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Probabilistic factor-membership and divergence summaries

Source: R/membership.R
bayesqm-membership.Rd

Posterior summaries of factor membership and statement interpretation, each computed entirely from posterior draws:

  • compute_threshold_prob() returns the N x K posterior probability that |lambda_ik| > threshold, i.e. the Bayesian version of the Brown (1980) flagging rule.

  • compute_dominant_prob() returns the N x K posterior probability that factor k is the dominant factor for participant i.

  • compute_dominant_sign() returns the length-N posterior probability that the dominant loading is positive; participants with probability below 0.5 are negative exemplars.

  • compute_divergence() returns the posterior of the viewpoint divergence D_j for every statement, together with the distinguishing and consensus probabilities it implies.

  • classify_membership() turns dominant probabilities into a per-participant descriptive tier (Strong / Moderate / Weak).

Usage

compute_threshold_prob(Lambda_draws, threshold)

compute_dominant_prob(Lambda_draws)

compute_dominant_sign(Lambda_draws)

compute_divergence(F_draws, delta = NULL, delta_grid = NULL)

classify_membership(Lambda_draws, strong = 0.8, moderate = 0.6)

Arguments

Lambda_draws

Array of shape [T, N, K] of aligned loading draws.

threshold

Numeric threshold; a natural default is 1.96 / sqrt(J) for the Brown rule.

F_draws

Array of shape [T, J, K] of aligned factor-score draws.

delta

Substantive separation for the distinguishing and consensus probabilities. The fit pipeline supplies the default, the reliability-adjusted critical difference of critical_delta(); suggest_delta() is an alternative. If NULL the D_j posterior (median, 95% CrI, g_jk) is still returned but the distinguishing/consensus probabilities are NA.

delta_grid

Optional numeric vector of delta values for a sensitivity sweep.

strong, moderate

Tier cutoffs on max P(dominant) (defaults 0.80 and 0.60).

Value

compute_threshold_prob() and compute_dominant_prob() return N x K matrices. compute_dominant_sign() returns a length-N named vector. compute_divergence() returns a list (see Details). classify_membership() returns a data frame.

Details

For statement j with standardized viewpoint scores f_{j1}, ..., f_{jK}, the divergence estimand is the mean absolute pairwise difference D_j = 2 / (K (K - 1)) * sum_{k < l} |f_jk - f_jl|. The mean is used rather than the maximum, which is an order statistic over the K (K - 1) / 2 contrasts and is inflated when the posterior is diffuse. compute_divergence() reports the posterior median and central 95% credible interval of D_j, pi_D = P(D_j > delta | Y) (distinguishing) and pi_C = P(D_j < delta | Y) = 1 - pi_D (consensus), and the per-viewpoint departure g_jk = f_jk - mean_{l != k} f_jl with its dominant viewpoint, sign, and P(|g_jk| > delta | Y). The probabilities are the reported quantities; no fixed probability cutoff defines a distinguishing or consensus statement.