Database Import

setwd("C:/Users/Gallese/Desktop/Mask Survey/")
cond <- readr::read_delim("cond.txt", "\t", escape_double = FALSE)
## 
## -- Column specification ----------------------------------------------------------------------------------------------------------------------------------------------
## cols(
##   Subj = col_double(),
##   stim = col_character(),
##   Mask = col_character(),
##   ActGen = col_character(),
##   Emo = col_character(),
##   Act = col_character(),
##   genere = col_double(),
##   generecat = col_character(),
##   eta = col_character(),
##   RegQua = col_character(),
##   cat = col_character(),
##   fis = col_double(),
##   soc = col_double(),
##   val = col_double(),
##   catn = col_double()
## )
print(cond)
## # A tibble: 6,912 x 15
##     Subj stim  Mask  ActGen Emo   Act   genere generecat eta   RegQua cat  
##    <dbl> <chr> <chr> <chr>  <chr> <chr>  <dbl> <chr>     <chr> <chr>  <chr>
##  1     1 Mask~ Mask  F      AN    AF18       1 F         25    Sicil~ SU   
##  2     1 Mask~ Mask  F      AN    AF20       1 F         25    Sicil~ AN   
##  3     1 Mask~ Mask  F      AN    AF35       1 F         25    Sicil~ AN   
##  4     1 Mask~ Mask  F      AN    BF23       1 F         25    Sicil~ FE   
##  5     1 Mask~ Mask  F      AN    BF26       1 F         25    Sicil~ AN   
##  6     1 Mask~ Mask  F      AN    BF28       1 F         25    Sicil~ FE   
##  7     1 Mask~ Mask  F      HA    AF18       1 F         25    Sicil~ HA   
##  8     1 Mask~ Mask  F      HA    AF20       1 F         25    Sicil~ HA   
##  9     1 Mask~ Mask  F      HA    AF23       1 F         25    Sicil~ HA   
## 10     1 Mask~ Mask  F      HA    AF26       1 F         25    Sicil~ HA   
## # ... with 6,902 more rows, and 4 more variables: fis <dbl>, soc <dbl>,
## #   val <dbl>, catn <dbl>

Valence

FINALval <- lme4::lmer(val ~ Emo + Mask + generecat + Emo:generecat + ActGen:Emo + (1|Subj) + (1|stim), data = cond)
car::Anova(FINALval)
## Registered S3 methods overwritten by 'car':
##   method                          from
##   influence.merMod                lme4
##   cooks.distance.influence.merMod lme4
##   dfbeta.influence.merMod         lme4
##   dfbetas.influence.merMod        lme4

R2

MuMIn::r.squaredGLMM(FINALval)
##            R2m       R2c
## [1,] 0.7155719 0.7584366

Model Parameters CI

confint(FINALval)
## Computing profile confidence intervals ...
##                       2.5 %      97.5 %
## .sig01             3.188703   4.4710535
## .sig02             3.529137   5.0847606
## .sigma            13.637646  14.1057899
## (Intercept)      -37.512535 -31.5037552
## EmoHA             61.685893  69.0663792
## EmoNE             22.260952  29.6414383
## MaskScar          -2.995607   1.1622738
## generecatM         6.057617   9.8484478
## EmoHA:generecatM -16.192929 -12.9883928
## EmoNE:generecatM  -3.797466  -0.5929303
## EmoAN:ActGenM     -4.283122   2.9185388
## EmoHA:ActGenM     -4.634685   2.5669763
## EmoNE:ActGenM     -1.245796   5.9558652

AIC

AIC(FINALval)
## [1] 56312.37

Post Hoc

Simple Effects Emotion

(emmvalEmo <- emmeans::emmeans(FINALval, pairwise ~ Emo))
## $emmeans
##  Emo emmean   SE  df asymp.LCL asymp.UCL
##  AN  -31.33 1.03 Inf    -33.34    -29.32
##  HA   26.57 1.03 Inf     24.56     28.59
##  NE   -4.96 1.03 Inf     -6.97     -2.95
## 
## Results are averaged over the levels of: Mask, generecat, ActGen 
## Degrees-of-freedom method: asymptotic 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast estimate   SE  df z.ratio p.value
##  AN - HA     -57.9 1.35 Inf -43.029 <.0001 
##  AN - NE     -26.4 1.35 Inf -19.597 <.0001 
##  HA - NE      31.5 1.35 Inf  23.432 <.0001 
## 
## Results are averaged over the levels of: Mask, generecat, ActGen 
## Degrees-of-freedom method: asymptotic 
## P value adjustment: tukey method for comparing a family of 3 estimates

Simple Effects Gender of Participants

(emmvalGen <- emmeans::emmeans(FINALval, pairwise ~ generecat))
## $emmeans
##  generecat emmean    SE  df asymp.LCL asymp.UCL
##  F          -4.42 0.798 Inf     -5.98    -2.853
##  M          -2.06 0.789 Inf     -3.61    -0.513
## 
## Results are averaged over the levels of: Mask, ActGen, Emo 
## Degrees-of-freedom method: asymptotic 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast estimate    SE  df z.ratio p.value
##  F - M       -2.36 0.844 Inf -2.794  0.0052 
## 
## Results are averaged over the levels of: Mask, ActGen, Emo 
## Degrees-of-freedom method: asymptotic

Interaction Emotion * Gender of Participants

(emmvalGenEmo <- emmeans::emmeans(FINALval, pairwise ~ Emo:generecat))
## $emmeans
##  Emo generecat emmean   SE  df asymp.LCL asymp.UCL
##  AN  F         -35.31 1.14 Inf     -37.5   -33.074
##  HA  F          29.89 1.14 Inf      27.7    32.127
##  NE  F          -7.84 1.14 Inf     -10.1    -5.604
##  AN  M         -27.35 1.13 Inf     -29.6   -25.137
##  HA  M          23.26 1.13 Inf      21.0    25.472
##  NE  M          -2.08 1.13 Inf      -4.3     0.137
## 
## Results are averaged over the levels of: Mask, ActGen 
## Degrees-of-freedom method: asymptotic 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast    estimate    SE  df z.ratio p.value
##  AN F - HA F   -65.20 1.409 Inf -46.277 <.0001 
##  AN F - NE F   -27.47 1.409 Inf -19.497 <.0001 
##  AN F - AN M    -7.95 0.967 Inf  -8.225 <.0001 
##  AN F - HA M   -58.56 1.606 Inf -36.468 <.0001 
##  AN F - NE M   -33.23 1.606 Inf -20.691 <.0001 
##  HA F - NE F    37.73 1.409 Inf  26.780 <.0001 
##  HA F - AN M    57.25 1.606 Inf  35.649 <.0001 
##  HA F - HA M     6.64 0.967 Inf   6.865 <.0001 
##  HA F - NE M    31.97 1.606 Inf  19.910 <.0001 
##  NE F - AN M    19.52 1.606 Inf  12.153 <.0001 
##  NE F - HA M   -31.09 1.606 Inf -19.362 <.0001 
##  NE F - NE M    -5.76 0.967 Inf  -5.955 <.0001 
##  AN M - HA M   -50.61 1.404 Inf -36.048 <.0001 
##  AN M - NE M   -25.27 1.404 Inf -18.002 <.0001 
##  HA M - NE M    25.34 1.404 Inf  18.045 <.0001 
## 
## Results are averaged over the levels of: Mask, ActGen 
## Degrees-of-freedom method: asymptotic 
## P value adjustment: tukey method for comparing a family of 6 estimates

Hierarchical Model Selection

null <- lm(val ~ 1, data = cond)
emo <- lm(val ~ Emo, data = cond)
emomask <- lm(val ~ Emo + Mask, data = cond)
emomaskgend <- lm(val ~ Emo + Mask + generecat, data = cond)
emomaskgend.emo <- lm(val ~ Emo + Mask + generecat + Emo:generecat, data = cond)
emomaskgend.emoact.emo <- lm(val ~ Emo + Mask + generecat + Emo:generecat + ActGen:Emo, data = cond)
emomaskgend.emoact.emo_subj <- lme4::lmer(val ~ Emo + Mask + generecat + Emo:generecat + ActGen:Emo + (1|Subj), data = cond)
emomaskgend.emoact.emo_subj_stim <- lme4::lmer(val ~ Emo + Mask + generecat + Emo:generecat + ActGen:Emo + (1|Subj) + (1|stim), data = cond)

Model <- c("null", "emo", "emomask", "emomaskgend", "emomaskgend.emo", "emomaskgend.emoact.emo", "emomaskgend.emoact.emo_subj", "emomaskgend.emoact.emo_subj_cond")

AIC <- c(AIC(null), AIC(emo), AIC(emomask), AIC(emomaskgend), AIC(emomaskgend.emo), AIC(emomaskgend.emoact.emo), AIC(emomaskgend.emoact.emo_subj), AIC(emomaskgend.emoact.emo_subj_stim))

BIC <- c(BIC(null), BIC(emo), BIC(emomask), BIC(emomaskgend), BIC(emomaskgend.emo), BIC(emomaskgend.emoact.emo), BIC(emomaskgend.emoact.emo_subj), BIC(emomaskgend.emoact.emo_subj_stim))

R2m <- c(MuMIn::r.squaredGLMM(null)[1], MuMIn::r.squaredGLMM(emo)[1], MuMIn::r.squaredGLMM(emomask)[1], MuMIn::r.squaredGLMM(emomaskgend)[1], MuMIn::r.squaredGLMM(emomaskgend.emo)[1], MuMIn::r.squaredGLMM(emomaskgend.emoact.emo)[1], MuMIn::r.squaredGLMM(emomaskgend.emoact.emo_subj)[1], MuMIn::r.squaredGLMM(emomaskgend.emoact.emo_subj_stim)[1])

R2c <- c(MuMIn::r.squaredGLMM(null)[2], MuMIn::r.squaredGLMM(emo)[2], MuMIn::r.squaredGLMM(emomask)[2], MuMIn::r.squaredGLMM(emomaskgend)[2], MuMIn::r.squaredGLMM(emomaskgend.emo)[2], MuMIn::r.squaredGLMM(emomaskgend.emoact.emo)[2], MuMIn::r.squaredGLMM(emomaskgend.emoact.emo_subj)[2], MuMIn::r.squaredGLMM(emomaskgend.emoact.emo_subj_stim)[2])


(Lrtval <- cbind(Model, lmtest::lrtest(null, emo, emomask, emomaskgend, emomaskgend.emo, emomaskgend.emoact.emo, emomaskgend.emoact.emo_subj, emomaskgend.emoact.emo_subj_stim), AIC, BIC, R2m, R2c))

Plot

require(ggplot2)
## Loading required package: ggplot2

Physical Distance

FINALfis <- lme4::lmer(fis ~ Emo + Mask + generecat + ActGen + Emo:generecat + Mask:generecat + (1|Subj) + (1|stim), data = cond)
car::Anova(FINALfis)

R2

MuMIn::r.squaredGLMM(FINALfis)
##            R2m       R2c
## [1,] 0.3665619 0.5558988

Model Parameters CI

confint(FINALfis)
## Computing profile confidence intervals ...
##                             2.5 %     97.5 %
## .sig01                9.815499509  13.165594
## .sig02                2.305038706   3.667917
## .sigma               17.788515501  18.399144
## (Intercept)          66.566924004  74.196497
## EmoHA               -50.127135037 -45.640595
## EmoNE               -30.086354895 -25.599815
## MaskScar              0.008212403   3.671457
## generecatM          -17.302755751  -7.558006
## ActGenM               1.764579193   4.996995
## EmoHA:generecatM     16.194427949  20.374316
## EmoNE:generecatM      8.446164808  12.626053
## MaskScar:generecatM   0.634569492   4.047439

AIC

AIC(FINALfis)
## [1] 60059.61

Post Hoc

Simple Effects Emotion

(emmFfisEmo <- emmeans::emmeans(FINALfis, pairwise ~ Emo))
## $emmeans
##  Emo emmean   SE  df asymp.LCL asymp.UCL
##  AN    67.4 1.37 Inf      64.7      70.1
##  HA    28.6 1.37 Inf      25.9      31.3
##  NE    44.8 1.37 Inf      42.1      47.5
## 
## Results are averaged over the levels of: Mask, generecat, ActGen 
## Degrees-of-freedom method: asymptotic 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast estimate   SE  df z.ratio p.value
##  AN - HA      38.7 1.03 Inf  37.741 <.0001 
##  AN - NE      22.6 1.03 Inf  21.992 <.0001 
##  HA - NE     -16.2 1.03 Inf -15.749 <.0001 
## 
## Results are averaged over the levels of: Mask, generecat, ActGen 
## Degrees-of-freedom method: asymptotic 
## P value adjustment: tukey method for comparing a family of 3 estimates

Simple Effects Condition

(emmFfisMask <- emmeans::emmeans(FINALfis, pairwise ~ Mask))
## $emmeans
##  Mask emmean   SE  df asymp.LCL asymp.UCL
##  Mask   45.4 1.31 Inf      42.9        48
##  Scar   48.4 1.31 Inf      45.9        51
## 
## Results are averaged over the levels of: Emo, generecat, ActGen 
## Degrees-of-freedom method: asymptotic 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast    estimate    SE  df z.ratio p.value
##  Mask - Scar    -3.01 0.838 Inf -3.592  0.0003 
## 
## Results are averaged over the levels of: Emo, generecat, ActGen 
## Degrees-of-freedom method: asymptotic

Simple Effects Gender of Stimuli

(emmFfisAct <- emmeans::emmeans(FINALfis, pairwise ~ ActGen))
## $emmeans
##  ActGen emmean   SE  df asymp.LCL asymp.UCL
##  F        45.2 1.31 Inf      42.7      47.8
##  M        48.6 1.31 Inf      46.1      51.2
## 
## Results are averaged over the levels of: Emo, Mask, generecat 
## Degrees-of-freedom method: asymptotic 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast estimate    SE  df z.ratio p.value
##  F - M       -3.38 0.838 Inf -4.034  0.0001 
## 
## Results are averaged over the levels of: Emo, Mask, generecat 
## Degrees-of-freedom method: asymptotic

Interaction Emotion * Gender of Participants

(emmFfisemo.gen <- emmeans::emmeans(FINALfis, pairwise ~ Emo:generecat))
## $emmeans
##  Emo generecat emmean   SE  df asymp.LCL asymp.UCL
##  AN  F           73.0 1.86 Inf      69.4      76.6
##  HA  F           25.1 1.86 Inf      21.5      28.7
##  NE  F           45.1 1.86 Inf      41.5      48.8
##  AN  M           61.7 1.82 Inf      58.2      65.3
##  HA  M           32.1 1.82 Inf      28.6      35.7
##  NE  M           44.4 1.82 Inf      40.9      48.0
## 
## Results are averaged over the levels of: Mask, ActGen 
## Degrees-of-freedom method: asymptotic 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast    estimate   SE  df z.ratio p.value
##  AN F - HA F   47.884 1.16 Inf  41.214 <.0001 
##  AN F - NE F   27.843 1.16 Inf  23.964 <.0001 
##  AN F - AN M   11.260 2.45 Inf   4.596 0.0001 
##  AN F - HA M   40.859 2.60 Inf  15.702 <.0001 
##  AN F - NE M   28.567 2.60 Inf  10.978 <.0001 
##  HA F - NE F  -20.041 1.16 Inf -17.249 <.0001 
##  HA F - AN M  -36.624 2.60 Inf -14.075 <.0001 
##  HA F - HA M   -7.024 2.45 Inf  -2.867 0.0476 
##  HA F - NE M  -19.317 2.60 Inf  -7.423 <.0001 
##  NE F - AN M  -16.583 2.60 Inf  -6.373 <.0001 
##  NE F - HA M   13.016 2.60 Inf   5.002 <.0001 
##  NE F - NE M    0.724 2.45 Inf   0.295 0.9997 
##  AN M - HA M   29.599 1.15 Inf  25.703 <.0001 
##  AN M - NE M   17.307 1.15 Inf  15.029 <.0001 
##  HA M - NE M  -12.293 1.15 Inf -10.674 <.0001 
## 
## Results are averaged over the levels of: Mask, ActGen 
## Degrees-of-freedom method: asymptotic 
## P value adjustment: tukey method for comparing a family of 6 estimates

Interaction Gender of Condition * Gender of Participants

(emmFfismask.gen <- emmeans::emmeans(FINALfis, pairwise ~ Mask:generecat))
## $emmeans
##  Mask generecat emmean   SE  df asymp.LCL asymp.UCL
##  Mask F           46.8 1.80 Inf      43.3      50.3
##  Scar F           48.7 1.80 Inf      45.2      52.2
##  Mask M           44.0 1.76 Inf      40.6      47.5
##  Scar M           48.2 1.76 Inf      44.7      51.6
## 
## Results are averaged over the levels of: Emo, ActGen 
## Degrees-of-freedom method: asymptotic 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast        estimate    SE  df z.ratio p.value
##  Mask F - Scar F   -1.840 0.949 Inf -1.939  0.2116 
##  Mask F - Mask M    2.824 2.411 Inf  1.171  0.6451 
##  Mask F - Scar M   -1.357 2.515 Inf -0.540  0.9493 
##  Scar F - Mask M    4.663 2.515 Inf  1.854  0.2481 
##  Scar F - Scar M    0.483 2.411 Inf  0.200  0.9972 
##  Mask M - Scar M   -4.181 0.940 Inf -4.446  0.0001 
## 
## Results are averaged over the levels of: Emo, ActGen 
## Degrees-of-freedom method: asymptotic 
## P value adjustment: tukey method for comparing a family of 4 estimates

Hierarchical Model Selection

null <- lm(fis ~ 1, data = cond)
emo <- lm(fis ~ Emo, data = cond)
emomask <- lm(fis ~ Emo + Mask, data = cond)
emomaskgend <- lm(fis ~ Emo + Mask + generecat, data = cond)
emomaskgendact <- lm(fis ~ Emo + Mask + generecat + ActGen, data = cond)
emomaskgendactgend.emo <- lm(fis ~ Emo + Mask + generecat + ActGen + Emo:generecat, data = cond)
emomaskgendactgend.emogend.mask <- lm(fis ~ Emo + Mask + generecat + ActGen + Emo:generecat + Mask:generecat, data = cond)
emomaskgendactgend.emogend.mask_subj <- lme4::lmer(fis ~ Emo + Mask + generecat + ActGen + Emo:generecat + Mask:generecat + (1|Subj), data = cond)
emomaskgendactgend.emogend.mask_subj_stim <- lme4::lmer(fis ~ Emo + Mask + generecat + ActGen + Emo:generecat + Mask:generecat + (1|Subj) + (1|stim), data = cond)

Model <- c("null", "emo", "emomask", "emomaskgend", "emomaskgendact", "emomaskgendactgend.emo", "emomaskgendactgend.emogend.mask", "emomaskgendactgend.emogend.mask_subj", "emomaskgendactgend.emogend.mask_subj_stim")

AIC <- c(AIC(null), AIC(emo), AIC(emomask), AIC(emomaskgend), AIC(emomaskgendact), AIC(emomaskgendactgend.emo), AIC(emomaskgendactgend.emogend.mask), AIC(emomaskgendactgend.emogend.mask_subj), AIC(emomaskgendactgend.emogend.mask_subj_stim))

BIC <- c(BIC(null), BIC(emo), BIC(emomask), BIC(emomaskgend), BIC(emomaskgendact), BIC(emomaskgendactgend.emo), BIC(emomaskgendactgend.emogend.mask), BIC(emomaskgendactgend.emogend.mask_subj), BIC(emomaskgendactgend.emogend.mask_subj_stim))

R2m <- c(MuMIn::r.squaredGLMM(null)[1], MuMIn::r.squaredGLMM(emo)[1], MuMIn::r.squaredGLMM(emomask)[1], MuMIn::r.squaredGLMM(emomaskgend)[1], MuMIn::r.squaredGLMM(emomaskgendact)[1], MuMIn::r.squaredGLMM(emomaskgendactgend.emo)[1], MuMIn::r.squaredGLMM(emomaskgendactgend.emogend.mask)[1], MuMIn::r.squaredGLMM(emomaskgendactgend.emogend.mask_subj)[1], MuMIn::r.squaredGLMM(emomaskgendactgend.emogend.mask_subj_stim)[1])

R2c <- c(MuMIn::r.squaredGLMM(null)[2], MuMIn::r.squaredGLMM(emo)[2], MuMIn::r.squaredGLMM(emomask)[2], MuMIn::r.squaredGLMM(emomaskgend)[2], MuMIn::r.squaredGLMM(emomaskgendact)[2], MuMIn::r.squaredGLMM(emomaskgendactgend.emo)[2], MuMIn::r.squaredGLMM(emomaskgendactgend.emogend.mask)[2], MuMIn::r.squaredGLMM(emomaskgendactgend.emogend.mask_subj)[2], MuMIn::r.squaredGLMM(emomaskgendactgend.emogend.mask_subj_stim)[2])

(Lrtfis <- cbind(Model, lmtest::lrtest(null, emo, emomask, emomaskgend, emomaskgendact, emomaskgendactgend.emo, emomaskgendactgend.emogend.mask, emomaskgendactgend.emogend.mask_subj, emomaskgendactgend.emogend.mask_subj_stim), AIC, BIC, R2m, R2c))

Social Distance

FINALsoc <- ordinal::clm(as.factor(soc) ~ Mask + Emo + ActGen + generecat + Emo:generecat + Mask:generecat, data = cond, method = c("Newton"),  threshold="equidistant")
summary(FINALsoc)
## formula: 
## as.factor(soc) ~ Mask + Emo + ActGen + generecat + Emo:generecat + Mask:generecat
## data:    cond
## 
##  link  threshold   nobs logLik    AIC      niter max.grad cond.H 
##  logit equidistant 6911 -10851.11 21722.22 5(0)  1.65e-08 3.9e+02
## 
## Coefficients:
##                     Estimate Std. Error z value Pr(>|z|)    
## MaskScar            -0.07064    0.06358  -1.111 0.266552    
## EmoHA                3.05403    0.08395  36.378  < 2e-16 ***
## EmoNE                1.60371    0.07935  20.210  < 2e-16 ***
## ActGenM             -0.21397    0.04375  -4.891 1.00e-06 ***
## generecatM           0.84781    0.08954   9.468  < 2e-16 ***
## EmoHA:generecatM    -0.75708    0.10840  -6.984 2.87e-12 ***
## EmoNE:generecatM    -0.41471    0.10788  -3.844 0.000121 ***
## MaskScar:generecatM -0.21284    0.08754  -2.431 0.015045 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Threshold coefficients:
##             Estimate Std. Error z value
## threshold.1  0.11180    0.06867   1.628
## spacing      1.21150    0.01432  84.573
## (1 observation deleted due to missingness)

Convergence Test

ordinal::convergence(FINALsoc)
##  nobs logLik    niter max.grad cond.H  logLik.Error
##  6911 -10851.11 5(0)  1.65e-08 3.9e+02 <1e-10      
## 
##                     Estimate Std.Err  Gradient     Error Cor.Dec Sig.Dig
## threshold.1          0.11180 0.06867 -8.24e-10  7.09e-13      11      11
## spacing              1.21150 0.01432 -1.65e-08 -3.23e-12      11      12
## MaskScar            -0.07064 0.06358  4.13e-10  1.39e-13      12      11
## EmoHA                3.05403 0.08395  7.27e-11 -6.72e-12      10      11
## EmoNE                1.60371 0.07935  3.34e-10 -2.81e-12      11      12
## ActGenM             -0.21397 0.04375  4.29e-10  5.26e-13      11      11
## generecatM           0.84781 0.08954  3.68e-10 -1.09e-12      11      11
## EmoHA:generecatM    -0.75708 0.10840 -6.99e-12  4.41e-13      12      12
## EmoNE:generecatM    -0.41471 0.10788  1.29e-10 -2.35e-13      12      12
## MaskScar:generecatM -0.21284 0.08754  1.92e-10  4.92e-13      12      12
## 
## Eigen values of Hessian:
## 12573.91  2461.92   905.60   692.12   587.72   369.68   216.25   132.61    80.93    31.92 
## 
## Convergence message from clm:
## (0) successful convergence 
## In addition: Absolute and relative convergence criteria were met

Deviance Table

car::Anova(FINALsoc)

Pseudo-R2 (pseudo R-squared measures are relative measures among similar models indicating how well the model explains the data)

rcompanion::nagelkerke(FINALsoc)
## $Models
##                                                                                                                                           
## Model: "ordinal::clm, as.factor(soc) ~ Mask + Emo + ActGen + generecat + Emo:generecat + Mask:generecat, cond, equidistant, c(\"Newton\")"
## Null:  "ordinal::clm, as.factor(soc) ~ 1, cond, equidistant, c(\"Newton\")"                                                               
## 
## $Pseudo.R.squared.for.model.vs.null
##                              Pseudo.R.squared
## McFadden                            0.0957983
## Cox and Snell (ML)                  0.2830160
## Nagelkerke (Cragg and Uhler)        0.2920780
## 
## $Likelihood.ratio.test
##  Df.diff LogLik.diff  Chisq p.value
##       -8     -1149.7 2299.3       0
## 
## $Number.of.observations
##            
## Model: 6911
## Null:  6911
## 
## $Messages
## [1] "Note: For models fit with REML, these statistics are based on refitting with ML"
## 
## $Warnings
## [1] "None"

Likelihood ratio tests of model terms in scale and nominal formulae (We should be safe requiring that the thresholds are equidistant or equally spaced) Nominal Test (Test evidence of non-proportional odds, Partial proportional odds assumption) Scale Test (Test evidence of scale effects)

#This function moves all terms in formula and copies all terms in scale to nominal one by one and produces an add1-like table with likelihood ratio tests of each term.
ordinal::nominal_test(FINALsoc)
# Scale effects offer an alternative to nominal effects (partial proportional odds) when nonproportional odds structures are encountered in the data. Using scale effects is often a better approach because the model is well-defined for all values of the explanatory variables irrespective of translocation and scaling of covariates. Scale effects also use fewer parameters which often lead to more sensitive tests than nominal effects. Potential scale effects of variables already included in formula can be discovered using scale_test. This function adds each model term in formula to scale in turn and reports the likelihood ratio statistic in an add1 fashion.
ordinal::scale_test(FINALsoc)

Spacing among consecutive equidistant thresholds

drop(FINALsoc$tJac %*% coef(FINALsoc)[c("threshold.1", "spacing")])
##       1|2       2|3       3|4       4|5       5|6       6|7 
## 0.1118034 1.3233084 2.5348134 3.7463184 4.9578234 6.1693284

Model Parameters CI

confint(FINALsoc)
##                          2.5 %      97.5 %
## MaskScar            -0.1952647  0.05396665
## EmoHA                2.8900294  3.21914032
## EmoNE                1.4485280  1.75961374
## ActGenM             -0.2997424 -0.12824707
## generecatM           0.6725471  1.02358715
## EmoHA:generecatM    -0.9697208 -0.54476703
## EmoNE:generecatM    -0.6262909 -0.20338315
## MaskScar:generecatM -0.3844412 -0.04127853

Post Hoc

Simple Effects Emotion

(emmEmoSocial <- emmeans::emmeans(FINALsoc, pairwise ~ Emo))
## $emmeans
##  Emo emmean     SE  df asymp.LCL asymp.UCL
##  AN  -2.912 0.0490 Inf     -3.01    -2.816
##  HA  -0.237 0.0376 Inf     -0.31    -0.163
##  NE  -1.516 0.0410 Inf     -1.60    -1.435
## 
## Results are averaged over the levels of: Mask, ActGen, generecat 
## Results are given on the as.factor (not the response) scale. 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast estimate     SE  df z.ratio p.value
##  AN - HA     -2.68 0.0603 Inf -44.373 <.0001 
##  AN - NE     -1.40 0.0553 Inf -25.245 <.0001 
##  HA - NE      1.28 0.0547 Inf  23.385 <.0001 
## 
## Results are averaged over the levels of: Mask, ActGen, generecat 
## Note: contrasts are still on the as.factor scale 
## P value adjustment: tukey method for comparing a family of 3 estimates

Simple Effects Gender of Stimuli

(emmactSocial  <- emmeans::emmeans(FINALsoc, pairwise ~ ActGen))
## $emmeans
##  ActGen emmean     SE  df asymp.LCL asymp.UCL
##  F       -1.45 0.0345 Inf     -1.52     -1.38
##  M       -1.66 0.0357 Inf     -1.73     -1.59
## 
## Results are averaged over the levels of: Mask, Emo, generecat 
## Results are given on the as.factor (not the response) scale. 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast estimate     SE  df z.ratio p.value
##  F - M       0.214 0.0437 Inf 4.891   <.0001 
## 
## Results are averaged over the levels of: Mask, Emo, generecat 
## Note: contrasts are still on the as.factor scale

Simple Effects Gender of Participants

(emmgenSocial  <- emmeans::emmeans(FINALsoc, pairwise ~ generecat))
## $emmeans
##  generecat emmean     SE  df asymp.LCL asymp.UCL
##  F          -1.73 0.0366 Inf     -1.80     -1.66
##  M          -1.38 0.0337 Inf     -1.45     -1.31
## 
## Results are averaged over the levels of: Mask, Emo, ActGen 
## Results are given on the as.factor (not the response) scale. 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast estimate     SE  df z.ratio p.value
##  F - M      -0.351 0.0439 Inf -7.991  <.0001 
## 
## Results are averaged over the levels of: Mask, Emo, ActGen 
## Note: contrasts are still on the as.factor scale

Interaction Emotion * Gender of Participants

(emmemo.genSocial  <- emmeans::emmeans(FINALsoc, pairwise ~ Emo:generecat))
## $emmeans
##  Emo generecat emmean     SE  df asymp.LCL asymp.UCL
##  AN  F         -3.283 0.0653 Inf    -3.411    -3.155
##  HA  F         -0.229 0.0547 Inf    -0.336    -0.122
##  NE  F         -1.679 0.0569 Inf    -1.791    -1.568
##  AN  M         -2.541 0.0599 Inf    -2.659    -2.424
##  HA  M         -0.245 0.0515 Inf    -0.346    -0.144
##  NE  M         -1.352 0.0538 Inf    -1.458    -1.247
## 
## Results are averaged over the levels of: Mask, ActGen 
## Results are given on the as.factor (not the response) scale. 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast    estimate     SE  df z.ratio p.value
##  AN F - HA F  -3.0540 0.0840 Inf -36.378 <.0001 
##  AN F - NE F  -1.6037 0.0794 Inf -20.210 <.0001 
##  AN F - AN M  -0.7414 0.0783 Inf  -9.471 <.0001 
##  AN F - HA M  -3.0383 0.0822 Inf -36.975 <.0001 
##  AN F - NE M  -1.9304 0.0786 Inf -24.549 <.0001 
##  HA F - NE F   1.4503 0.0781 Inf  18.565 <.0001 
##  HA F - AN M   2.3126 0.0800 Inf  28.908 <.0001 
##  HA F - HA M   0.0157 0.0750 Inf   0.209 0.9999 
##  HA F - NE M   1.1237 0.0760 Inf  14.778 <.0001 
##  NE F - AN M   0.8623 0.0761 Inf  11.335 <.0001 
##  NE F - HA M  -1.4346 0.0761 Inf -18.851 <.0001 
##  NE F - NE M  -0.3267 0.0745 Inf  -4.388 0.0002 
##  AN M - HA M  -2.2970 0.0781 Inf -29.413 <.0001 
##  AN M - NE M  -1.1890 0.0751 Inf -15.831 <.0001 
##  HA M - NE M   1.1080 0.0739 Inf  14.989 <.0001 
## 
## Results are averaged over the levels of: Mask, ActGen 
## Note: contrasts are still on the as.factor scale 
## P value adjustment: tukey method for comparing a family of 6 estimates

Interaction Condition * Gender of Participants

(emmmask.genSocial  <- emmeans::emmeans(FINALsoc, pairwise ~ Mask:generecat))
## $emmeans
##  Mask generecat emmean     SE  df asymp.LCL asymp.UCL
##  Mask F          -1.69 0.0484 Inf     -1.79     -1.60
##  Scar F          -1.77 0.0485 Inf     -1.86     -1.67
##  Mask M          -1.24 0.0444 Inf     -1.32     -1.15
##  Scar M          -1.52 0.0459 Inf     -1.61     -1.43
## 
## Results are averaged over the levels of: Emo, ActGen 
## Results are given on the as.factor (not the response) scale. 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast        estimate     SE  df z.ratio p.value
##  Mask F - Scar F   0.0706 0.0636 Inf  1.111  0.6827 
##  Mask F - Mask M  -0.4572 0.0619 Inf -7.391  <.0001 
##  Mask F - Scar M  -0.1737 0.0622 Inf -2.793  0.0269 
##  Scar F - Mask M  -0.5278 0.0618 Inf -8.541  <.0001 
##  Scar F - Scar M  -0.2444 0.0621 Inf -3.934  0.0005 
##  Mask M - Scar M   0.2835 0.0602 Inf  4.708  <.0001 
## 
## Results are averaged over the levels of: Emo, ActGen 
## Note: contrasts are still on the as.factor scale 
## P value adjustment: tukey method for comparing a family of 4 estimates

Hierarchical Model Selection

null <- ordinal::clm(as.factor(soc) ~ 1 , data = cond, method = c("Newton"),  threshold="equidistant")
mask <- ordinal::clm(as.factor(soc) ~ Mask, data = cond, method = c("Newton"),  threshold="equidistant")
maskemo  <- ordinal::clm(as.factor(soc) ~ Mask + Emo, data = cond, method = c("Newton"),  threshold="equidistant")
maskemoact <- ordinal::clm(as.factor(soc) ~ Mask + Emo + ActGen, data = cond, method = c("Newton"),  threshold="equidistant")
maskemoactgen <- ordinal::clm(as.factor(soc) ~ Mask + Emo + ActGen + generecat, data = cond, method = c("Newton"),  threshold="equidistant")
maskemoactgen.emo <- ordinal::clm(as.factor(soc) ~ Mask + Emo + ActGen + generecat + Emo:generecat, data = cond, method = c("Newton"),  threshold="equidistant")
maskemoactgen.emogen.mask <- ordinal::clm(as.factor(soc) ~ Mask + Emo + ActGen + generecat + Emo:generecat + Mask:generecat, data = cond, method = c("Newton"),  threshold="equidistant")


Model <- c("null", "mask", "maskemo", "maskemoact", "maskemoactgen", "maskemoactgen.emo", "maskemoactgen.emogen.mask")

AIC <- c(AIC(null), AIC(mask), AIC(maskemo), AIC(maskemoact), AIC(maskemoactgen), AIC(maskemoactgen.emo), AIC(maskemoactgen.emogen.mask))

BIC <- c(BIC(null), BIC(mask), BIC(maskemo), BIC(maskemoact), BIC(maskemoactgen), BIC(maskemoactgen.emo), BIC(maskemoactgen.emogen.mask))

Nagelkerke_PseudoR2 <- c(rcompanion::nagelkerke(null)[["Pseudo.R.squared.for.model.vs.null"]][3], rcompanion::nagelkerke(mask)[["Pseudo.R.squared.for.model.vs.null"]][3], rcompanion::nagelkerke(maskemo)[["Pseudo.R.squared.for.model.vs.null"]][3], rcompanion::nagelkerke(maskemoact)[["Pseudo.R.squared.for.model.vs.null"]][3], rcompanion::nagelkerke(maskemoactgen)[["Pseudo.R.squared.for.model.vs.null"]][3], rcompanion::nagelkerke(maskemoactgen.emo)[["Pseudo.R.squared.for.model.vs.null"]][3], rcompanion::nagelkerke(maskemoactgen.emogen.mask)[["Pseudo.R.squared.for.model.vs.null"]][3])


(Lrtsoc <- cbind(Model, lmtest::lrtest(null, mask, maskemo, maskemoact, maskemoactgen, maskemoactgen.emo, maskemoactgen.emogen.mask), AIC, BIC, Nagelkerke_PseudoR2))

Categorization

Cross Tabulation & Chi-Square Test

cond$Emogen <- paste(cond$Emo,cond$generecat)
descr::CrossTable(cond$Emogen, cond$cat, digits = 2, sresid= T, asresid = T, expected = T, prop.r = T, prop.c = F, prop.t = F, prop.chisq = T,chisq = T, row.labels = T, format = "SPSS")
##    Cell Contents 
## |-------------------------|
## |                   Count | 
## |         Expected Values | 
## | Chi-square contribution | 
## |             Row Percent | 
## |            Std Residual | 
## |           Adj Std Resid | 
## |-------------------------|
## 
## ========================================================================================
##                   cond$cat
## cond$Emogen            AN       DI       FE        HA        NE       SA      SU   Total
## ----------------------------------------------------------------------------------------
## AN F                  803      160       62         2         0       31      70    1128
## expected           251.81    59.89    44.55    297.34    320.51    81.76   72.13        
## chisq             1206.52   167.33     6.83    293.35    320.51    31.51    0.06        
## row %               71.19    14.18     5.50      0.18      0.00     2.75    6.21   16.32
## std. res.           34.73    12.94     2.61    -17.13    -17.90    -5.61   -0.25        
## adj. std. res.      43.08    14.53     2.92    -21.82    -23.13    -6.37   -0.28        
## ----------------------------------------------------------------------------------------
## AN M                  735      150      115         3        49       41      83    1176
## expected           262.52    62.44    46.45    309.99    334.15    85.24   75.20        
## chisq              850.33   122.78   101.18    304.02    243.34    22.96    0.81        
## row %               62.50    12.76     9.78      0.26      4.17     3.49    7.06   17.01
## std. res.           29.16    11.08    10.06    -17.44    -15.60    -4.79    0.90        
## adj. std. res.      36.32    12.50    11.27    -22.30    -20.24    -5.46    1.02        
## ----------------------------------------------------------------------------------------
## HA F                    0        7        7       925        61       26     102    1128
## expected           251.81    59.89    44.55    297.34    320.51    81.76   72.13        
## chisq              251.81    46.71    31.65   1324.94    210.12    38.03   12.37        
## row %                0.00     0.62     0.62     82.00      5.41     2.30    9.04   16.32
## std. res.          -15.87    -6.83    -5.63     36.40    -14.50    -6.17    3.52        
## adj. std. res.     -19.68    -7.68    -6.28     46.37    -18.73    -7.00    3.97        
## ----------------------------------------------------------------------------------------
## HA M                    0        5        2       884       176        5     104    1176
## expected           262.52    62.44    46.45    309.99    334.15    85.24   75.20        
## chisq              262.52    52.84    42.53   1062.88     74.85    75.53   11.03        
## row %                0.00     0.43     0.17     75.17     14.97     0.43    8.84   17.01
## std. res.          -16.20    -7.27    -6.52     32.60     -8.65    -8.69    3.32        
## adj. std. res.     -20.18    -8.20    -7.30     41.70    -11.23    -9.91    3.77        
## ----------------------------------------------------------------------------------------
## NE F                    1       22       52         0       756      253      44    1128
## expected           251.81    59.89    44.55    297.34    320.51    81.76   72.13        
## chisq              249.81    23.97     1.25    297.34    591.70   358.65   10.97        
## row %                0.09     1.95     4.61      0.00     67.02    22.43    3.90   16.32
## std. res.          -15.81    -4.90     1.12    -17.24     24.32    18.94   -3.31        
## adj. std. res.     -19.60    -5.50     1.24    -21.97     31.43    21.50   -3.74        
## ----------------------------------------------------------------------------------------
## NE M                    4       23       35         8       922      145      39    1176
## expected           262.52    62.44    46.45    309.99    334.15    85.24   75.20        
## chisq              254.59    24.91     2.82    294.20   1034.15    41.90   17.43        
## row %                0.34     1.96     2.98      0.68     78.40    12.33    3.32   17.01
## std. res.          -15.96    -4.99    -1.68    -17.15     32.16     6.47   -4.17        
## adj. std. res.     -19.87    -5.63    -1.88    -21.94     41.72     7.38   -4.74        
## ----------------------------------------------------------------------------------------
## Total                1543      367      273      1822      1964      501     442    6912
## ========================================================================================
## 
## Statistics for All Table Factors
## 
## Pearson's Chi-squared test 
## ------------------------------------------------------------
## Chi^2 = 10373.04      d.f. = 30      p <2e-16 
## 
##         Minimum expected frequency: 44.55208

Psy Test Correlations

Database Import

setwd("C:/Users/Gallese/Desktop/Mask Survey/")
test_scoring <- readxl::read_excel("Scoring_EBLCOVID_last_1giugno2020.xlsx")
print(test_scoring)
## # A tibble: 98 x 10
##     Subj Q     paura_covid_tot ansia_salute_tot TAS_20_tot TAS_20_SUB1_des~
##    <dbl> <chr>           <dbl>            <dbl>      <dbl>            <dbl>
##  1     1 S                  17               37         65               20
##  2     2 S                   8               25         23                6
##  3     3 S                   7               25         74               20
##  4     4 S                   9               32         35               13
##  5     5 S                  14               28         29                5
##  6     6 S                   9               29         42               10
##  7     7 S                  15               27         29                7
##  8     8 F                  15               31         33               12
##  9     9 S                  11               34         37               10
## 10    10 F                   9               30         50               17
## # ... with 88 more rows, and 4 more variables: TAS_20_SUB2_identify <dbl>,
## #   TAS_20_SUB3_thinking <dbl>, IRI_EC <dbl>, IRI_PD <dbl>

Fear of COVID-19 Scale (Bonferroni correction 0.05/3 = 0.025) (Kendal Confidence Interval estimation based on Hollander, M., Wolfe, D. A., & Chicken, E. (2013). Nonparametric statistical methods (Vol. 751). John Wiley & Sons)

cor.test(test_scoring$paura_covid_tot, test_scoring$ansia_salute_tot, method = "kendal")
## 
##  Kendall's rank correlation tau
## 
## data:  test_scoring$paura_covid_tot and test_scoring$ansia_salute_tot
## z = 4.1798, p-value = 2.918e-05
## alternative hypothesis: true tau is not equal to 0
## sample estimates:
##       tau 
## 0.3010034
NSM3::kendall.ci(test_scoring$paura_covid_tot, test_scoring$ansia_salute_tot, type="t", bootstrap=F, B=1000)
## fANCOVA 0.5-1 loaded
## 
## 1 - alpha = 0.95 two-sided CI for tau:
## 0.181, 0.421
cor.test(test_scoring$paura_covid_tot, test_scoring$IRI_PD, method = "kendal")
## 
##  Kendall's rank correlation tau
## 
## data:  test_scoring$paura_covid_tot and test_scoring$IRI_PD
## z = 3.9022, p-value = 9.533e-05
## alternative hypothesis: true tau is not equal to 0
## sample estimates:
##       tau 
## 0.2837924
NSM3::kendall.ci(test_scoring$paura_covid_tot, test_scoring$IRI_PD, type="t", bootstrap=F, B=1000)
## 
## 1 - alpha = 0.95 two-sided CI for tau:
## 0.156, 0.411
cor.test(test_scoring$paura_covid_tot, test_scoring$IRI_EC, method = "kendal")  # n.s
## 
##  Kendall's rank correlation tau
## 
## data:  test_scoring$paura_covid_tot and test_scoring$IRI_EC
## z = 2.1946, p-value = 0.02819
## alternative hypothesis: true tau is not equal to 0
## sample estimates:
##      tau 
## 0.159501

ScatterPlot Fear of COVID-19 Scale * Health Anxiety Scale

ggstatsplot::ggscatterstats(
  data = test_scoring,
  x = paura_covid_tot,
  y = ansia_salute_tot,
  type = "nonparametric",
  xlab = "Fear of COVID-19 Scale",
  ylab = "Health Anxiety Scale",
  point.args = list(size = 5, alpha = 0.4),
  results.subtitle = FALSE,
  smooth.line.args = list(size = 1.5, color = "black"),
  ggstatsplot.layer = FALSE,
  marginal.type = "density",
  xfill = "grey30",
  yfill = "grey70",
  centrality.parameter = "median",
  centrality.label.args = list(size = 5),
  messages = FALSE,
  ggtheme = ggplot2::theme_classic(base_size=20))
## Registered S3 method overwritten by 'broom.mixed':
##   method      from 
##   tidy.gamlss broom

ScatterPlot Fear of COVID-19 Scale * Health Anxiety Scale

ggstatsplot::ggscatterstats(
  data = test_scoring,
  x = paura_covid_tot,
  y = IRI_PD,
  type = "nonparametric",
  xlab = "Fear of COVID-19 Scale",
  ylab = "IRI Personal Distress Subscale",
  point.args = list(size = 5, alpha = 0.4),
  results.subtitle = FALSE,
  smooth.line.args = list(size = 1.5, color = "black"),
  ggstatsplot.layer = FALSE,
  marginal.type = "density",
  xfill = "grey30",
  yfill = "grey70",
  centrality.parameter = "median",
  centrality.label.args = list(size = 5),
  messages = FALSE,
  ggtheme = ggplot2::theme_classic(base_size=20))

Health anxiety Scale (Bonferroni correction 0.05/6 = 0.008333333) (Kendal Confidence Interval estimation based on Hollander, M., Wolfe, D. A., & Chicken, E. (2013). Nonparametric statistical methods (Vol. 751). John Wiley & Sons)

cor.test(test_scoring$ansia_salute_tot, test_scoring$TAS_20_tot, method = "kendal")
## 
##  Kendall's rank correlation tau
## 
## data:  test_scoring$ansia_salute_tot and test_scoring$TAS_20_tot
## z = 3.4637, p-value = 0.0005328
## alternative hypothesis: true tau is not equal to 0
## sample estimates:
##      tau 
## 0.243811
NSM3::kendall.ci(test_scoring$ansia_salute_tot, test_scoring$TAS_20_tot, type="t", bootstrap=F, B=1000)
## 
## 1 - alpha = 0.95 two-sided CI for tau:
## 0.109, 0.378
cor.test(test_scoring$ansia_salute_tot, test_scoring$TAS_20_SUB1_describe, method = "kendal")
## 
##  Kendall's rank correlation tau
## 
## data:  test_scoring$ansia_salute_tot and test_scoring$TAS_20_SUB1_describe
## z = 2.7764, p-value = 0.005496
## alternative hypothesis: true tau is not equal to 0
## sample estimates:
##       tau 
## 0.1983113
NSM3::kendall.ci(test_scoring$ansia_salute_tot, test_scoring$TAS_20_SUB1_describe, type="t", bootstrap=F, B=1000)
## 
## 1 - alpha = 0.95 two-sided CI for tau:
## 0.063, 0.334
cor.test(test_scoring$ansia_salute_tot, test_scoring$TAS_20_SUB2_identify, method = "kendal")
## 
##  Kendall's rank correlation tau
## 
## data:  test_scoring$ansia_salute_tot and test_scoring$TAS_20_SUB2_identify
## z = 4.7677, p-value = 1.863e-06
## alternative hypothesis: true tau is not equal to 0
## sample estimates:
##       tau 
## 0.3403081
NSM3::kendall.ci(test_scoring$ansia_salute_tot, test_scoring$TAS_20_SUB2_identify, type="t", bootstrap=F, B=1000)
## 
## 1 - alpha = 0.95 two-sided CI for tau:
## 0.208, 0.473
cor.test(test_scoring$ansia_salute_tot, test_scoring$TAS_20_SUB3_thinking, method = "kendal")  # n.s
## 
##  Kendall's rank correlation tau
## 
## data:  test_scoring$ansia_salute_tot and test_scoring$TAS_20_SUB3_thinking
## z = 0.89989, p-value = 0.3682
## alternative hypothesis: true tau is not equal to 0
## sample estimates:
##       tau 
## 0.0642696
cor.test(test_scoring$ansia_salute_tot, test_scoring$IRI_PD, method = "kendal")
## 
##  Kendall's rank correlation tau
## 
## data:  test_scoring$ansia_salute_tot and test_scoring$IRI_PD
## z = 3.155, p-value = 0.001605
## alternative hypothesis: true tau is not equal to 0
## sample estimates:
##       tau 
## 0.2259924
NSM3::kendall.ci(test_scoring$ansia_salute_tot, test_scoring$IRI_PD, type="t", bootstrap=F, B=1000)
## 
## 1 - alpha = 0.95 two-sided CI for tau:
## 0.099, 0.353
cor.test(test_scoring$ansia_salute_tot, test_scoring$IRI_EC, method = "kendal")  # n.s
## 
##  Kendall's rank correlation tau
## 
## data:  test_scoring$ansia_salute_tot and test_scoring$IRI_EC
## z = 0.99274, p-value = 0.3208
## alternative hypothesis: true tau is not equal to 0
## sample estimates:
##        tau 
## 0.07106205

Bibliography

sessionInfo()
## R version 4.0.3 (2020-10-10)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 18362)
## 
## Matrix products: default
## 
## locale:
## [1] LC_COLLATE=English_United States.1252 
## [2] LC_CTYPE=English_United States.1252   
## [3] LC_MONETARY=English_United States.1252
## [4] LC_NUMERIC=C                          
## [5] LC_TIME=English_United States.1252    
## system code page: 65001
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
## [1] ggplot2_3.3.2
## 
## loaded via a namespace (and not attached):
##   [1] estimability_1.3          SparseM_1.78             
##   [3] descr_1.1.4               coda_0.19-4              
##   [5] tidyr_1.1.2               BSDA_1.2.0               
##   [7] Rfit_0.24.2               knitr_1.30               
##   [9] multcomp_1.4-14           data.table_1.13.0        
##  [11] rpart_4.1-15              inline_0.3.16            
##  [13] generics_0.0.2            waveslim_1.8.2           
##  [15] callr_3.5.0               cowplot_1.1.0            
##  [17] TH.data_1.0-10            combinat_0.0-8           
##  [19] correlation_0.4.0         httpuv_1.5.4             
##  [21] StanHeaders_2.21.0-6      assertthat_0.2.1         
##  [23] agricolae_1.3-3           WRS2_1.1-0               
##  [25] xfun_0.18                 hms_0.5.3                
##  [27] evaluate_0.14             promises_1.1.1           
##  [29] tidyBF_0.3.0              fansi_0.4.1              
##  [31] readxl_1.3.1              km.ci_0.5-2              
##  [33] htmlwidgets_1.5.2         reshape_0.8.8            
##  [35] kSamples_1.2-9            stats4_4.0.3             
##  [37] Rmpfr_0.8-1               paletteer_1.2.0          
##  [39] purrr_0.3.4               ellipsis_0.3.1           
##  [41] rcompanion_2.3.25         dplyr_1.0.2              
##  [43] backports_1.1.10          SemiPar_1.0-4.2          
##  [45] binom_1.1-1               V8_3.2.0                 
##  [47] insight_0.9.6             ggcorrplot_0.1.3         
##  [49] RcppParallel_5.0.2        libcoin_1.0-6            
##  [51] vctrs_0.3.4               quantreg_5.73            
##  [53] abind_1.4-5               withr_2.3.0              
##  [55] metaBMA_0.6.3             bdsmatrix_1.3-4          
##  [57] checkmate_2.0.0           emmeans_1.5.1            
##  [59] prettyunits_1.1.1         fastGHQuad_1.0           
##  [61] cluster_2.1.0             crayon_1.3.4             
##  [63] labeling_0.3              pkgconfig_2.0.3          
##  [65] SuppDists_1.1-9.5         ordinal_2019.12-10       
##  [67] nlme_3.1-149              statsExpressions_0.5.1   
##  [69] nnet_7.3-14               rlang_0.4.8              
##  [71] questionr_0.7.3           lifecycle_0.2.0          
##  [73] miniUI_0.1.1.1            LaplacesDemon_16.1.4     
##  [75] MatrixModels_0.4-1        sandwich_3.0-0           
##  [77] EMT_1.1                   cellranger_1.1.0         
##  [79] matrixStats_0.57.0        broomExtra_4.0.6         
##  [81] lmtest_0.9-38             np_0.60-10               
##  [83] Matrix_1.2-18             loo_2.3.1                
##  [85] mc2d_0.1-18               carData_3.0-4            
##  [87] boot_1.3-25               zoo_1.8-8                
##  [89] base64enc_0.1-3           processx_3.4.4           
##  [91] png_0.1-7                 PMCMRplus_1.5.1          
##  [93] parameters_0.8.6          rootSolve_1.8.2.1        
##  [95] ggExtra_0.9               stringr_1.4.0            
##  [97] multcompView_0.1-8        coin_1.3-1               
##  [99] readr_1.4.0               jpeg_0.1-8.1             
## [101] ggsignif_0.6.0            klaR_0.6-15              
## [103] scales_1.1.1              memoise_1.1.0            
## [105] magrittr_1.5              plyr_1.8.6               
## [107] compiler_4.0.3            rstantools_2.1.1         
## [109] bbmle_1.0.23.1            RColorBrewer_1.1-2       
## [111] ash_1.0-15                lme4_1.1-23              
## [113] cli_2.0.2                 pbapply_1.4-3            
## [115] ps_1.4.0                  TMB_1.7.18               
## [117] Brobdingnag_1.2-6         htmlTable_2.1.0          
## [119] Formula_1.2-3             MASS_7.3-53              
## [121] mgcv_1.8-33               tidyselect_1.1.0         
## [123] stringi_1.5.3             forcats_0.5.0            
## [125] highr_0.8                 yaml_2.2.1               
## [127] latticeExtra_0.6-29       ggrepel_0.8.2            
## [129] bridgesampling_1.0-0      grid_4.0.3               
## [131] polynom_1.4-0             tools_4.0.3              
## [133] lmom_2.8                  parallel_4.0.3           
## [135] rio_0.5.16                rstudioapi_0.11          
## [137] foreign_0.8-80            gridExtra_2.3            
## [139] cubature_2.0.4.1          ipmisc_4.0.0             
## [141] gld_2.6.2                 pairwiseComparisons_3.0.0
## [143] NSM3_1.15                 farver_2.0.3             
## [145] digest_0.6.25             shiny_1.5.0              
## [147] nortest_1.0-4             quadprog_1.5-8           
## [149] BWStest_0.2.2             Rcpp_1.0.5.2             
## [151] car_3.0-10                broom_0.7.1              
## [153] metafor_2.4-0             ez_4.4-0                 
## [155] BayesFactor_0.9.12-4.2    performance_0.5.0        
## [157] metaplus_0.7-11           later_1.1.0.1            
## [159] ucminf_1.1-4              effectsize_0.3.3         
## [161] colorspace_1.4-1          splines_4.0.3            
## [163] statmod_1.4.34            rematch2_2.1.2           
## [165] expm_0.999-5              conquer_1.0.2            
## [167] Exact_2.1                 MuMIn_1.43.17            
## [169] xtable_1.8-4              gmp_0.6-1                
## [171] jsonlite_1.7.1            nloptr_1.2.2.2           
## [173] AlgDesign_1.2.0           rstan_2.21.2             
## [175] zeallot_0.1.0             modeltools_0.2-23        
## [177] R6_2.4.1                  partitions_1.9-22        
## [179] broom.mixed_0.2.6         Hmisc_4.4-1              
## [181] pillar_1.4.6              htmltools_0.5.0          
## [183] mime_0.9                  glue_1.4.2               
## [185] fastmap_1.0.1             minqa_1.2.4              
## [187] class_7.3-17              codetools_0.2-16         
## [189] pkgbuild_1.1.0            mvtnorm_1.1-1            
## [191] utf8_1.1.4                lattice_0.20-41          
## [193] tibble_3.0.3              numDeriv_2016.8-1.1      
## [195] curl_4.3                  DescTools_0.99.38        
## [197] gtools_3.8.2              logspline_2.1.16         
## [199] zip_2.1.1                 openxlsx_4.2.2           
## [201] survival_3.2-7            rmarkdown_2.4            
## [203] munsell_0.5.0             e1071_1.7-3              
## [205] fANCOVA_0.5-1             labelled_2.7.0           
## [207] ggstatsplot_0.6.1         haven_2.3.1              
## [209] reshape2_1.4.4            gtable_0.3.0             
## [211] bayestestR_0.7.2
citation("lme4")
## 
## To cite lme4 in publications use:
## 
##   Douglas Bates, Martin Maechler, Ben Bolker, Steve Walker (2015).
##   Fitting Linear Mixed-Effects Models Using lme4. Journal of
##   Statistical Software, 67(1), 1-48. doi:10.18637/jss.v067.i01.
## 
## A BibTeX entry for LaTeX users is
## 
##   @Article{,
##     title = {Fitting Linear Mixed-Effects Models Using {lme4}},
##     author = {Douglas Bates and Martin M{\"a}chler and Ben Bolker and Steve Walker},
##     journal = {Journal of Statistical Software},
##     year = {2015},
##     volume = {67},
##     number = {1},
##     pages = {1--48},
##     doi = {10.18637/jss.v067.i01},
##   }
citation("car")
## 
## To cite the car package in publications use:
## 
##   John Fox and Sanford Weisberg (2019). An {R} Companion to Applied
##   Regression, Third Edition. Thousand Oaks CA: Sage. URL:
##   https://socialsciences.mcmaster.ca/jfox/Books/Companion/
## 
## A BibTeX entry for LaTeX users is
## 
##   @Book{,
##     title = {An {R} Companion to Applied Regression},
##     edition = {Third},
##     author = {John Fox and Sanford Weisberg},
##     year = {2019},
##     publisher = {Sage},
##     address = {Thousand Oaks {CA}},
##     url = {https://socialsciences.mcmaster.ca/jfox/Books/Companion/},
##   }
citation("MuMIn")
## 
## To cite package 'MuMIn' in publications use:
## 
##   Kamil Barton (2020). MuMIn: Multi-Model Inference. R package version
##   1.43.17. https://CRAN.R-project.org/package=MuMIn
## 
## A BibTeX entry for LaTeX users is
## 
##   @Manual{,
##     title = {MuMIn: Multi-Model Inference},
##     author = {Kamil Barton},
##     year = {2020},
##     note = {R package version 1.43.17},
##     url = {https://CRAN.R-project.org/package=MuMIn},
##   }
## 
## ATTENTION: This citation information has been auto-generated from the
## package DESCRIPTION file and may need manual editing, see
## 'help("citation")'.
citation("emmeans")
## 
## To cite package 'emmeans' in publications use:
## 
##   Russell Lenth (2020). emmeans: Estimated Marginal Means, aka
##   Least-Squares Means. R package version 1.5.1.
##   https://CRAN.R-project.org/package=emmeans
## 
## A BibTeX entry for LaTeX users is
## 
##   @Manual{,
##     title = {emmeans: Estimated Marginal Means, aka Least-Squares Means},
##     author = {Russell Lenth},
##     year = {2020},
##     note = {R package version 1.5.1},
##     url = {https://CRAN.R-project.org/package=emmeans},
##   }
citation("lmtest")
## 
## To cite lmtest in publications use:
## 
##   Achim Zeileis, Torsten Hothorn (2002). Diagnostic Checking in
##   Regression Relationships. R News 2(3), 7-10. URL
##   https://CRAN.R-project.org/doc/Rnews/
## 
## A BibTeX entry for LaTeX users is
## 
##   @Article{,
##     title = {Diagnostic Checking in Regression Relationships},
##     author = {Achim Zeileis and Torsten Hothorn},
##     journal = {R News},
##     year = {2002},
##     volume = {2},
##     number = {3},
##     pages = {7--10},
##     url = {https://CRAN.R-project.org/doc/Rnews/},
##   }
citation("ordinal")
## 
## To cite the ordinal-package in publications use:
## 
##   Christensen, R. H. B. (2019). ordinal - Regression Models for Ordinal
##   Data. R package version 2019.12-10.
##   https://CRAN.R-project.org/package=ordinal.
## 
## A BibTeX entry for LaTeX users is
## 
##   @Misc{,
##     title = {ordinal---Regression Models for Ordinal Data },
##     author = {R. H. B. Christensen},
##     year = {2019},
##     note = {R package version 2019.12-10. https://CRAN.R-project.org/package=ordinal},
##   }
citation("rcompanion")
## 
## To cite package 'rcompanion' in publications use:
## 
##   Salvatore Mangiafico (2020). rcompanion: Functions to Support
##   Extension Education Program Evaluation. R package version 2.3.25.
##   https://CRAN.R-project.org/package=rcompanion
## 
## A BibTeX entry for LaTeX users is
## 
##   @Manual{,
##     title = {rcompanion: Functions to Support Extension Education Program Evaluation},
##     author = {Salvatore Mangiafico},
##     year = {2020},
##     note = {R package version 2.3.25},
##     url = {https://CRAN.R-project.org/package=rcompanion},
##   }
citation("descr")
## 
## To cite package 'descr' in publications use:
## 
##   Jakson Aquino. Includes R source code and/or documentation written by
##   Dirk Enzmann, Marc Schwartz, Nitin Jain and Stefan Kraft (2018).
##   descr: Descriptive Statistics. R package version 1.1.4.
##   https://CRAN.R-project.org/package=descr
## 
## A BibTeX entry for LaTeX users is
## 
##   @Manual{,
##     title = {descr: Descriptive Statistics},
##     author = {Jakson Aquino. Includes R source code and/or documentation written by Dirk Enzmann and Marc Schwartz and Nitin Jain and Stefan Kraft},
##     year = {2018},
##     note = {R package version 1.1.4},
##     url = {https://CRAN.R-project.org/package=descr},
##   }
## 
## ATTENTION: This citation information has been auto-generated from the
## package DESCRIPTION file and may need manual editing, see
## 'help("citation")'.
citation("NSM3")
## 
## To cite package 'NSM3' in publications use:
## 
##   Grant Schneider, Eric Chicken and Rachel Becvarik (2020). NSM3:
##   Functions and Datasets to Accompany Hollander, Wolfe, and Chicken -
##   Nonparametric Statistical Methods, Third Edition. R package version
##   1.15. https://CRAN.R-project.org/package=NSM3
## 
## A BibTeX entry for LaTeX users is
## 
##   @Manual{,
##     title = {NSM3: Functions and Datasets to Accompany Hollander, Wolfe, and
## Chicken - Nonparametric Statistical Methods, Third Edition},
##     author = {Grant Schneider and Eric Chicken and Rachel Becvarik},
##     year = {2020},
##     note = {R package version 1.15},
##     url = {https://CRAN.R-project.org/package=NSM3},
##   }
## 
## ATTENTION: This citation information has been auto-generated from the
## package DESCRIPTION file and may need manual editing, see
## 'help("citation")'.
citation("effects")
## 
## To cite effects in publications use:
## 
##   John Fox and Sanford Weisberg (2019). An R Companion to Applied
##   Regression, 3rd Edition. Thousand Oaks, CA
##   <https://socialsciences.mcmaster.ca/jfox/Books/Companion/index.html>
## 
## For predictor effects or partial residuals also cite:
## 
##   John Fox, Sanford Weisberg (2018). Visualizing Fit and Lack of Fit in
##   Complex Regression Models with Predictor Effect Plots and Partial
##   Residuals. Journal of Statistical Software, 87(9), 1-27. URL
##   https://www.jstatsoft.org/article/view/v087i09.
## 
## For generalized linear models also cite:
## 
##   John Fox (2003). Effect Displays in R for Generalised Linear Models.
##   Journal of Statistical Software, 8(15), 1-27. URL
##   https://www.jstatsoft.org/article/view/v008i15.
## 
## For usage in multinomial and proportional-odds logit models also cite:
## 
##   John Fox, Jangman Hong (2009). Effect Displays in R for Multinomial
##   and Proportional-Odds Logit Models: Extensions to the effects
##   Package. Journal of Statistical Software, 32(1), 1-24. URL
##   https://www.jstatsoft.org/article/view/v032i01.
## 
## To see these entries in BibTeX format, use 'print(<citation>,
## bibtex=TRUE)', 'toBibtex(.)', or set
## 'options(citation.bibtex.max=999)'.
citation("Rmisc")
## 
## To cite package 'Rmisc' in publications use:
## 
##   Ryan M. Hope (2013). Rmisc: Rmisc: Ryan Miscellaneous. R package
##   version 1.5. https://CRAN.R-project.org/package=Rmisc
## 
## A BibTeX entry for LaTeX users is
## 
##   @Manual{,
##     title = {Rmisc: Rmisc: Ryan Miscellaneous},
##     author = {Ryan M. Hope},
##     year = {2013},
##     note = {R package version 1.5},
##     url = {https://CRAN.R-project.org/package=Rmisc},
##   }
## 
## ATTENTION: This citation information has been auto-generated from the
## package DESCRIPTION file and may need manual editing, see
## 'help("citation")'.
citation("ggplot2")
## 
## To cite ggplot2 in publications, please use:
## 
##   H. Wickham. ggplot2: Elegant Graphics for Data Analysis.
##   Springer-Verlag New York, 2016.
## 
## A BibTeX entry for LaTeX users is
## 
##   @Book{,
##     author = {Hadley Wickham},
##     title = {ggplot2: Elegant Graphics for Data Analysis},
##     publisher = {Springer-Verlag New York},
##     year = {2016},
##     isbn = {978-3-319-24277-4},
##     url = {https://ggplot2.tidyverse.org},
##   }
citation("ggsignif")
## 
## To cite package 'ggsignif' in publications use:
## 
##   Constantin Ahlmann-Eltze (2019). ggsignif: Significance Brackets for
##   'ggplot2'. R package version 0.6.0.
##   https://CRAN.R-project.org/package=ggsignif
## 
## A BibTeX entry for LaTeX users is
## 
##   @Manual{,
##     title = {ggsignif: Significance Brackets for 'ggplot2'},
##     author = {Constantin Ahlmann-Eltze},
##     year = {2019},
##     note = {R package version 0.6.0},
##     url = {https://CRAN.R-project.org/package=ggsignif},
##   }
citation("ggstatsplot")
## 
##   Patil, I. (2018). ggstatsplot: 'ggplot2' Based Plots with Statistical
##   Details. CRAN. Retrieved from
##   https://cran.r-project.org/web/packages/ggstatsplot/index.html
## 
## A BibTeX entry for LaTeX users is
## 
##   @Article{,
##     title = {{ggstatsplot}: 'ggplot2' Based Plots with Statistical Details},
##     author = {Indrajeet Patil},
##     year = {2018},
##     journal = {CRAN},
##     url = {https://CRAN.R-project.org/package=ggstatsplot},
##     doi = {10.5281/zenodo.2074621},
##   }