Author: Daniel Lüdecke
Date: 2020-01-23

# Summary of Bayesian Models as HTML Table

#### Daniel Lüdecke

#### 2020-01-23

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(insight)
    library(httr)
    library(brms)

    # load 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()
    # )
    m1 <- insight::download_model("brms_zi_2")

    # 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)
    m2 <- insight::download_model("brms_mv_3")

## 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%)
Intercept | 0.43 | 0.21 – 1.06
persons | 2.31 | 1.70 – 2.99
child | 0.32 | 0.26 – 0.39
camper | 2.08 | 1.73 – 2.52
Random Effects
σ2 | -0.21
τ00 | 33.86
ICC | -0.01
N persons | 4
Observations | 250
Marginal R2 / Conditional R2 | 0.188 / 0.191

## 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 | 24.33 | 12.60 – 54.21 | -15.22 | -24.86 – 10.73
Age | -0.14 | -1.59 – 0.09 | 0.96 | 0.32 – 1.14
count | 0.00 | -0.00 – 0.00 |  |
Trt: Trt 1 |  |  | 0.90 | -0.85 – 3.11
Random Effects
σ2 | 132.04
τ00 | 1.28
ICC | 0.98
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 | 24.33 | 19.40 – 33.81 | 12.60 – 54.21 | -15.22 | -22.98 – -3.37 | -24.86 – 10.73
Age | -0.14 | -0.64 – 0.05 | -1.59 – 0.09 | 0.96 | 0.68 – 1.12 | 0.32 – 1.14
count | 0.00 | -0.00 – 0.00 | -0.00 – 0.00 |  |  |
Trt: Trt 1 |  |  |  | 0.90 | 0.41 – 1.49 | -0.85 – 3.11
Random Effects
σ2 | 133.64
τ00 | 1.37
ICC | 0.98
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,Base 2
--- | --- | ---
Predictors | Incidence Rate Ratios | CI (95%) | Estimates | CI (95%) | Response
Intercept | 0.43 | 0.21 – 1.06 | 24.33 | 12.60 – 54.21 | Base
Intercept | 0.43 | 0.21 – 1.06 | -15.22 | -24.86 – 10.73 | Base2
persons | 2.31 | 1.70 – 2.99 |  |  |
child | 0.32 | 0.26 – 0.39 |  |  |
camper | 2.08 | 1.73 – 2.52 |  |  |
Age |  |  | -0.14 | -1.59 – 0.09 | Base
count |  |  | 0.00 | -0.00 – 0.00 | Base
Age |  |  | 0.96 | 0.32 – 1.14 | Base2
Trt: Trt 1 |  |  | 0.90 | -0.85 – 3.11 | Base2
Random Effects
σ2 | -0.01 | 130.57
τ00 | 33.87 | 1.35
ICC | -0.00 | 0.98
N | 4 persons | 59 patient
Observations | 250 | 236
Marginal R2 / Conditional R2 | 0.188 / 0.191 | NA