Prior Predictive Checks with marginaleffects and brms

Author

Vincent Arel-Bundock

Published

May 1, 2023

Bayesians often advocate for the use of prior predictive checks (Gelman et al. 2020). The idea is to simulate from the model, without using the data, in order to refine the model before fitting. For example, we could draw parameter values from the priors, and use the model to simulate values of the outcome. Then, could inspect those to determine if the simulated outcomes (and thus the priors) make sense substantively. Prior predictive checks allow us to iterate on the model without looking at the data multiple times.

One major challenge lies in interpretation: When the parameters of a model are hard to interpret, the analyst will often need to transform before they can assess if the generated quantities make sense, and if the priors are an appropriate representation of available information.

In this post I show how to use the marginaleffects and brms packages for R to facilitate this process. The benefit of the approach described below is that it allows us to conduct prior predictive checks on the actual quantities of interest. For example, if the ultimate quantity that we want to estimate is a contrast or an Average Treatment Effect, then we can use marginaleffects to simulate the specific quantity of interest using just the priors and the model.

In this example, we create two model objects with brms. In one of them, we set sample_prior="only" to indicate that we do not want to use the dataset at all, and that we only want to use the priors and model for simulation:

library(brms)
library(ggplot2)
library(marginaleffects)
library(modelsummary)
theme_set(theme_minimal())

titanic <- read.csv("https://vincentarelbundock.github.io/Rdatasets/csv/Stat2Data/Titanic.csv")
titanic <- subset(titanic, PClass != "*")

f <- Survived ~ SexCode + Age + PClass

mod_prior <- brm(f,
    data = titanic,
    prior = c(prior(normal(0, .2), class = b)),
    cores = 4,
    sample_prior = "only")

mod_posterior <- brm(f,
    data = titanic,
    cores = 4,
    prior = c(prior(normal(0, .2), class = b)))

Now, we use the avg_comparisons() function from the marginaleffects package to compute contrasts of interest:

cmp <- list(
    "Prior" = avg_comparisons(mod_prior),
    "Posterior" = avg_comparisons(mod_posterior))

Finally, we compare the results with and without the data in tables and plots:

modelsummary(
    cmp,
    output = "markdown",
    statistic = "conf.int",
    fmt = fmt_significant(2),
    gof_map = NA,
    shape = term : contrast ~ model)
Prior Posterior
Age +1 0.0024 -0.0058
[-0.3810, 0.4155] [-0.0079, -0.0037]
PClass 2nd - 1st 0.0031 -0.19
[-0.3940, 0.3917] [-0.27, -0.12]
PClass 3rd - 1st 0.0021 -0.38
[-0.3714, 0.3794] [-0.45, -0.31]
SexCode 1 - 0 0.00077 0.49
[-0.39562, 0.39821] [0.44, 0.55] 
draws <- lapply(names(cmp), \(x) transform(get_draws(cmp[[x]]), Label = x))
draws <- do.call("rbind", draws)

ggplot(draws, aes(x = draw, color = Label)) +
    xlim(c(-1, 1)) +
    geom_density() +
    facet_wrap(~term + contrast, scales = "free")

This kind of approach is particularly useful with more complicated models, such as this one with categorical outcomes. In such models, it would be hard to know if a normal prior is appropriate for the different parameters:

modcat_posterior <- brm(
    PClass ~ SexCode + Age,
    prior = c(
        prior(normal(0, 3), class = b, dpar = "mu2nd"),
        prior(normal(0, 3), class = b, dpar = "mu3rd")),
    family = categorical(link = logit),
    cores = 4,
    data = titanic)

modcat_prior <- brm(
    PClass ~ SexCode + Age,
    prior = c(
        prior(normal(0, 3), class = b, dpar = "mu2nd"),
        prior(normal(0, 3), class = b, dpar = "mu3rd")),
    family = categorical(link = logit),
    sample_prior = "only",
    cores = 4,
    data = titanic)
pd <- get_draws(comparisons(modcat_prior))

comparisons(modcat_prior) |> summary()
     rowid           term              group             contrast        
 Min.   :  1.0   Length:4536        Length:4536        Length:4536       
 1st Qu.:189.8   Class :character   Class :character   Class :character  
 Median :378.5   Mode  :character   Mode  :character   Mode  :character  
 Mean   :378.5                                                           
 3rd Qu.:567.2                                                           
 Max.   :756.0                                                           
                                                                         
    estimate             conf.low            conf.high            rownames     
 Min.   :-5.676e-03   Min.   :-8.209e-01   Min.   :1.169e-05   Min.   :   1.0  
 1st Qu.: 0.000e+00   1st Qu.:-3.574e-01   1st Qu.:1.711e-02   1st Qu.: 248.8  
 Median : 0.000e+00   Median :-9.820e-02   Median :9.987e-02   Median : 523.0  
 Mean   :-3.748e-06   Mean   :-2.047e-01   Mean   :2.049e-01   Mean   : 520.5  
 3rd Qu.: 0.000e+00   3rd Qu.:-1.746e-02   3rd Qu.:3.414e-01   3rd Qu.: 746.2  
 Max.   : 4.333e-03   Max.   :-1.609e-05   Max.   :8.423e-01   Max.   :1313.0  
                                                                               
     Name              PClass               Age            Sex           
 Length:4536        Length:4536        Min.   : 0.17   Length:4536       
 Class :character   Class :character   1st Qu.:21.00   Class :character  
 Mode  :character   Mode  :character   Median :28.00   Mode  :character  
                                       Mean   :30.40                     
                                       3rd Qu.:39.00                     
                                       Max.   :71.00                     
                                                                         
    Survived        SexCode       predicted_lo        predicted_hi      
 Min.   :0.000   Min.   :0.000   Min.   :0.000e+00   Min.   :0.000e+00  
 1st Qu.:0.000   1st Qu.:0.000   1st Qu.:4.000e-09   1st Qu.:4.000e-09  
 Median :0.000   Median :0.000   Median :1.408e-05   Median :1.503e-05  
 Mean   :0.414   Mean   :0.381   Mean   :1.572e-02   Mean   :1.546e-02  
 3rd Qu.:1.000   3rd Qu.:1.000   3rd Qu.:2.794e-03   3rd Qu.:2.853e-03  
 Max.   :1.000   Max.   :1.000   Max.   :1.804e-01   Max.   :1.804e-01  
                                                                        
   predicted       tmp_idx     
 Min.   : NA    Min.   :  1.0  
 1st Qu.: NA    1st Qu.:189.8  
 Median : NA    Median :378.5  
 Mean   :NaN    Mean   :378.5  
 3rd Qu.: NA    3rd Qu.:567.2  
 Max.   : NA    Max.   :756.0  
 NA's   :4536                  
comparisons(modcat_posterior) |> summary()
     rowid           term              group             contrast        
 Min.   :  1.0   Length:4536        Length:4536        Length:4536       
 1st Qu.:189.8   Class :character   Class :character   Class :character  
 Median :378.5   Mode  :character   Mode  :character   Mode  :character  
 Mean   :378.5                                                           
 3rd Qu.:567.2                                                           
 Max.   :756.0                                                           
                                                                         
    estimate             conf.low           conf.high            rownames     
 Min.   :-0.1413142   Min.   :-0.216622   Min.   :-0.065444   Min.   :   1.0  
 1st Qu.:-0.0122733   1st Qu.:-0.039035   1st Qu.:-0.008223   1st Qu.: 248.8  
 Median : 0.0005478   Median :-0.008381   Median : 0.005259   Median : 523.0  
 Mean   :-0.0001095   Mean   :-0.034000   Mean   : 0.035321   Mean   : 520.5  
 3rd Qu.: 0.0263220   3rd Qu.: 0.010666   3rd Qu.: 0.092674   3rd Qu.: 746.2  
 Max.   : 0.1392075   Max.   : 0.054036   Max.   : 0.226326   Max.   :1313.0  
                                                                              
     Name              PClass               Age            Sex           
 Length:4536        Length:4536        Min.   : 0.17   Length:4536       
 Class :character   Class :character   1st Qu.:21.00   Class :character  
 Mode  :character   Mode  :character   Median :28.00   Mode  :character  
                                       Mean   :30.40                     
                                       3rd Qu.:39.00                     
                                       Max.   :71.00                     
                                                                         
    Survived        SexCode       predicted_lo      predicted_hi    
 Min.   :0.000   Min.   :0.000   Min.   :0.02479   Min.   :0.02696  
 1st Qu.:0.000   1st Qu.:0.000   1st Qu.:0.21608   1st Qu.:0.22366  
 Median :0.000   Median :0.000   Median :0.29571   Median :0.31335  
 Mean   :0.414   Mean   :0.381   Mean   :0.33301   Mean   :0.33288  
 3rd Qu.:1.000   3rd Qu.:1.000   3rd Qu.:0.45999   3rd Qu.:0.42046  
 Max.   :1.000   Max.   :1.000   Max.   :0.89623   Max.   :0.90880  
                                                                    
   predicted       tmp_idx     
 Min.   : NA    Min.   :  1.0  
 1st Qu.: NA    1st Qu.:189.8  
 Median : NA    Median :378.5  
 Mean   :NaN    Mean   :378.5  
 3rd Qu.: NA    3rd Qu.:567.2  
 Max.   : NA    Max.   :756.0  
 NA's   :4536

References

Gelman, Andrew, Aki Vehtari, Daniel Simpson, Charles C. Margossian, Bob Carpenter, Yuling Yao, Lauren Kennedy, Jonah Gabry, Paul-Christian Bürkner, and Martin Modrák. 2020. “Bayesian Workflow.” https://arxiv.org/abs/2011.01808.