Bayesian Comparison of Group Transition Structures (Dirichlet-Multinomial)

Closed-form Bayesian alternative to compare_lsa() for comparing the transition structures of two (or, pairwise, more) groups. Each state's outgoing transitions are modelled as Dirichlet-Multinomial with a Jeffreys prior, so each transition probability is marginally Beta. The per-edge posterior mean difference prob_a - prob_b is exact; a credible interval, the probability of direction pd, and a two-sided Bayesian p-equivalent 2 * (1 - pd) come from a Monte Carlo draw on the Beta marginals.

Usage

bayes_compare_lsa(
  x,
  y = NULL,
  prior = 0.5,
  draws = 10000L,
  ci = 0.95,
  mean_threshold = 0.01,
  bound_threshold = 0.001,
  adjust = "none",
  seed = NULL
)

Arguments

x: An lsa_group (two or more groups), or a single lsa fit for the first group.
y: The second group's lsa fit when x is a single fit; otherwise NULL.
prior: Numeric > 0. Dirichlet prior concentration added to every cell. Default 0.5 (Jeffreys). Use 1 for a uniform (Laplace) prior.
draws: Integer. Monte Carlo posterior draws for the credible intervals. Default 10000.
ci: Numeric in (0, 1). Credible-interval mass. Default 0.95.
mean_threshold, bound_threshold: An edge is flagged credibly different only if its credible interval excludes zero, |posterior mean diff| exceeds mean_threshold (default 0.01), and the credible bound nearest zero exceeds bound_threshold (default 0.001). The thresholds guard against differences that are detectable but negligibly small.
adjust: Multiple-comparison correction applied to the two-sided Bayesian p across edges (and family-wide across pairs); any method of stats::p.adjust(). Default "none".
seed: Optional integer for reproducible credible intervals.

Value

For two groups, class c("lsa_bayes", "lsa_comparison", "list") with an edges data frame (from, to, prob_a, prob_b, diff, ci_low, ci_high, pd, effect_size, p_value, p_adj, significant), the two fits, and the Bayesian settings. For more than two groups, an all-pairwise c("lsa_bayes_pairwise", "lsa_comparison_pairwise", "list").

Details

This complements compare_lsa(): the permutation test asks whether a difference is more extreme than chance; the Bayesian comparison asks for the plausible range of the true difference and how precisely it is estimated. An edge whose source state is rarely visited gets a wide credible interval even when its row-normalised probability looks decisive.

The result carries class c("lsa_bayes", "lsa_comparison") (and the pairwise object c("lsa_bayes_pairwise", "lsa_comparison_pairwise")), so plot() (barrel / heatmap) and as.data.frame() work as for a permutation comparison.

References

Johnston, L. & Jendoubi, T. (2026). How Delivery Mode Reshapes Resource Engagement: A Bayesian Differential Network Analysis. TNA Workshop 2026.

Examples

# \donttest{
g <- lsa(group_regulation,
         group = ifelse(group_regulation$T1 == "plan", "p", "o"))
bc <- bayes_compare_lsa(g, seed = 1)
head(as.data.frame(bc))
#>         from    to      prob_a      prob_b          diff       ci_low
#> 1      adapt adapt 0.001166861 0.005586592 -0.0044197310 -0.027133070
#> 2   cohesion adapt 0.003850193 0.001814882  0.0020353105 -0.005554945
#> 3  consensus adapt 0.004742088 0.005548442 -0.0008063537 -0.006101002
#> 4 coregulate adapt 0.016252683 0.018651363 -0.0023986798 -0.020029418
#> 5    discuss adapt 0.071332032 0.072164948 -0.0008329166 -0.023384136
#> 6    emotion adapt 0.002758328 0.003064351 -0.0003060234 -0.007038335
#>       ci_high     pd effect_size p_value  p_adj significant
#> 1 0.003861497 0.7288 -0.56057932  0.5424 0.5424       FALSE
#> 2 0.007019141 0.8324  0.67017951  0.3352 0.3352       FALSE
#> 3 0.003256711 0.6010 -0.34274817  0.7980 0.7980       FALSE
#> 4 0.010899959 0.5969 -0.30189745  0.8062 0.8062       FALSE
#> 5 0.020201560 0.5158 -0.07450965  0.9684 0.9684       FALSE
#> 6 0.003725192 0.5305 -0.11245333  0.9390 0.9390       FALSE
# }