这是一个 MARKETING MIX MODEL 考虑 adstock 效应，其中 Delta 和 Peak 受先验影响，而 Lag 固定为 8。我想知道如何更改 STAN CODE 以便为每个频道提供不同的 LAG（我会修复滞后的先前 beta (2,6)。
# 2.2 Marketing Mix Model
df_mmm, sc_mmm = mean_log1p_trandform(df, ['sales', 'base_sales'])
mu_mdip = df[mdip_cols].apply(np.mean, axis=0).values
max_lag = 8
num_media = len(mdip_cols)
# padding zero * (max_lag-1) rows
X_media = np.concatenate((np.zeros((max_lag-1, num_media)), df[mdip_cols].values), axis=0)
X_ctrl = df_mmm['base_sales'].values.reshape(len(df),1)
model_data2 = {
'N': len(df),
'max_lag': max_lag,
'num_media': num_media,
'X_media': X_media,
'mu_mdip': mu_mdip,
'num_ctrl': X_ctrl.shape[1],
'X_ctrl': X_ctrl,
'y': df_mmm['sales'].values
}
model_code2 = '''
functions {
// the adstock transformation with a vector of weights
real Adstock(vector t, row_vector weights) {
return dot_product(t, weights) / sum(weights);
}
}
data {
// the total number of observations
int<lower=1> N;
// the vector of sales
real y[N];
// the maximum duration of lag effect, in weeks
int<lower=1> max_lag;
// the number of media channels
int<lower=1> num_media;
// matrix of media variables
matrix[N+max_lag-1, num_media] X_media;
// vector of media variables' mean
real mu_mdip[num_media];
// the number of other control variables
int<lower=1> num_ctrl;
// a matrix of control variables
matrix[N, num_ctrl] X_ctrl;
}
parameters {
// residual variance
real<lower=0> noise_var;
// the intercept
real tau;
// the coefficients for media variables and base sales
vector<lower=0>[num_media+num_ctrl] beta;
// the decay and peak parameter for the adstock transformation of
// each media
vector<lower=0,upper=1>[num_media] decay;
vector<lower=0,upper=ceil(max_lag/2)>[num_media] peak;
}
transformed parameters {
// the cumulative media effect after adstock
real cum_effect;
// matrix of media variables after adstock
matrix[N, num_media] X_media_adstocked;
// matrix of all predictors
matrix[N, num_media+num_ctrl] X;
// adstock, mean-center, log1p transformation
row_vector[max_lag] lag_weights;
for (nn in 1:N) {
for (media in 1 : num_media) {
for (lag in 1 : max_lag) {
lag_weights[max_lag-lag+1] <- pow(decay[media], (lag - 1 - peak[media]) ^ 2);
}
cum_effect <- Adstock(sub_col(X_media, nn, media, max_lag), lag_weights);
X_media_adstocked[nn, media] <- log1p(cum_effect/mu_mdip[media]);
}
X <- append_col(X_media_adstocked, X_ctrl);
}
}
model {
decay ~ beta(3,3);
peak ~ uniform(0, ceil(max_lag/2));
tau ~ normal(0, 5);
for (i in 1 : num_media+num_ctrl) {
beta[i] ~ normal(0, 1);
}
noise_var ~ inv_gamma(0.05, 0.05 * 0.01);
y ~ normal(tau + X * beta, sqrt(noise_var));
}
'''
sm2 = pystan.StanModel(model_code=model_code2, verbose=True)
fit2 = sm2.sampling(data=model_data2, iter=1000, chains=3)
fit2_result = fit2.extract()