Anova-Freak and Bayesian Hipster #rstats

[This article was first published on R – Strenge Jacke!, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

I’m pleased to announce an update of my sjstats-package. New features are specifically implemented for the Anova and Bayesian statistic and summary functions. Here’s a short overview of what’s new…

Anova statistics

Beside the already implemented functions to calculate eta-squared, partial eta-squared and omega-squared, it is now also possible to calculate partial omega-squared statistics for Anova-tables.

library(sjstats)
<span style="color:#999999;"># load sample data</span>
data(efc)

<span style="color:#999999;"># fit linear model</span>
fit <- aov(
  c12hour ~ as.factor(e42dep) + as.factor(c172code) + c160age,
  data = efc
)

omega_sq(fit, partial = TRUE)
<span style="color:#999999;">#> # A tibble: 3 x 2
#>   term                partial.omegasq
#> 1 as.factor(e42dep)           0.278  
#> 2 as.factor(c172code)         0.00547
#> 3 c160age                     0.0649</span>

Furthermore, eta_sq() and omega_sq() have a ci.lvl-argument, which – if not NULL – also computes a confidence interval.

For eta-squared, i.e. eta_sq() with partial = FALSE, due to non-symmetry, confidence intervals are based on bootstrap-methods. Confidence intervals for partial omega-squared, i.e. omega_sq() with partial = TRUE – are also based on bootstrapping. In these cases, n indicates the number of bootstrap samples to be drawn to compute the confidence intervals.

eta_sq(fit, partial = TRUE, ci.lvl = .8)
<span style="color:#999999;">#> # A tibble: 3 x 4
#>   term                partial.etasq conf.low conf.high
#> 1 as.factor(e42dep)         0.281    0.247      0.310 
#> 2 as.factor(c172code)       0.00788  0.00109    0.0160
#> 3 c160age                   0.0665   0.0467     0.0885</span>

Bayiasian statistics and summaries

Some of the summary-functions for Bayesian models were polished in the current update, e.g. hdi(). Let’s fit a (non-sense) model with the great brms-package first (you’ll see later why I don’t use rstanarm here):

library(lme4)
library(brms)
library(dplyr)
data(sleepstudy)

sleepstudy$mygrp <- sample(1:5, size = 180, replace = TRUE)
sleepstudy %
  group_by(mygrp) %>%
  mutate(mysubgrp = sample(1:30, size = n(), replace = TRUE))

m <- brm(
  Reaction ~ Days + (1 | mygrp / mysubgrp) + (1 | Subject),
  data = sleepstudy
)

Highest Density Intervals

hdi() calculates by default the 89% HDI for Bayesian regression models:

hdi(m)
<span style="color:#999999;">#> # A tibble: 3 x 3
#>   term        hdi.low hdi.high
#> 1 b_Intercept  232.00    268.0
#> 2 b_Days         9.15     11.8
#> 3 sigma         27.20     33.5</span>

Now you can calculate the HDI for multiple tresholds (probabilities) at once, using the prob-argument:

hdi(m, prob = c(.5, .8, .95))
<span style="color:#999999;">#> # A tibble: 3 x 7
#>   term        hdi.low_0.5 hdi.high_0.5 hdi.low_0.8 hdi.high_0.8 hdi.low_0.95 hdi.high_0.95
#> 1 b_Intercept      244.00        258.0      237.00        265.0       229.00         274.0
#> 2 b_Days             9.97         11.1        9.51         11.6         8.90          12.1
#> 3 sigma             28.90         31.5       27.60         32.5        26.60          33.8</span>

Tidy summary

A tidy summary, similar to the tidy()-function from the broom-package, can be obtained with tidy_stan(). By default, for multilevel models, this function only shows the fixed effects. Use the different options from the type-argument if you want random effects only or both random and fixed effects to be printed.

tidy_stan(m)
<span style="color:#999999;">#> # A tibble: 3 x 8
#>   term        estimate std.error hdi.low hdi.high n_eff  Rhat   mcse
#> 1 b_Intercept    250.0    10.900  233.00    268.0 0.326  1.00  0.312 
#> 2 b_Days          10.6     0.835    9.18     11.8 1.000  1.00  0.013
#> 3 sigma           30.2     1.930   27.30     33.4 1.000  1.00  0.202 </span>

Intraclass Correlation Coefficient (ICC)

The ICC is a useful statistic for random-intercept models, which describes the proportion of variance that is explained by the random effects structure (see ?icc for more details). The ICC is based on the variance and correlation components of the model, which you typically get with the VarCorr function. According to the brms-package, there’s a good and a bad news: from a developers perspective, the „bad“ news is that VarCorr.brmsfit has recently changed in its internal code structure, so I had to revise my icc()-function to work with brms-models again, with success:

icc(m)
<span style="color:#999999;">#> Bayesian mixed model
#>  Family: gaussian (identity)
#> Formula: list() Reaction ~ Days + (1 | mygrp/mysubgrp) + (1 | Subject) list()
#> 
#>            ICC (mygrp): 0.032317
#>   ICC (mygrp:mysubgrp): 0.013529
#>          ICC (Subject): 0.598439</span>

The good news is, that VarCorr.brmsfit has recently changed in its internal code structure. Now it is also possible to get the variance and correlation components for each sample of the model, which allows us to compute the ICC for each sample of the model, which again in turn allows us to compute an ICC including uncertainty intervals very quickly – simply add posterior = TRUE to the icc()-function call:

icc(m, posterior = TRUE)
<span style="color:#999999;">#> <em># Random Effect Variances and ICC</em>
#> 
#> Family: gaussian (identity)
#> Formula: Reaction ~ Days + (1 | mygrp/mysubgrp) + (1 | Subject)
#> 
#> <span style="color:#333399;">## mygrp</span>
#>           ICC: 0.022 (HDI 89%: 0.000-0.104)
#> Between-group: 57.406 (HDI 89%: 0.000-277.588)
#> 
#> <span style="color:#339966;">## mygrp:mysubgrp</span>
#>           ICC: 0.011 (HDI 89%: 0.000-0.050)
#> Between-group: 28.535 (HDI 89%: 0.000-127.271)
#> 
#> <span style="color:#993399;">## Subject</span>
#>           ICC: 0.578 (HDI 89%: 0.419-0.737)
#> Between-group: 1449.446 (HDI 89%: 682.362-2413.380)
#> 
#> <span style="color:#993333;">## Residuals</span>
#> Within-group: 909.039 (HDI 89%: 722.154-1085.644)</span>

By default, the 89% interval around the ICC „point estimate“ is shown in the output, however, the print()-method has an argument to change the interval range to any value, e.g.
print(icc(m, posterior = TRUE), prob = .5, digits = 2).

Final words

The colored output above is not just playing with CSS, the R console output is indeed colored! ?

To leave a comment for the author, please follow the link and comment on their blog: R – Strenge Jacke!.

R-bloggers.com offers daily e-mail updates about R news and tutorials about learning R and many other topics. Click here if you're looking to post or find an R/data-science job.
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

Never miss an update!
Subscribe to R-bloggers to receive
e-mails with the latest R posts.
(You will not see this message again.)

Click here to close (This popup will not appear again)