# Notation to specify crossed random effects mixed effects model in python

by StreetHawk   Last Updated May 16, 2019 00:19 AM

I'm trying to model a binary response variable based on some continuous variables (fixed effects) and categorical variables (random effects). Here is the model equation: $$Y_{ijk}=\beta X_i + Z_j + Z_k + \epsilon$$.

$$Y_{ijk}$$: whether the session i got a click or not

$$X_i$$: fixed effect features of customer in session i: num_purchases_cat1, num_purchases_cat2, num_purchases_cat3

$$Z_j$$: random effect: ad_category (100 categories)

$$Z_k$$: random effect: ad_price (5 buckets)

Say my data_train contains all these columns: [clicked, num_purchases_cat1, num_purchases_cat2, num_purchases_cat3, ad_category, ad_price]. The two random effects ad_category and ad_price are independent and hence I'd like to fit a crossed effects mixed effects model.

Python's Documentation states that I need to treat the entire dataset as a single group so here's what I'm trying:

import statsmodels.regression.mixed_linear_model as mlm
lmm = mlm.MixedLM(data_train.clicked, data_train[['num_purchases_cat1', 'num_purchases_cat2', 'num_purchases_cat3']], groups=np.ones(data_train.shape[0]))


Now I'm struggling how to specify exog_re and exog_vc. Do I simply put data_train[['ad_category','ad_price']] or should I transform it to one-hot-encoding? How does this change if I want to have Random slopes vs Random Intercepts only?

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