BayesianBLP.elasticities

BayesianBLP.elasticities(*, at='mean', periods=None, regions=None, n_samples=500)

Posterior price elasticities ε[market, share, price].

Computes the closed-form mixed-logit elasticity from posterior draws:

ε_jk(m) = (p_km / s_jm) · (1/R) Σ_r α_ir(m)
           · s_jmr · (δ_jk − s_kmr)

which is negative on the diagonal (own-price) and positive off-diagonal (cross-price substitutes). The integral over consumer types is approximated with the same Halton draws used for the likelihood, so it is essentially free.

Parameters:

at{“mean”, “samples”}

"mean" (default) returns the posterior mean elasticity per cell, dims (market, share, price). "samples" returns the full per-sample array, dims (sample, market, share, price).

periodssequence of period labels or slice, optional

Slice the returned DataArray to these periods (coord labels). Only valid when time_col was set on the model. The elasticity is still computed across the whole panel; the returned array is restricted at the output boundary.

regionssequence of region labels, optional

Slice the returned DataArray to these regions (coord labels).

n_samplesint

Number of posterior samples to use. With at="mean" the samples are averaged after computation (correct for Jensen’s inequality, unlike plugging in posterior-mean parameters); with at="samples" they are returned as-is. The default of 500 is sufficient for smooth posterior densities on typical panels; increase for finer KDE resolution at the cost of memory O(n_samples · M · J · n_mc_draws).

Returns:

xr.DataArray