Predict Metric

Predict Metric

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

Next we’ll run the Bayesian model to analyze the cats

# 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  524

Uhm. That’s a lot of obscure output

Let’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      0.809

First, 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).

References

• Field, A. (2017). Discovering statistics using IBM SPSS statistics (5th edition). Thousand Oaks, CA: SAGE Publications.