I am trying to understand how to properly use the ‘dims’ and ‘shape’ in the hierarchical modeling.
I am attempting to build a Hierarchical marketing mix model for 10 promotional channels, 4 control variables across 5 regions throughout a time period of 24 months.
Here is sample code to mimic how I wrote it:
import pymc as pm
import aesara as at
import pandas as pd
import numpy as np
#generate some random data
num_channels= 10
num_cont_vars= 4
num_months= 24
num_regions= 5
dict_1= {
'Region': np.repeat(np.arange(num_regions), num_weeks),
'Week': np.repeat(np.arange(num_weeks), num_channels),
'Sales': np.random.randint(low= 10, high= 100, size= num_weeks*num_regions),
}
dict_2= {f'Channel_{col}': np.random.randint(low=1, high=20, size=(num_weeks*num_regions)) for col in range(num_channels)}
dict_3= {f'cont_var{cont}': np.random.random(size= (num_weeks * num_regions)) for cont in range(num_cont_vars)}
dict_1.update(dict_2)
dict_1.update(dict_3)
df= pd.DataFrame(dict_1)
#defining adstock and saturation functions
def geometric_adstock(x, alpha: float, l: int):
"""Geometric adstock transformation."""
cycles = [
at.concatenate(
[at.zeros(i), x[: x.shape[0] - i]]
)
for i in range(l)
]
x_cycle = at.stack(cycles)
w = at.as_tensor_variable([at.power(alpha, i) for i in range(l)])
return at.dot(w, x_cycle)
def logistic_saturation(x, lam: float):
"""Logistic saturation transformation."""
return (1 - at.exp(-lam * x)) / (1 + at.exp(-lam * x)
# Building the model:
coords= {'region' : list(df['Region'].unique())}
with pm.Model(coords= coords) as model:
#defining the hyperpriors
adstock_a= pm.Exponential('adstock_a', lam=10.0)
adstock_b= pm.Exponential('adstock_b', lam=10.0)
sat_lam_lam= pm.Exponential('sat_lam', lam= 10.0)
channel_beta_lam= pm.Exponential('coef_lam', lam=10.0)
cont_beta_mu= pm.Normal('cont_lam', mu=0, sigma=10.0)
cont_beta_sigma= pm.HalfCauchy('cont_sig', beta= 10.0)
#then I loop over the marketing channels and calculate their priors and add them to the response list
response_lst= []
for channel in [channel for channel in df.columns if channel.startswith('Channel')]:
x= df[channel].values
adstock_param= pm.Beta(f'{channel_name}_adstock', alpha= adstock_a, beta=
adstock_b, dims= 'Regions' )
sat_lam= pm.Exponential(f'{channel_name}_sat',
lam= sat_lam_lam,
dims= 'Region')
channel_b = pm.Exponential(f"{channel_name}_coef",
lam=chan_beta_lam,
dims= 'Region')
x_new = geometric_adstock(x, adstock_param, 6)
saturation_tensor = logistic_saturation(x_new, saturation_lam )
channel_contribution= pm.Deterministic(
f'contribution_{channel_name}',
channel_b * saturation_tensor)
response_mean.append(channel_contribution)
for control_var in [var for var in df.columns if var.startswith('cont_var')]:
x = df[control_var].values
control_beta = pm.Normal(f"{control_var}_control_coef",
mu=cont_beta_mu,
sigma=cont_beta_sigma,
dims= 'Region')
control_x = control_beta * x
response_mean.append(control_x)\
intercept= pm.Exponential('intercept', lam= 0.1)
sigma = pm.Exponential('sigma', lam=0.01)
likelihood = pm.Normal("outcome", mu = sum(response_mean) + intercept , sigma = sigma,
observed = data_transformed[target].values,
dims= 'Region'
)
trace= pm.sample(1000, tune= 500)
#running it give me the below error
ValueError: Shape mismatch:
Here my questions are:
1. Am I using the dims args wrong?
2. should I be adding the dims argument to the likelihood equation?
3. what are the use cases of shape?
I am using
pymc v4.4.0
linux system (not sure its specs, its the company VDI)
would appreciate any help explaining this to me…and sorry for the long code, wanted to be as clear as possible
