Summary of Bayesian Models as HTML Table

Daniel Lüdecke

2024-08-28

## Install package "strengejacke" from GitHub (`devtools::install_github("strengejacke/strengejacke")`) to load all sj-packages at once!

## Loading required package: Rcpp

## Loading 'brms' package (version 2.21.0). Useful instructions
## can be found by typing help('brms'). A more detailed introduction
## to the package is available through vignette('brms_overview').

## 
## Attaching package: 'brms'

## The following object is masked from 'package:stats':
## 
##     ar

This vignette shows examples for using tab_model() to create HTML tables for mixed models. Basically, tab_model() behaves in a very similar way for mixed models as for other, simple regression models, as shown in this vignette.

# load required packages
library(sjPlot)
library(brms)

# sample models
zinb <- read.csv("http://stats.idre.ucla.edu/stat/data/fish.csv")
set.seed(123)
m1 <- brm(bf(
    count ~ persons + child + camper + (1 | persons),
    zi ~ child + camper + (1 | persons)
  ),
  data = zinb,
  family = zero_inflated_poisson()
)

data(epilepsy)
set.seed(123)
epilepsy$visit <- as.numeric(epilepsy$visit)
epilepsy$Base2 <- sample(epilepsy$Base, nrow(epilepsy), replace = TRUE)
f1 <- bf(Base ~ zAge + count + (1 |ID| patient))
f2 <- bf(Base2 ~ zAge + Trt + (1 |ID| patient))
m2 <- brm(f1 + f2 + set_rescor(FALSE), data = epilepsy)

Bayesian models summaries as HTML table

For Bayesian regression models, some of the differences to the table output from simple models or mixed models of tab_models() are the use of Highest Density Intervals instead of confidence intervals, the Bayes-R-squared values, and a different “point estimate” (which is, by default, the median from the posterior draws).

tab_model(m1)

	count
Predictors	Incidence Rate Ratios	CI (95%)
Count Model
Intercept	0.42	0.22 – 0.88
persons	2.32	1.86 – 2.93
child	0.32	0.26 – 0.38
camper	2.08	1.73 – 2.53
Zero-Inflated Model
Intercept	0.52	0.11 – 2.21
child	6.44	3.46 – 12.95
camper	0.43	0.21 – 0.87
Random Effects
σ2	5.21
τ00	33.72
ICC	0.13
N persons	4
Observations	250
Marginal R2 / Conditional R2	0.186 / 0.248

Multivariate response models

For multivariate response models, like mediator-analysis-models, it is recommended to print just one model in the table, as each regression is displayed as own “model” in the output.

tab_model(m2)

	Base		Base2
Predictors	Estimates	CI (95%)	Estimates	CI (95%)
Intercept	28.61	11.35 – 34.20	26.61	11.24 – 29.03
zAge	-4.85	-5.42 – -1.76	1.21	-0.31 – 2.15
count	0.00	-0.00 – 0.00
Trt: Trt1			-0.32	-4.36 – 1.43
Random Effects
σ2	54.29
τ00	4.54
ICC	0.96
N patient	59
Observations	236

Show two Credible Interval-column

To show a second CI-column, use show.ci50 = TRUE.

tab_model(m2, show.ci50 = TRUE)

	Base			Base2
Predictors	Estimates	CI (50%)	CI (95%)	Estimates	CI (50%)	CI (95%)
Intercept	28.61	24.07 – 30.23	11.35 – 34.20	26.61	21.53 – 28.45	11.24 – 29.03
zAge	-4.85	-5.17 – -3.89	-5.42 – -1.76	1.21	0.74 – 1.54	-0.31 – 2.15
count	0.00	-0.00 – 0.00	-0.00 – 0.00
Trt: Trt1				-0.32	-1.91 – 0.69	-4.36 – 1.43
Random Effects
σ2	54.49
τ00	3.96
ICC	0.96
N patient	59
Observations	236

Mixing multivariate and univariate response models

When both multivariate and univariate response models are displayed in one table, a column Response is added for the multivariate response model, to indicate the different outcomes.

tab_model(m1, m2)

	count		Base, Base2
Predictors	Incidence Rate Ratios	CI (95%)	Estimates	CI (95%)	Response
Intercept	0.42	0.22 – 0.88	28.61	11.35 – 34.20	Base
Intercept	0.42	0.22 – 0.88	26.61	11.24 – 29.03	Base2
persons	2.32	1.86 – 2.93
child	0.32	0.26 – 0.38
camper	2.08	1.73 – 2.53
zAge			-4.85	-5.42 – -1.76	Base
count			0.00	-0.00 – 0.00	Base
zAge			1.21	-0.31 – 2.15	Base2
Trt: Trt1			-0.32	-4.36 – 1.43	Base2
Zero-Inflated Model
Intercept	0.52	0.11 – 2.21
child	6.44	3.46 – 12.95
camper	0.43	0.21 – 0.87
Random Effects
σ2	5.49		55.22
τ00	33.50		4.43
ICC	0.14		0.96
N	4 persons		59 patient
Observations	250		236
Marginal R2 / Conditional R2	0.186 / 0.248		NA