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)
options(brms.backend = "cmdstanr")
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 mean(+1) 0.004 -0.0059
[-0.378, 0.387] [-0.0080, -0.0037]
PClass mean(2nd) - mean(1st) 0.0016 -0.19
[-0.3941, 0.3960] [-0.27, -0.12]
PClass mean(3rd) - mean(1st) 0.005 -0.38
[-0.383, 0.402] [-0.45, -0.31]
SexCode mean(1) - mean(0) -0.0013 0.49
[-0.3910, 0.3884] [0.43, 0.55] 
draws <- lapply(names(cmp), \(x) transform(posteriordraws(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 <- posteriordraws(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        
 Min.   :-3.397e-03   Min.   :-0.8089043   Min.   :0.0000085  
 1st Qu.: 0.000e+00   1st Qu.:-0.3127726   1st Qu.:0.0174662  
 Median : 0.000e+00   Median :-0.1015558   Median :0.0994095  
 Mean   : 6.530e-06   Mean   :-0.2002571   Mean   :0.2011653  
 3rd Qu.: 0.000e+00   3rd Qu.:-0.0168535   3rd Qu.:0.3291096  
 Max.   : 4.388e-03   Max.   :-0.0000266   Max.   :0.8221026  
  predicted_lo        predicted_hi         predicted            tmp_idx     
 Min.   :0.000e+00   Min.   :0.000e+00   Min.   :0.000e+00   Min.   :  1.0  
 1st Qu.:0.000e+00   1st Qu.:0.000e+00   1st Qu.:0.000e+00   1st Qu.:189.8  
 Median :1.865e-05   Median :2.029e-05   Median :1.865e-05   Median :378.5  
 Mean   :1.582e-02   Mean   :1.570e-02   Mean   :1.569e-02   Mean   :378.5  
 3rd Qu.:2.232e-03   3rd Qu.:2.604e-03   3rd Qu.:2.324e-03   3rd Qu.:567.2  
 Max.   :1.983e-01   Max.   :1.983e-01   Max.   :1.983e-01   Max.   :756.0  
    PClass             SexCode           Age       
 Length:4536        Min.   :0.000   Min.   : 0.17  
 Class :character   1st Qu.:0.000   1st Qu.:21.00  
 Mode  :character   Median :0.000   Median :28.00  
                    Mean   :0.381   Mean   :30.40  
                    3rd Qu.:1.000   3rd Qu.:39.00  
                    Max.   :1.000   Max.   :71.00  
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          predicted_lo    
 Min.   :-0.1400135   Min.   :-0.217763   Min.   :-0.067315   Min.   :0.02483  
 1st Qu.:-0.0122534   1st Qu.:-0.043127   1st Qu.:-0.008258   1st Qu.:0.21587  
 Median : 0.0005224   Median :-0.008488   Median : 0.005366   Median :0.29646  
 Mean   :-0.0001023   Mean   :-0.035289   Mean   : 0.035449   Mean   :0.33291  
 3rd Qu.: 0.0260982   3rd Qu.: 0.010511   3rd Qu.: 0.093869   3rd Qu.:0.45905  
 Max.   : 0.1379084   Max.   : 0.049241   Max.   : 0.223777   Max.   :0.89539  
  predicted_hi       predicted          tmp_idx         PClass         
 Min.   :0.02703   Min.   :0.02515   Min.   :  1.0   Length:4536       
 1st Qu.:0.22474   1st Qu.:0.21587   1st Qu.:189.8   Class :character  
 Median :0.31442   Median :0.29885   Median :378.5   Mode  :character  
 Mean   :0.33293   Mean   :0.33291   Mean   :378.5                     
 3rd Qu.:0.41974   3rd Qu.:0.44152   3rd Qu.:567.2                     
 Max.   :0.90783   Max.   :0.89539   Max.   :756.0                     
    SexCode           Age       
 Min.   :0.000   Min.   : 0.17  
 1st Qu.:0.000   1st Qu.:21.00  
 Median :0.000   Median :28.00  
 Mean   :0.381   Mean   :30.40  
 3rd Qu.:1.000   3rd Qu.:39.00  
 Max.   :1.000   Max.   :71.00

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.