Adding Multilevel to my hierarchical switchpoint model

Questions
1

Hello guys,

I have a hierarchical switchpoint model built and the convergence looks great, incorporating individual and group level model with my “mean” parameters.
However, I am now stuck at adding a new multilevel comparison. My data consists of body length measurement with respect to Age. I would like to explore if any sex effect has on the switchpoint.

How should I add in the multilevel effect…something like pm.Binomial() …? for instance I am testing between Male and Female, say I have df.Sex with 2 levels - Male and Female encoded with 0 and 1.

And any suggestion if I am adding multinomial groups? such as country difference, for instance USA, Canada and Britain, encoded with 0,1,2?

Many thanks!!

with pm.Model() as model:
# Switchpoint
mean_switchpoint = pm.Normal(‘mean_switchpoint’, 4.0, sd=2)
switchpoint = pm.TruncatedNormal(‘switchpoint’, mean_switchpoint, sd=2., lower=0., upper=10., shape=n_sample)

# Hyperpriors for intercept & slope
intercept_pre_mean = pm.Normal('intercept_pre_mean', 17.0, sd=5.0)
intercept_post_mean = pm.Normal('intercept_post_mean', 13.0, sd = 5.0 )
slope_pre_mean = pm.TruncatedNormal('slope_pre_mean', 0, sd=2, upper=0.)
slope_post_mean = pm.Normal('slope_post_mean', 0, sd=2)

# Priors for pre- and post-switch intercepts and slopes
intercept_pre = pm.Normal('intercept_pre', mu = intercept_pre_mean, sd= 2.0, shape=n_sample)
intercept_post = pm.Normal('intercept_post', mu = intercept_post_mean, sd = 2.0, shape=n_sample)
slope_pre = pm.Normal('slope_pre', slope_pre_mean, sd=2, shape=n_sample)
slope_post = pm.Normal('slope_post', slope_post_mean, sd=2, shape=n_sample)

intercept = pm.math.switch(switchpoint[id_idx] >= df.Age, intercept_pre[id_idx], intercept_post[id_idx])
x_coeff = pm.math.switch(switchpoint[id_dx] >= df.Age, slope_pre[id_idx], slope_post[sousa_idx])

likelihood = pm.Normal('likelihood', mu = intercept + x_coeff * df.Age, observed=df.length)

pm.model_to_graphviz(model)

2

You need to code it in a design matrix, and do switch point on the linear predictor (since the switch is always conditioned on age, you can essentially do pm.math.switch on any linear predictor that has age on it, being it age*sex or age*body_length).

You can have a look at one of the analysis i did for a paper: https://github.com/iBMLab/Static_dynamic the repo is a bit dated, and if I were to do the same analysis again I will use a continues switch point model. But hopefully it will be useful for you.