I’m working my way through the exercises in Richard McElreath’s Statistical Rethinking. In one exercise, the ask is to replicate a model from the chapter and then re-estimate with new priors. The original model can be fit in {brms} as follows:
# remotes::install_github("rmcelreath/rethinking")
library(rethinking)
library(brms)
data(tulips)
d <- tulips
d$blooms_std <- d$blooms / max(d$blooms)
d$water_cent <- d$water - mean(d$water)
d$shade_cent <- d$shade - mean(d$shade)
mod <- brm(blooms_std ~ 1 + water_cent + shade_cent + water_cent:shade_cent,
data = d, family = gaussian,
prior = c(prior(normal(0.5, 0.25), class = Intercept),
prior(normal(0, 0.25), class = b, coef = water_cent),
prior(normal(0, 0.25), class = b, coef = shade_cent),
prior(normal(0, 0.25), class = b, coef = "water_cent:shade_cent"),
prior(exponential(1), class = sigma)),
iter = 4000, warmup = 2000, chains = 4, cores = 4, seed = 1234)
summary(mod)
#> Family: gaussian
#> Links: mu = identity; sigma = identity
#> Formula: blooms_std ~ 1 + water_cent + shade_cent + water_cent:shade_cent
#> Data: d (Number of observations: 27)
#> Samples: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
#> total post-warmup samples = 8000
#>
#> Population-Level Effects:
#> Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
#> Intercept 0.36 0.03 0.30 0.41 1.00 8764
#> water_cent 0.21 0.03 0.14 0.27 1.00 9244
#> shade_cent -0.11 0.03 -0.18 -0.05 1.00 10097
#> water_cent:shade_cent -0.14 0.04 -0.22 -0.06 1.00 9670
#> Tail_ESS
#> Intercept 5307
#> water_cent 6043
#> shade_cent 5108
#> water_cent:shade_cent 5938
#>
#> Family Specific Parameters:
#> Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> sigma 0.14 0.02 0.11 0.19 1.00 6132 5473
#>
#> Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
#> and Tail_ESS are effective sample size measures, and Rhat is the potential
#> scale reduction factor on split chains (at convergence, Rhat = 1).
Created on 2020-09-20 by the reprex package (v0.3.0)
In the exercise, we are asked to use new priors that constrain water_cent to be positive and shade_cent to be negative. I can constrain water_cent by using a lognormal distribution. However, I have not been able to figure out how to define a prior that will constrain shade_cent to be negative. I have tried setting boundaries:
mod <- brm(blooms_std ~ 1 + water_cent + shade_cent + water_cent:shade_cent,
data = d, family = gaussian,
prior = c(prior(normal(0.5, 0.25), class = Intercept),
prior(normal(0, 0.25), class = b, coef = water_cent, lb = 0),
prior(normal(0, 0.25), class = b, coef = shade_cent, ub = 0),
prior(normal(0, 0.25), class = b, coef = "water_cent:shade_cent"),
prior(exponential(1), class = sigma)),
iter = 4000, warmup = 2000, chains = 4, cores = 4, seed = 1234)
#> Error: Argument 'coef' may not be specified when using boundaries.
But as you can see, I can’t specify priors for specific coefficients while setting boundaries.
Following this discussion, I tried to use a positive lognormal prior and multiply by -1, but that fails also:
mod <- brm(blooms_std ~ 1 + water_cent + (-1 * shade_cent) + water_cent:shade_cent,
data = d, family = gaussian,
prior = c(prior(normal(0.5, 0.25), class = Intercept),
prior(lognormal(0, 1), class = b, coef = water_cent),
prior(lognormal(0, 1), class = b, coef = shade_cent),
prior(normal(0, 0.25), class = b, coef = "water_cent:shade_cent"),
prior(exponential(1), class = sigma)),
iter = 4000, warmup = 2000, chains = 4, cores = 4, seed = 1234)
#> Error: The following priors do not correspond to any model parameter:
#> Intercept ~ normal(0.5, 0.25)
#> b_shade_cent ~ lognormal(0, 1)
#> Function 'get_prior' might be helpful to you.
Is there any documentation I have missed for specifying a prior distribution that will constrain a specific coefficient to be negative?
- Operating System: macOS 10.14.6
- brms Version: 2.13.9
sessioninfo::session_info()
#> ─ Session info ─────────────────────────────────────────────────────────────────────────────
#> setting value
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#> language (EN)
#> collate en_US.UTF-8
#> ctype en_US.UTF-8
#> tz America/Chicago
#> date 2020-09-20
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