Cross-Entropy (KL) Objective: Expected respondent distribution vs population

Minimizes expected KL divergence between expected respondent shares and population shares. Expected respondent counts per stratum are S_h = n_h_omega + u_h_omegapi_hsigmoid(X beta). The additional respondents from the next wave are A_h * Sigma; their expected shares are q_h = (A_hSigma)/sum(A_hSigma). We compare q_h against pop_pct via KL(pop || q) or KL(q || pop). Here we use KL(pop || q) for stability where pop_pct>0.

Usage

calculate_entropy(beta, X, pop_pct, u_h_omega, n_h_omega, pi_h, ...)

Arguments

beta

A numeric vector of coefficients for the selection probability model.

X

A model matrix for the strata (H rows x K columns).

pop_pct

A numeric vector of the population proportion in each stratum.

u_h_omega

A numeric vector of the number of un-responded units in each stratum.

n_h_omega

A numeric vector of the number of already responded units in each stratum.

pi_h

A numeric vector of the estimated response propensity in each stratum.

...

Additional arguments (not used, for compatibility with optimisers).

Value

A single numeric value for cross-entropy objective.