Enjoy this brief demonstration of the predict metric module
First, we steal Field’s (2017) dancing cat example (please see Cats.R)
# Define data
data <- bfw::Cats
# Aggregate data
aggregate.data <- stats::aggregate(list(Ratings = data$Ratings),
by=list(Reward = data$Reward ,
Dance = data$Dance ,
Alignment = data$Alignment),
FUN=function(x) c(Mean = mean(x), SD = sd(x)))
# Describe data
describe.data <- psych::describe(data)[,c(2:5,10:12)]
describe.data
#> n mean sd median range skew kurtosis
#> Reward* 2000 1.81 0.39 2.00 1 -1.58 0.49
#> Dance* 2000 1.38 0.49 1.00 1 0.49 -1.76
#> Alignment* 2000 1.35 0.48 1.00 1 0.63 -1.61
#> Ratings 2000 3.37 1.92 2.69 6 0.38 -1.40
# Print data
print(aggregate.data, digits = 3)
#> Reward Dance Alignment Ratings.Mean Ratings.SD
#> 1 Food No Evil 5.078 0.991
#> 2 Affection No Evil 1.785 0.602
#> 3 Food Yes Evil 4.887 0.925
#> 4 Affection Yes Evil 1.692 0.604
#> 5 Food No Good 3.789 0.934
#> 6 Affection No Good 5.528 0.857
#> 7 Food Yes Good 3.898 1.097
#> 8 Affection Yes Good 5.734 0.809# Use the three categorical variables and mixed contrast.
mcmc <- bfw::bfw(project.data = data,
y = "Ratings",
x = "Reward,Dance,Alignment",
saved.steps = 50000,
jags.model = "metric",
run.contrasts = TRUE,
use.contrast = "mixed",
contrasts = "1,2,3",
jags.seed = 100,
silent = TRUE)
# ... and just show the most likely parameter estimate of effect sizes.
round(normal$summary.MCMC[grep("Effect size:",
rownames(normal$summary.MCMC)), c(2,5:7)],3)
# Median HDIlo HDIhi n
# Effect size: Food/Affection -0.832 -0.992 -0.667 2000
# Effect size: No/Yes -0.012 -0.163 0.148 2000
# Effect size: Evil/Good -1.600 -1.775 -1.419 2000
# Effect size: Food/Affection @ No -0.893 -1.151 -0.632 1240
# Effect size: Food vs. No/Yes -0.079 -0.248 0.100 380
# Effect size: Food/Affection vs. No/Yes -0.830 -1.015 -0.650 2000
# Effect size: Affection/Food vs. No/Yes 0.836 0.571 1.110 2000
# Effect size: Affection vs. No/Yes 0.035 -0.194 0.274 1620
# Effect size: Food/Affection @ Yes -0.773 -0.968 -0.582 760
# Effect size: Food/Affection @ Evil -4.007 -4.458 -3.541 1299
# Effect size: Food vs. Evil/Good -5.320 -5.696 -4.952 380
# Effect size: Food/Affection vs. Evil/Good -2.500 -2.811 -2.186 2000
# Effect size: Affection/Food vs. Evil/Good -0.725 -0.940 -0.506 2000
# Effect size: Affection vs. Evil/Good 1.134 0.882 1.393 1620
# Effect size: Food/Affection @ Good 1.911 1.663 2.154 701
# Effect size: No/Yes @ Evil 0.168 -0.082 0.401 1299
# Effect size: No vs. Evil/Good -1.445 -1.712 -1.169 1240
# Effect size: No/Yes vs. Evil/Good -1.573 -1.831 -1.323 2000
# Effect size: Yes/No vs. Evil/Good -1.631 -1.878 -1.380 2000
# Effect size: Yes vs. Evil/Good -1.752 -1.974 -1.532 760
# Effect size: No/Yes @ Good -0.164 -0.357 0.033 701
# Effect size: Food/Affection @ No @ Evil -3.971 -4.708 -3.192 1063
# Effect size: Food vs. No/Yes @ Evil 0.147 -0.148 0.442 230
# Effect size: Food/Affection vs. No/Yes @ Evil -3.969 -4.301 -3.634 1299
# Effect size: Food @ No vs. Evil/Good -5.040 -5.530 -4.549 100
# Effect size: Food/Affection @ No vs. Evil/Good -2.543 -2.964 -2.095 1240
# Effect size: Food vs. No/Yes vs. Evil/Good -5.530 -5.811 -5.253 380
# Effect size: Food/Affection vs. No/Yes vs. Evil/Good -2.381 -2.734 -1.999 2000
# Effect size: Affection/Food vs. No/Yes @ Evil 4.049 3.216 4.892 1299
# Effect size: Affection vs. No/Yes @ Evil 0.181 -0.153 0.508 1069
# Effect size: Affection/Food @ No vs. Evil/Good -0.499 -0.879 -0.135 1240
# Effect size: Affection @ No vs. Evil/Good 1.301 0.888 1.735 1140
# Effect size: Affection/Food vs. No/Yes vs. Evil/Good -0.735 -1.073 -0.376 2000
# Effect size: Affection vs. No/Yes vs. Evil/Good 1.103 0.709 1.494 1620
# Effect size: Food/Affection @ Yes @ Evil -4.059 -4.539 -3.586 236
# Effect size: Food vs. Yes/No vs. Evil/Good -5.120 -5.792 -4.475 380
# Effect size: Food/Affection vs. Yes/No vs. Evil/Good -2.636 -3.147 -2.119 2000
# Effect size: Food @ Yes vs. Evil/Good -5.624 -6.197 -5.065 280
# Effect size: Food/Affection @ Yes vs. Evil/Good -2.468 -2.913 -2.031 760
# Effect size: Affection/Food vs. Yes/No vs. Evil/Good -0.718 -0.944 -0.482 2000
# Effect size: Affection vs. Yes/No vs. Evil/Good 1.171 0.865 1.479 1620
# Effect size: Affection/Food @ Yes vs. Evil/Good -0.970 -1.157 -0.788 760
# Effect size: Affection @ Yes vs. Evil/Good 0.972 0.699 1.230 480
# Effect size: Food/Affection @ No @ Good 1.923 1.554 2.297 177
# Effect size: Food vs. No/Yes @ Good -0.242 -0.446 -0.036 150
# Effect size: Food/Affection vs. No/Yes @ Good 1.649 1.317 1.971 701
# Effect size: Affection/Food vs. No/Yes @ Good -2.209 -2.565 -1.843 701
# Effect size: Affection vs. No/Yes @ Good -0.102 -0.402 0.200 551
# Effect size: Food/Affection @ Yes @ Good 1.899 1.586 2.196 524Let’s try to break it down. For instance, the effect size is an approximation of Cohen’s d. Now, if we take a look at Effect size: Food/Affection vs. No/Yes vs. Evil/Good, it clearly indicate a large, negative effect of some sort. From the aggregate table at the beginning of the vignette, we can try to interpret the result.
# Let's print the aggregate table again.
print(aggregate.data, digits = 3)
#> Reward Dance Alignment Ratings.Mean Ratings.SD
#> 1 Food No Evil 5.078 0.991
#> 2 Affection No Evil 1.785 0.602
#> 3 Food Yes Evil 4.887 0.925
#> 4 Affection Yes Evil 1.692 0.604
#> 5 Food No Good 3.789 0.934
#> 6 Affection No Good 5.528 0.857
#> 7 Food Yes Good 3.898 1.097
#> 8 Affection Yes Good 5.734 0.809First, we can see that regardless of whether the evil cats dance or not, they prefer food (M = 4.98) as reward over affection (M = 1.73). Second we can see that good cats prefer affection (M = 5.63) over food (M = 2.43). Furthermore, we can also infer that evil cats that dance (M = 2.02) rate their owners about the same as evil cats that do not dance (M = 2.11). Good cats, similarly have fairly equal ratings regardless of whether they dance (M = 2.88) or not (M = 2.77). Finally, evil cats (M = 2.07) rate their owners somewhat lower than good cats (M = 2.83), as seen by Effect size: Evil/Good = -1.60.
From the results we can claim that evil cats, in general, rate their owners higher if they get food rather than affection (d = -4.01), and that the opposite is true for good cats (d = -1.91).
Please note that by conducting mixed contrasts results will include both between and within contrasts, in addition to any possible combination (including ones that does not necessarily give any meaning).