critical_delta: Reliability-adjusted critical difference (default 'delta')

In bayesqm: Bayesian Q Methodology: Probabilistic Factor Analysis

Reliability-adjusted critical difference (default delta)

Description

The default separation for the distinguishing and consensus probabilities: the reliability-adjusted critical difference used to flag distinguishing statements in classical Q analysis (Brown 1980; Zabala & Pascual 2016), here generalized by computing it from the posterior dominant-factor counts. With p_f the number of participants whose posterior dominant factor is f, ⁠r_f = p_f r0 / (1 + (p_f - 1) r0)⁠ and SE_f = sqrt(1 - r_f), ⁠delta = z * mean_{k < l} sqrt(SE_k^2 + SE_l^2)⁠. The reliability is the stable population reliability of the design, not the posterior estimation spread.

Usage

critical_delta(Lambda_draws, level = 0.05, r0 = 0.8)

Arguments

Lambda_draws	Array of shape ⁠[T, N, K]⁠ of aligned loading draws.
level	Two-sided level for the critical value, z = qnorm(1 - level/2). 0.05 (default) gives z = 1.96; 0.01 gives z = 2.58. Report sensitivity over level.
r0	Conventional single-sort reliability (default 0.80; Brown 1980).

Value

A single numeric value, the critical-difference delta.

Examples

critical_delta(array(rnorm(200 * 8 * 3), c(200, 8, 3)))

bayesqm documentation built on June 18, 2026, 1:07 a.m.