How can I solve "bfmi-low" problem?

Modeling
22

should be:

target += bilognormal_lpdf(nu_tau | [0.57, -2.3]‘, [0.2462207, 1.26]’, rho);

Sorry, it was the uncorrected model in my copy&paste, since I got problems with discourse
formatting, I re-pasted the “old” model. I checked again, should compile now. But its after midnight,
my time, time is already late for me.

1 Like
24

I’m working to extend my model with an AR(1) component. I also ran into the low energy issue. I’ve done some background reading on “energy” and also read Michael’s low energy guide.

I used @claudiofronterre’s pairs function above that focuses on “energy” with the mu hyperparameter and three of the ~ 20 or so group specific estimates. As an aside @claudiofronterre, somehow my extract function was masked in the global env, so I had to add rstan::extract.

Am I right to conclude this bimodality in mu_phi is a likely source of the issue?

low_energy
low_energy.jpg1920×1006 307 KB

Here’s the model for reference,

data {
  int<lower=1> J; // number of apps
  int<lower=1> N; // number of observations, the rows
  int K; // number of features, the columns
  int<lower=0> y[N]; // dependent variable index by the number of rows
  matrix[N, K] X; // trend covariates
  matrix[N, K] X2; // action covariates
  matrix[N, K] X3; // lagged y
  int IDs[N]; // apps
}
parameters {
  real mu_alpha_raw;
  real<lower=0> tau_alpha_raw; // hyper parameter for alpha variance
  // I split out the intercept from other paraters in the design matrix;
  vector[J] alpha; // the intercepts indexed by J apps
  vector[K] beta; // a feature parameter K in length
  vector[K] action_slope; // a feature parameter K in length
  vector<lower=0>[J] theta;
  real<lower=0> mu_theta;
  real<lower=0> tau_theta;
  real mu_action_slope_raw;
  real<lower=0> tau_action_slope_raw;
  real mu_beta_raw;
  real<lower=0> tau_beta_raw;
  real mu_phi;
  real tau_phi;
  vector[K] phi;
}
transformed parameters {
  real mu_action_slope = 0.5 + 0.2 * mu_action_slope_raw;
  real<lower=0> tau_action_slope = 0.6 + 0.05 * tau_action_slope_raw;
  real mu_beta =  (0.05 * mu_beta_raw) - 0.3;
  real<lower=0> tau_beta = 0.07 + 0.05 * tau_beta_raw;
}
model {
  real mu_alpha;
  real tau_alpha;

  mu_phi ~ normal(0, 0.25);
  tau_phi ~ normal(0.5, 0.5);
  phi ~ normal(mu_phi, tau_phi);

  mu_theta ~ normal(1, 5);
  tau_theta ~ normal(3.6, 4);
  theta ~ normal(mu_theta, tau_theta);

  mu_alpha = 0.56 + 0.2 * mu_alpha_raw;
  mu_alpha_raw ~ normal(0, 1);
  tau_alpha = 2.4 + 0.3 * tau_alpha_raw;
  tau_alpha_raw ~ normal(0, 1);
  alpha ~ normal(mu_alpha, tau_alpha);

  mu_beta_raw ~ normal(0, 1);
  tau_beta_raw ~ normal(0, 1);
  beta ~ normal(mu_beta, tau_beta);

  mu_action_slope_raw ~ normal(0, 1);
  tau_action_slope_raw ~ normal(0, 0.05);
  action_slope ~ normal(mu_action_slope, tau_action_slope);

  y ~ neg_binomial_2_log(alpha[IDs] + X * beta + X2 * action_slope + X3 * phi, theta[IDs]);
}

EDIT: perhaps it was naive to slap a simple AR(1) process into this model? It looks like the condition (?) of stationarity is not so simple for discrete distributions (another source). For those following along, here’s a previous post where Bob walks through a Poisson AR(1) model.

25

The first thing I’d try here is non-centering phi.

1 Like