I have panel data from 1251 people over 4-time points and want to construct a partially pooled (random effects) panel model. I use lagged regressors and therefore only can use 3-time points; so T=3, total_N =3753, with 1251 unique subjects (each with three observations for the regressors and D.V.). My df is in long format, with both time-variant and invariant regressors.
This is a similar issue to a prior post titled Multinomial with Random Effects on panel data, and thus I try to use practically the same model for my example (Y can be 0,1,2). However, I am having difficulty integrating the hierarchical temporal component into my model as recommended in that post’s proposed solution. I have drawn heavily from the classic radon example, but still am stuck.
My question: how to account for the RE across different time periods AND the multiple observations per person? I want to estimate a single beta per regressor (thus am not trying to estimate random slopes).
My model below does run, however, there are many divergences, and it uses time_idx and not respondents_idx, thus I think it does not properly account for the multi-responses per person nature of my data.
Any suggestions would be greatly welcome.
with pm.Model() as panel_model:
s = pm.HalfStudentT(‘sd_1’, nu=3, sd=186)
b = pm.Normal(‘b’, mu = 0, sd = 1, shape=3)
common_mu = pm.Normal(‘common_mu’, mu=0., sd=2)
common_sd = pm.Exponential(“common_sd”, 1.0)
#could also use dot product, but I like the visual
b1 = pm.Normal(“b1”, mu=common_mu, sigma=common_sd)
b2 = pm.Normal(“b2”, mu=common_mu, sigma=common_sd)
b3 = pm.Normal(“b3”, mu=common_mu, sigma=common_sd)
b4 = pm.Normal(“b4”, mu=common_mu, sigma=common_sd)
#mu mu = (b1* data['X1'] + b2* data['X2'] + b3* data['X3'] + b4* data['X4']) r_1 = pm.Deterministic('r_1', s*b) #link func #T=3 p = T.nnet.softmax(mu + r_1[time_idx]) #Y can be 0,1,2 y = pm.Categorical('y', p=p, observed=data['Y'].values)