterations: 5We can break down the interaction by looking at how the beta-delta X condition interaction changes as a function of the test-retest measure. We can start with just a basic median split. It appears that preferences (beta-delta) only interact with condition when people’s preferences are relatively stable. Also, default condition only seems to have an effect on choice when preferences are stable.
LLcontrol$diffcen<-LLcontrol$diffcen-mean(LLcontrol$diffcen)
summary(LLcontrol$diffcen)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -0.921100 -0.070220 0.001368 0.000000 0.070400 0.761600stable<-subset(LLcontrol, diffcen<0.001368)
notstable<-subset(LLcontrol, diffcen>0.001368)
summary(glm(SS~bd1*cond, data=stable, family="binomial"))##
## Call:
## glm(formula = SS ~ bd1 * cond, family = "binomial", data = stable)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.6931 -0.9988 -0.7644 1.2742 3.0910
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.5849 0.3322 1.761 0.078274 .
## bd1 -10.0092 2.7106 -3.693 0.000222 ***
## condLL -0.8363 0.3966 -2.109 0.034967 *
## bd1:condLL 8.4555 2.9466 2.870 0.004111 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 290.58 on 213 degrees of freedom
## Residual deviance: 258.69 on 210 degrees of freedom
## AIC: 266.69
##
## Number of Fisher Scoring iterations: 5summary(glm(SS~bd1*cond, data=notstable, family="binomial"))##
## Call:
## glm(formula = SS ~ bd1 * cond, family = "binomial", data = notstable)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.7195 -1.0162 -0.9193 1.1933 1.8889
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.10806 0.23479 -0.460 0.645
## bd1 -3.18979 1.47853 -2.157 0.031 *
## condLL -0.09385 0.29617 -0.317 0.751
## bd1:condLL 0.28817 1.79152 0.161 0.872
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 294.71 on 212 degrees of freedom
## Residual deviance: 279.71 on 209 degrees of freedom
## AIC: 287.71
##
## Number of Fisher Scoring iterations: 4We can also use diff and bd1 as predictors - the more stable preferences are, the less likely people are to choose SS:
summary(glm(SS~diff+bd1, data=r, family="binomial"))##
## Call:
## glm(formula = SS ~ diff + bd1, family = "binomial", data = r)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.7732 -0.9941 -0.6017 1.1662 2.2597
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 3.2369 0.8113 3.990 6.62e-05 ***
## diff -2.1720 0.5386 -4.032 5.52e-05 ***
## bd1 -4.9945 0.6169 -8.096 5.66e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 900.37 on 650 degrees of freedom
## Residual deviance: 806.31 on 648 degrees of freedom
## AIC: 812.31
##
## Number of Fisher Scoring iterations: 4And we can check if using the mean of the two DEEP measures (rather than their difference) provides any new insights. The mean does interact with the LL condition, in the same way as the first DEEP measure (i.e. in the counter-intuitive way).
r$mean<-(r$bd1+r$bd2)/2
summary(glm(SS~mean*cond, data=r, family="binomial"))##
## Call:
## glm(formula = SS ~ mean * cond, family = "binomial", data = r)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.8730 -1.0008 -0.5357 1.1378 1.9556
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 5.9964 1.2601 4.759 1.95e-06 ***
## mean -7.9756 1.5811 -5.044 4.55e-07 ***
## condSS -0.5644 1.6150 -0.349 0.72674
## condLL -4.3135 1.4035 -3.073 0.00212 **
## mean:condSS 1.0323 2.0288 0.509 0.61088
## mean:condLL 5.4818 1.7686 3.100 0.00194 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 900.37 on 650 degrees of freedom
## Residual deviance: 788.59 on 645 degrees of freedom
## AIC: 800.59
##
## Number of Fisher Scoring iterations: 5LLcontrol<-subset(r, cond!="SS")
LLcontrol<-droplevels(LLcontrol)
f5<-(glm(SS~mean*cond, data=LLcontrol,family="binomial"))
col<-c("red", "black")
col2<-c("indianred1" , "gray80")
col3<-adjustcolor(col2, alpha=.45)
visreg(f5, "mean", by="cond", line=list(col=col), fill=list(col=col3), overlay=TRUE, partial=FALSE, xlab="Present value of LL", scale="response", ylab="P (choosing SS)")