Hierarchical model with Additional Features for Certain Groups

Questions v5
1

Hi there,

Is it possible to build a multi-level model with additional features for some of the groups and not others?

For example, in the simplest case I can think of, say I had two groups and I wanted a hierarchy on an intercept term and one feature, and I also wanted group 1 to have one additional feature.

def model(X, y, group_idx):
    b0 = pm.Normal(0,1, shape=2)
    b1 = pm.Normal(0,1,shape=2)
    b2 = pm.Normal(0,1)
    mu = b0[group_idx] + b1[group_idx]*X[0] *  ??b2?? * X[1]
    sigma = pm.HalfNormal(5)
    y = pm.Normal(mu, sigma, observed=y)

I made this code up, so apologies if any mistakes, but I think it conveys the point. If anything is unclear I would be happy to clarify, thanks!

2

You can use pm.math.where(pm.math.eq(group_idx, 1), b2 * X[1], 0)

1 Like
3

That’s pm.math, just to be clear, not the python built-in math library

1 Like
4

Thanks!

Do you know if these types of implementations would lead to slower sampling with NUTS?

5

Not sure what your concern is?

It’s fine to have variables that only affect a subset of observations. The where can be thought of as a vectorized if statement that does this. It’s pretty cheap under the hood.

1 Like