hlaoModel: Population Analysis for Heterogeneous List-Based Attention...

In ramchoice: Revealed Preference and Attention Analysis in Random Limited Attention Models

Population Analysis for Heterogeneous List-Based Attention Overload

Description

'hlaoModel' recovers list-based reach probabilities and prefix masses on a suffix-closed menu domain. It evaluates recovered-attention restrictions, constructs sharp independent, dependence-robust, or path-independence-robust preference polytopes, and computes sharp bounds for supplied preference events. The first two modes require a suffix-closed domain because they use Sequential Path Independence to recover attention. The '"noPI"' mode treats prefix masses as latent and is available on any observed-menu domain. With full menu data and positive terminal reach, the SPI modes also recover the full-attention choice rule and report Block–Marschak diagnostics. Optional agreement targets measure whether observed and full-attention choices agree. Under benchmark independence, structured events support status-checked column generation with mixed-integer pricing over linear orders. Returned diagnostics report solver statuses, tolerance, reduced costs, primal and dual residuals, an optimality-gap bound, and whether the numerical certificate checks succeeded.

Usage

hlaoModel(
  menu,
  prob,
  outside_prob = NULL,
  list_order = NULL,
  events = NULL,
  dependence = c("independent", "robust", "noPI", "both", "all"),
  tolerance = sqrt(.Machine$double.eps),
  agreement = FALSE,
  algorithm = c("auto", "enumerate", "column_generation"),
  max_rankings = 5000L,
  max_iterations = 1000L
)

Arguments

menu	Numeric matrix of zeros and ones with one row per distinct menu.
prob	Numeric matrix of inside choice probabilities with the same dimensions as 'menu'.
outside_prob	Optional vector of outside-option probabilities. When omitted, it is computed as one minus the row sum of 'prob'.
list_order	Permutation giving the observed presentation order. The default is the column order of 'menu'.
events	Optional zero-one event indicators over the rows returned by [hlaoRankings()], or one or more structured [hlaoEvent()] objects.
dependence	Which population polytope to construct: '"independent"', '"robust"', '"noPI"', '"both"', or '"all"'. For backward compatibility, '"both"' continues to request the independent and dependence-robust SPI polytopes; '"all"' adds the no-SPI polytope.
tolerance	Nonnegative numerical tolerance for model diagnostics.
agreement	'FALSE', 'TRUE', or observed-menu indices. 'TRUE' computes full-attention agreement bounds for every observed menu.
algorithm	Computational method: '"auto"', '"enumerate"', or '"column_generation"'. Column generation currently applies to the benchmark independent model and structured events.
max_rankings	Maximum number of ranking columns to enumerate.
max_iterations	Maximum number of master and pricing iterations under column generation.

Value

An object of class 'ramchoiceHLAOModel' containing recovered 'attention', attention 'diagnostics', population 'pairwise' shares, compatibility by dependence mode, event 'bounds', full-attention 'agreement', ranking columns used by the selected algorithm, computation diagnostics, and, when available, 'full_attention' and 'block_marschak' results.

References

M. D. Cattaneo, P. H. Y. Cheung, X. Ma, and Y. Masatlioglu (2026). Attention Overload. Working paper.

Examples

menu <- rbind(c(1, 0), c(0, 1), c(1, 1))
prob <- rbind(c(.8, 0), c(0, .75), c(.56, .24))
rankings <- hlaoRankings(1:2)
event <- rankings[, 1] == 2
hlaoModel(menu, prob, events = list(`2 above 1` = event))
hlaoModel(
  menu, prob,
  events = hlaoEvent(2, 1, name = "2 above 1"),
  agreement = TRUE
)

ramchoice documentation built on Sept. 4, 2026, 9:07 a.m.