Set up
# Load libraries
library(dplyr)
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
library(afex)
## Loading required package: lme4
## Loading required package: Matrix
## ************
## Welcome to afex. For support visit: http://afex.singmann.science/
## - Functions for ANOVAs: aov_car(), aov_ez(), and aov_4()
## - Methods for calculating p-values with mixed(): 'S', 'KR', 'LRT', and 'PB'
## - 'afex_aov' and 'mixed' objects can be passed to emmeans() for follow-up tests
## - Get and set global package options with: afex_options()
## - Set sum-to-zero contrasts globally: set_sum_contrasts()
## - For example analyses see: browseVignettes("afex")
## ************
##
## Attaching package: 'afex'
## The following object is masked from 'package:lme4':
##
## lmer
library(emmeans)
library(readr)
library(ggplot2)
# Read in data -----------
dat = read.csv("data/intent-ability-whitestim-b-w-a-models-clean.csv")
dat$race_cond = as.factor(dat$race_cond)
options(scipen=999)
afex::set_sum_contrasts()
## setting contr.sum globally: options(contrasts=c('contr.sum', 'contr.poly'))
contrasts(dat$race_cond)
## [,1] [,2]
## asian 1 0
## black 0 1
## white -1 -1
Intent Model
# Linear
mod1_intent = mixed(intent ~ sd_level*race_cond + (sd_level*race_cond ||ResponseId) +
(sd_level*race_cond ||base),
data = dat, expand_re = TRUE)
## boundary (singular) fit: see help('isSingular')
summary(mod1_intent)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: intent ~ sd_level * race_cond + (1 + re1.sd_level + re1.race_cond1 +
## re1.race_cond2 + re1.sd_level_by_race_cond1 + re1.sd_level_by_race_cond2 ||
## ResponseId) + (1 + re2.sd_level + re2.race_cond1 + re2.race_cond2 +
## re2.sd_level_by_race_cond1 + re2.sd_level_by_race_cond2 || base)
## Data: data
##
## REML criterion at convergence: 39521.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -5.2071 -0.5983 0.0438 0.6100 5.7801
##
## Random effects:
## Groups Name Variance Std.Dev.
## ResponseId (Intercept) 0.3887682244208 0.62351281
## ResponseId.1 re1.sd_level 0.0061704260930 0.07855206
## ResponseId.2 re1.race_cond1 0.0000000004637 0.00002153
## ResponseId.3 re1.race_cond2 0.0051687415018 0.07189396
## ResponseId.4 re1.sd_level_by_race_cond1 0.0000000000000 0.00000000
## ResponseId.5 re1.sd_level_by_race_cond2 0.0001972749689 0.01404546
## base (Intercept) 0.0299473193298 0.17305294
## base.1 re2.sd_level 0.0006171268274 0.02484204
## base.2 re2.race_cond1 0.0000000321817 0.00017939
## base.3 re2.race_cond2 0.0000000030443 0.00005518
## base.4 re2.sd_level_by_race_cond1 0.0000000001271 0.00001128
## base.5 re2.sd_level_by_race_cond2 0.0000531195695 0.00728832
## Residual 1.0051869910684 1.00259014
## Number of obs: 13425, groups: ResponseId, 179; base, 25
##
## Fixed effects:
## Estimate Std. Error df
## (Intercept) 3.6318050812348 0.0586981713633 107.7439508105619
## sd_level -0.2324479371261 0.0078429588067 81.8131854128698
## race_cond1 -0.0304655541434 0.0122372308452 11992.0155735671979
## race_cond2 -0.0356052143096 0.0133650402276 284.6417380717882
## sd_level:race_cond1 -0.0000000000373 0.0021632490788 12573.8184417872581
## sd_level:race_cond2 0.0198977248097 0.0028121246667 41.8494320208125
## t value Pr(>|t|)
## (Intercept) 61.873 < 0.0000000000000002 ***
## sd_level -29.638 < 0.0000000000000002 ***
## race_cond1 -2.490 0.01280 *
## race_cond2 -2.664 0.00816 **
## sd_level:race_cond1 0.000 1.00000
## sd_level:race_cond2 7.076 0.0000000116 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) sd_lvl rc_cn1 rc_cn2 sd_:_1
## sd_level 0.000
## race_cond1 0.000 0.000
## race_cond2 0.000 0.000 -0.458
## sd_lvl:rc_1 0.000 0.000 0.000 0.000
## sd_lvl:rc_2 0.000 0.000 0.000 0.000 -0.385
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
# Quadratic
mod2_intent = mixed(intent ~ sd_level + race_cond + sd_level:race_cond + I(sd_level^2) +
(sd_level*race_cond||ResponseId) + (sd_level*race_cond||base),
data = dat, expand_re = TRUE)
## boundary (singular) fit: see help('isSingular')
summary(mod2_intent)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: intent ~ sd_level + race_cond + sd_level:race_cond + I(sd_level^2) +
## (1 + re1.sd_level + re1.race_cond1 + re1.race_cond2 + re1.sd_level_by_race_cond1 +
## re1.sd_level_by_race_cond2 || ResponseId) + (1 + re2.sd_level +
## re2.race_cond1 + re2.race_cond2 + re2.sd_level_by_race_cond1 +
## re2.sd_level_by_race_cond2 || base)
## Data: data
##
## REML criterion at convergence: 38320
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -5.8030 -0.5548 -0.0260 0.5401 5.7330
##
## Random effects:
## Groups Name Variance Std.Dev.
## ResponseId (Intercept) 0.3898113862135 0.62434877
## ResponseId.1 re1.sd_level 0.0062072190060 0.07878591
## ResponseId.2 re1.race_cond1 0.0000000000000 0.00000000
## ResponseId.3 re1.race_cond2 0.0070034731472 0.08368676
## ResponseId.4 re1.sd_level_by_race_cond1 0.0000000000000 0.00000000
## ResponseId.5 re1.sd_level_by_race_cond2 0.0002539462137 0.01593569
## base (Intercept) 0.0301112324802 0.17352588
## base.1 re2.sd_level 0.0006215598025 0.02493110
## base.2 re2.race_cond1 0.0000000004847 0.00002202
## base.3 re2.race_cond2 0.0000000030705 0.00005541
## base.4 re2.sd_level_by_race_cond1 0.0000000000000 0.00000000
## base.5 re2.sd_level_by_race_cond2 0.0000601068906 0.00775286
## Residual 0.9131302307860 0.95557848
## Number of obs: 13425, groups: ResponseId, 179; base, 25
##
## Fixed effects:
## Estimate Std. Error
## (Intercept) 3.2796412160438386251826 0.0595665388910883719653
## sd_level -0.2324480105896724047021 0.0078537028092123869344
## race_cond1 -0.0304655494264724803488 0.0116633750784500018344
## race_cond2 -0.0356052143109821181421 0.0132348014745728610742
## I(sd_level^2) 0.0110052540569301974399 0.0003080421990283515959
## sd_level:race_cond1 -0.0000000000000000008929 0.0020618127553014052936
## sd_level:race_cond2 0.0198985214581194058692 0.0028417771196621180799
## df t value Pr(>|t|)
## (Intercept) 114.3432475542602162477124 55.058 < 0.0000000000000002
## sd_level 82.4628716071241143481529 -29.597 < 0.0000000000000002
## race_cond1 12632.0744243883164017461240 -2.612 0.00901
## race_cond2 273.8777596397180786880199 -2.690 0.00758
## I(sd_level^2) 12647.5940046301129768835381 35.726 < 0.0000000000000002
## sd_level:race_cond1 12647.5940050547960709081963 0.000 1.00000
## sd_level:race_cond2 43.7250170283717096708642 7.002 0.0000000117
##
## (Intercept) ***
## sd_level ***
## race_cond1 **
## race_cond2 **
## I(sd_level^2) ***
## sd_level:race_cond1
## sd_level:race_cond2 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) sd_lvl rc_cn1 rc_cn2 I(_^2) sd_:_1
## sd_level 0.000
## race_cond1 0.000 0.000
## race_cond2 0.000 0.000 -0.441
## I(sd_lvl^2) -0.165 0.000 0.000 0.000
## sd_lvl:rc_1 0.000 0.000 0.000 0.000 0.000
## sd_lvl:rc_2 0.000 0.000 0.000 0.000 0.000 -0.363
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
# Model comparison
anova(mod1_intent, mod2_intent, refit = TRUE)
## refitting model(s) with ML (instead of REML)
## Data: data
## Models:
## mod1_intent: intent ~ sd_level * race_cond + (1 + re1.sd_level + re1.race_cond1 + re1.race_cond2 + re1.sd_level_by_race_cond1 + re1.sd_level_by_race_cond2 || ResponseId) + (1 + re2.sd_level + re2.race_cond1 + re2.race_cond2 + re2.sd_level_by_race_cond1 + re2.sd_level_by_race_cond2 || base)
## mod2_intent: intent ~ sd_level + race_cond + sd_level:race_cond + I(sd_level^2) + (1 + re1.sd_level + re1.race_cond1 + re1.race_cond2 + re1.sd_level_by_race_cond1 + re1.sd_level_by_race_cond2 || ResponseId) + (1 + re2.sd_level + re2.race_cond1 + re2.race_cond2 + re2.sd_level_by_race_cond1 + re2.sd_level_by_race_cond2 || base)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## mod1_intent 19 39514 39656 -19738 39476
## mod2_intent 20 38299 38449 -19130 38259 1216.2 1 < 0.00000000000000022
##
## mod1_intent
## mod2_intent ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# Post-hoc trends
emtrends(mod2_intent, pairwise ~ race_cond, var = "sd_level", pbkrtest.limit = 13425)
## $emtrends
## race_cond sd_level.trend SE df lower.CL upper.CL
## asian -0.232 0.00812 101 -0.248 -0.216
## black -0.212 0.00835 111 -0.229 -0.196
## white -0.252 0.00835 110 -0.269 -0.236
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## asian - black -0.0199 0.00407 150.8 -4.887 <.0001
## asian - white 0.0199 0.00407 27.6 4.887 0.0001
## black - white 0.0398 0.00530 33.1 7.514 <.0001
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 3 estimates
Plot the data
plot_grid <- ref_grid(mod2_intent$full_model, at = list(sd_level = c(-8, -4, 0, 4, 8)))
## Note: D.f. calculations have been disabled because the number of observations exceeds 3000.
## To enable adjustments, add the argument 'pbkrtest.limit = 13425' (or larger)
## [or, globally, 'set emm_options(pbkrtest.limit = 13425)' or larger];
## but be warned that this may result in large computation time and memory use.
## Note: D.f. calculations have been disabled because the number of observations exceeds 3000.
## To enable adjustments, add the argument 'lmerTest.limit = 13425' (or larger)
## [or, globally, 'set emm_options(lmerTest.limit = 13425)' or larger];
## but be warned that this may result in large computation time and memory use.
plot_dat <- emmeans(plot_grid, specs = "sd_level", by = "race_cond")
plot_dat <- as.data.frame(plot_dat)
p1 = ggplot(data = plot_dat, aes(x = sd_level, y = emmean, color = race_cond, ymin = asymp.LCL, ymax = asymp.UCL)) +
geom_line(position = position_dodge(0.5)) +
geom_point(size = 2, position = position_dodge(0.5)) +
geom_errorbar(width = 0.5, position = position_dodge(0.5), show.legend = FALSE) +
ylim(1,7) +
labs(x = "Trustworthiness Dimension (SD)", y = "Intends to Harm") +
scale_x_continuous(breaks = c(-8, -4, 0, 4, 8)) +
scale_color_discrete(name = "", breaks = c("black", "white", "asian"),
labels = c("Black Model", "White Model", "East Asian Model")) +
theme(legend.position = "top",
legend.key = element_blank())
p1
Changing Contrasts for Intent
dat <- dat |>
mutate(race_cond2 = case_match(race_cond,
"asian" ~ "3asian",
"black" ~ "1black",
"white" ~ "2white"
))
dat$race_cond2 <- forcats::fct(dat$race_cond2, levels = c("1black", "2white", "3asian"))
contrasts(dat$race_cond2)
## [,1] [,2]
## 1black 1 0
## 2white 0 1
## 3asian -1 -1
mod2b_intent <- mixed(intent ~ sd_level + race_cond2 + sd_level:race_cond2 + I(sd_level^2) +
(sd_level*race_cond2||ResponseId) + (sd_level*race_cond2||base),
data = dat, expand_re = TRUE)
## boundary (singular) fit: see help('isSingular')
summary(mod2b_intent)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula:
## intent ~ sd_level + race_cond2 + sd_level:race_cond2 + I(sd_level^2) +
## (1 + re1.sd_level + re1.race_cond21 + re1.race_cond22 + re1.sd_level_by_race_cond21 +
## re1.sd_level_by_race_cond22 || ResponseId) + (1 + re2.sd_level +
## re2.race_cond21 + re2.race_cond22 + re2.sd_level_by_race_cond21 +
## re2.sd_level_by_race_cond22 || base)
## Data: data
##
## REML criterion at convergence: 38345.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -5.9226 -0.5573 -0.0266 0.5414 5.5736
##
## Random effects:
## Groups Name Variance Std.Dev.
## ResponseId (Intercept) 0.3898844440048 0.62440727
## ResponseId.1 re1.sd_level 0.0062030514707 0.07875945
## ResponseId.2 re1.race_cond21 0.0000000005646 0.00002376
## ResponseId.3 re1.race_cond22 0.0000000000000 0.00000000
## ResponseId.4 re1.sd_level_by_race_cond21 0.0000826528924 0.00909136
## ResponseId.5 re1.sd_level_by_race_cond22 0.0000000000000 0.00000000
## base (Intercept) 0.0300225052025 0.17327004
## base.1 re2.sd_level 0.0006210881603 0.02492164
## base.2 re2.race_cond21 0.0000000000000 0.00000000
## base.3 re2.race_cond22 0.0000001716246 0.00041428
## base.4 re2.sd_level_by_race_cond21 0.0000254348824 0.00504330
## base.5 re2.sd_level_by_race_cond22 0.0000080355798 0.00283471
## Residual 0.9222493995394 0.96033817
## Number of obs: 13425, groups: ResponseId, 179; base, 25
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 3.2796387 0.0595540 114.8583211 55.070
## sd_level -0.2324480 0.0078524 82.4025717 -29.602
## race_cond21 -0.0356052 0.0117215 12792.2697731 -3.038
## race_cond22 0.0660708 0.0117218 5606.9912831 5.637
## I(sd_level^2) 0.0110053 0.0003096 12792.3962547 35.549
## sd_level:race_cond21 0.0198986 0.0024028 37.7465589 8.281
## sd_level:race_cond22 -0.0198873 0.0021483 35.3778984 -9.257
## Pr(>|t|)
## (Intercept) < 0.0000000000000002 ***
## sd_level < 0.0000000000000002 ***
## race_cond21 0.00239 **
## race_cond22 0.0000000181909 ***
## I(sd_level^2) < 0.0000000000000002 ***
## sd_level:race_cond21 0.0000000005145 ***
## sd_level:race_cond22 0.0000000000554 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) sd_lvl rc_c21 rc_c22 I(_^2) s_:_21
## sd_level 0.000
## race_cond21 0.000 0.000
## race_cond22 0.000 0.000 -0.500
## I(sd_lvl^2) -0.166 0.000 0.000 0.000
## sd_lvl:r_21 0.000 0.000 0.000 0.000 0.000
## sd_lvl:r_22 0.000 0.000 0.000 0.000 0.000 -0.416
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
# Post-hoc trends
emtrends(mod2b_intent, pairwise ~ race_cond2, var = "sd_level", pbkrtest.limit = 13425)
## $emtrends
## race_cond2 sd_level.trend SE df lower.CL upper.CL
## 1black -0.212 0.00821 105 -0.229 -0.196
## 2white -0.252 0.00814 102 -0.268 -0.236
## 3asian -0.232 0.00823 105 -0.249 -0.216
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## 1black - 2white 0.0398 0.00383 171.2 10.383 <.0001
## 1black - 3asian 0.0199 0.00437 26.6 4.553 0.0003
## 2white - 3asian -0.0199 0.00396 23.9 -5.024 0.0001
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 3 estimates
Plot the data
plot_grid2 <- ref_grid(mod2b_intent$full_model, at = list(sd_level = c(-8, -4, 0, 4, 8)))
## Note: D.f. calculations have been disabled because the number of observations exceeds 3000.
## To enable adjustments, add the argument 'pbkrtest.limit = 13425' (or larger)
## [or, globally, 'set emm_options(pbkrtest.limit = 13425)' or larger];
## but be warned that this may result in large computation time and memory use.
## Note: D.f. calculations have been disabled because the number of observations exceeds 3000.
## To enable adjustments, add the argument 'lmerTest.limit = 13425' (or larger)
## [or, globally, 'set emm_options(lmerTest.limit = 13425)' or larger];
## but be warned that this may result in large computation time and memory use.
plot_dat2 <- emmeans(plot_grid2, specs = "sd_level", by = "race_cond2")
plot_dat2 <- as.data.frame(plot_dat2)
p2 = ggplot(data = plot_dat2, aes(x = sd_level, y = emmean, color = race_cond2, ymin = asymp.LCL, ymax = asymp.UCL)) +
geom_line(position = position_dodge(0.5)) +
geom_point(size = 2, position = position_dodge(0.5)) +
geom_errorbar(width = 0.5, position = position_dodge(0.5), show.legend = FALSE) +
ylim(1,7) +
labs(x = "Trustworthiness Dimension (SD)", y = "Intends to Harm") +
scale_x_continuous(breaks = c(-8, -4, 0, 4, 8)) +
scale_color_discrete(name = "", breaks = c("1black", "2white", "3asian"),
labels = c("Black Model", "White Model", "East Asian Model")) +
theme(legend.position = "top",
legend.key = element_blank())
p2
Ability Model
# Linear
mod1_ability = mixed(ability ~ sd_level*race_cond + (sd_level*race_cond ||ResponseId) +
(sd_level*race_cond ||base),
data = dat, expand_re = TRUE)
## boundary (singular) fit: see help('isSingular')
summary(mod1_ability)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: ability ~ sd_level * race_cond + (1 + re1.sd_level + re1.race_cond1 +
## re1.race_cond2 + re1.sd_level_by_race_cond1 + re1.sd_level_by_race_cond2 ||
## ResponseId) + (1 + re2.sd_level + re2.race_cond1 + re2.race_cond2 +
## re2.sd_level_by_race_cond1 + re2.sd_level_by_race_cond2 || base)
## Data: data
##
## REML criterion at convergence: 38194.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -5.2233 -0.5095 0.0415 0.5671 5.5962
##
## Random effects:
## Groups Name Variance Std.Dev.
## ResponseId (Intercept) 0.46253885 0.68010
## ResponseId.1 re1.sd_level 0.00924006 0.09613
## ResponseId.2 re1.race_cond1 0.00148391 0.03852
## ResponseId.3 re1.race_cond2 0.01020322 0.10101
## ResponseId.4 re1.sd_level_by_race_cond1 0.00000000 0.00000
## ResponseId.5 re1.sd_level_by_race_cond2 0.00067226 0.02593
## base (Intercept) 0.01109775 0.10535
## base.1 re2.sd_level 0.00006021 0.00776
## base.2 re2.race_cond1 0.00000000 0.00000
## base.3 re2.race_cond2 0.00000000 0.00000
## base.4 re2.sd_level_by_race_cond1 0.00000000 0.00000
## base.5 re2.sd_level_by_race_cond2 0.00000000 0.00000
## Residual 0.89583924 0.94649
## Number of obs: 13425, groups: ResponseId, 179; base, 25
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 5.070776 0.055633 183.238778 91.147
## sd_level -0.011416 0.007491 183.221691 -1.524
## race_cond1 0.006853 0.011906 237.001094 0.576
## race_cond2 -0.074488 0.013801 235.945937 -5.397
## sd_level:race_cond1 0.003371 0.002042 12565.814999 1.650
## sd_level:race_cond2 0.012002 0.002815 235.905322 4.263
## Pr(>|t|)
## (Intercept) < 0.0000000000000002 ***
## sd_level 0.1293
## race_cond1 0.5654
## race_cond2 0.000000164 ***
## sd_level:race_cond1 0.0989 .
## sd_level:race_cond2 0.000029183 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) sd_lvl rc_cn1 rc_cn2 sd_:_1
## sd_level 0.000
## race_cond1 0.000 0.000
## race_cond2 0.000 0.000 -0.406
## sd_lvl:rc_1 0.000 0.000 0.000 0.000
## sd_lvl:rc_2 0.000 0.000 0.000 0.000 -0.363
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
# Quadratic
mod2_ability = mixed(ability ~ sd_level + race_cond + sd_level:race_cond + I(sd_level^2) +
(sd_level*race_cond ||ResponseId) +
(sd_level*race_cond ||base),
data = dat, expand_re = TRUE)
## boundary (singular) fit: see help('isSingular')
summary(mod2_ability)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: ability ~ sd_level + race_cond + sd_level:race_cond + I(sd_level^2) +
## (1 + re1.sd_level + re1.race_cond1 + re1.race_cond2 + re1.sd_level_by_race_cond1 +
## re1.sd_level_by_race_cond2 || ResponseId) + (1 + re2.sd_level +
## re2.race_cond1 + re2.race_cond2 + re2.sd_level_by_race_cond1 +
## re2.sd_level_by_race_cond2 || base)
## Data: data
##
## REML criterion at convergence: 38074.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -5.1306 -0.5074 0.0476 0.5601 5.5053
##
## Random effects:
## Groups Name Variance Std.Dev.
## ResponseId (Intercept) 0.462915017306 0.68037858
## ResponseId.1 re1.sd_level 0.009245864910 0.09615542
## ResponseId.2 re1.race_cond1 0.001609765701 0.04012189
## ResponseId.3 re1.race_cond2 0.010362661972 0.10179716
## ResponseId.4 re1.sd_level_by_race_cond1 0.000000000000 0.00000000
## ResponseId.5 re1.sd_level_by_race_cond2 0.000677726521 0.02603318
## base (Intercept) 0.011085948265 0.10528983
## base.1 re2.sd_level 0.000060832777 0.00779954
## base.2 re2.race_cond1 0.000032883870 0.00573445
## base.3 re2.race_cond2 0.000000004103 0.00006406
## base.4 re2.sd_level_by_race_cond1 0.000000000000 0.00000000
## base.5 re2.sd_level_by_race_cond2 0.000000000000 0.00000000
## Residual 0.886377105300 0.94147602
## Number of obs: 13425, groups: ResponseId, 179; base, 25
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 4.9579794 0.0564828 194.7881133 87.779
## sd_level -0.0114157 0.0074935 183.3066926 -1.523
## race_cond1 0.0068495 0.0119314 42.2371897 0.574
## race_cond2 -0.0744879 0.0137819 235.0199254 -5.405
## I(sd_level^2) 0.0035249 0.0003035 12540.5776310 11.614
## sd_level:race_cond1 0.0033706 0.0020314 12540.5776350 1.659
## sd_level:race_cond2 0.0120019 0.0028130 235.3676739 4.267
## Pr(>|t|)
## (Intercept) < 0.0000000000000002 ***
## sd_level 0.1294
## race_cond1 0.5690
## race_cond2 0.000000159 ***
## I(sd_level^2) < 0.0000000000000002 ***
## sd_level:race_cond1 0.0971 .
## sd_level:race_cond2 0.000028767 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) sd_lvl rc_cn1 rc_cn2 I(_^2) sd_:_1
## sd_level 0.000
## race_cond1 0.000 0.000
## race_cond2 0.000 0.000 -0.402
## I(sd_lvl^2) -0.172 0.000 0.000 0.000
## sd_lvl:rc_1 0.000 0.000 0.000 0.000 0.000
## sd_lvl:rc_2 0.000 0.000 0.000 0.000 0.000 -0.361
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
# Post-hoc trends
emtrends(mod2_ability, pairwise ~ race_cond, var = "sd_level", pbkrtest.limit = 13425)
## $emtrends
## race_cond sd_level.trend SE df lower.CL upper.CL
## asian -0.007989 0.00776 205 -0.0233 0.00732
## black 0.000643 0.00800 229 -0.0151 0.01641
## white -0.026732 0.00800 225 -0.0425 -0.01096
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## asian - black -0.00863 0.00402 264.7 -2.147 0.0826
## asian - white 0.01874 0.00402 33.9 4.661 0.0001
## black - white 0.02737 0.00525 66.9 5.218 <.0001
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 3 estimates