Reproducible Sequence Analysis: A Synthetic Case Study

In gp3sequences: Transparent Analysis of Ordered Categorical Sequences

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.width = 7,
  fig.height = 4.5
)
library(gp3sequences)

Study objective

This synthetic example examines navigation-path structure under two assigned interface conditions. It demonstrates an auditable workflow rather than a claim that sequence structure reveals hidden attention, preference, cognition, emotion, intention, or causality.

Synthetic study data

The data contain 12 independent participant-level sequences of equal maximum length. Interface condition is assigned as sequence-level metadata and all state labels are directly observed navigation locations.

paths <- list(
  s01 = c("home", "search", "product", "cart", "checkout", "confirmation"),
  s02 = c("home", "search", "product", "reviews", "cart", "checkout"),
  s03 = c("home", "category", "product", "cart", "checkout", "confirmation"),
  s04 = c("home", "search", "category", "product", "cart", "checkout"),
  s05 = c("home", "category", "product", "reviews", "cart", "checkout"),
  s06 = c("home", "search", "product", "cart", "home", "search"),
  s07 = c("home", "category", "search", "product", "checkout", "confirmation"),
  s08 = c("home", "category", "product", "compare", "cart", "checkout"),
  s09 = c("home", "search", "compare", "product", "checkout", "home"),
  s10 = c("home", "category", "compare", "product", "cart", "checkout"),
  s11 = c("home", "search", "product", "compare", "cart", "checkout"),
  s12 = c("home", "category", "product", "checkout", "confirmation", "home")
)

case_data <- do.call(
  rbind,
  lapply(seq_along(paths), function(i) {
    data.frame(
      sequence_id = names(paths)[i],
      sequence_order = seq_along(paths[[i]]),
      state = paths[[i]],
      duration = 75 + 6 * seq_along(paths[[i]]) + 2 * i,
      participant_id = sprintf("p%02d", i),
      interface = if (i <= 6L) "interface_a" else "interface_b",
      stringsAsFactors = FALSE
    )
  })
)

head(case_data, 12L)

Prespecified preparation

The synthetic input is expected to be complete and uniquely ordered. Policies therefore refuse missing states and duplicate positions while preserving repeated states and positive durations.

case_audit <- audit_sequence_data(
  case_data,
  sequence_id_col = "sequence_id",
  order_col = "sequence_order",
  state_col = "state",
  duration_col = "duration",
  metadata_cols = c("participant_id", "interface")
)

case_prepared <- prepare_sequence_data(
  case_data,
  sequence_id_col = "sequence_id",
  order_col = "sequence_order",
  state_col = "state",
  duration_col = "duration",
  metadata_cols = c("participant_id", "interface"),
  missing_state_policy = "error",
  duplicate_position_policy = "error",
  repeated_state_policy = "preserve",
  zero_duration_policy = "preserve",
  unknown_state_policy = "preserve",
  unused_state_levels = "preserve"
)

case_audit
case_prepared$status
case_prepared$decisions

Structural summaries

state_summary <- summarise_sequence_states(
  case_prepared$data,
  sequence_id_col = "sequence_id",
  order_col = "sequence_order",
  state_col = "state",
  duration_col = "duration",
  metadata_cols = c("participant_id", "interface")
)

transition_summary <- summarise_sequence_transitions(
  case_prepared$data,
  sequence_id_col = "sequence_id",
  order_col = "sequence_order",
  state_col = "state",
  metadata_cols = c("participant_id", "interface"),
  include_self = TRUE
)

path_summary <- format_sequence_paths(
  case_prepared$data,
  sequence_id_col = "sequence_id",
  order_col = "sequence_order",
  state_col = "state",
  metadata_cols = c("participant_id", "interface")
)

state_summary$overall
head(transition_summary$overall)
path_summary$paths

Recurring contiguous motifs

case_motifs <- extract_sequence_ngrams(
  case_prepared$data,
  sequence_id_col = "sequence_id",
  order_col = "sequence_order",
  state_col = "state",
  metadata_cols = "interface",
  min_length = 2L,
  max_length = 3L,
  overlap = "allow"
)

case_motif_summary <- summarise_sequence_motifs(case_motifs)
case_motif_filter <- filter_sequence_motifs(
  case_motif_summary,
  min_occurrences = 2L,
  min_sequences = 2L,
  min_prevalence = 0.15,
  motif_lengths = c(2L, 3L),
  top_n = 12L,
  rank_by = "sequence_prevalence",
  ties = "include"
)

format_sequence_motifs(
  case_motif_filter,
  prevalence = "percent",
  digits = 1L
)$table

Consensus and condition contrasts

state_order <- sort(unique(case_prepared$data$state), method = "radix")

case_consensus <- create_consensus_sequence(
  case_prepared$data,
  group_cols = "interface",
  tie_method = "first",
  state_levels = state_order
)

case_comparison <- compare_sequence_groups(
  case_prepared$data,
  group_col = "interface"
)

format_consensus_sequence(case_consensus, include_agreement = TRUE)
summarise_consensus_agreement(case_consensus, by = "group")
head(case_comparison$state_contrasts)
head(case_comparison$transition_contrasts)
case_comparison$length_contrasts

Distance, clustering, and representatives

The clustering layer is declared in advance as normalised LCS distance, two-cluster average-linkage hierarchical clustering, and standard structural validation summaries.

case_distance <- compute_sequence_distance(
  case_prepared$data,
  method = "lcs",
  normalise = "max_length"
)

case_cluster <- cluster_sequences(
  case_distance,
  k = 2L,
  method = "hierarchical",
  linkage = "average"
)

case_cluster_validation <- validate_sequence_clusters(case_cluster)
case_representatives <- extract_representative_sequences(case_cluster)

summarise_sequence_distance(case_distance)$overall
case_cluster$assignments
case_cluster_validation$overall
case_representatives

Transition network and recent-context model

case_network <- create_transition_network(
  case_prepared$data,
  normalise = "from",
  include_self = TRUE
)

case_centrality <- summarise_transition_centrality(case_network)
case_communities <- detect_transition_communities(case_network)

case_order2 <- fit_higher_order_transition_model(
  case_prepared$data,
  order = 2L,
  smoothing = 0.5,
  backoff = TRUE
)

case_network
case_centrality
case_communities
predict_next_state(case_order2, c("home", "search"))
predict_next_state(case_order2, c("unseen"))

Compact categorical HMM sensitivity description

The native HMM is included as a compact statistical summary, not as a source of substantive state labels. A one-state and two-state model are compared descriptively using the same observations and symbol coding.

one_state <- fit_sequence_hmm(
  case_prepared$data,
  n_states = 1L,
  max_iter = 30L,
  seed = 42L
)

two_state <- fit_sequence_hmm(
  case_prepared$data,
  n_states = 2L,
  max_iter = 50L,
  seed = 42L
)

summarise_sequence_hmm(two_state)$fit
head(decode_sequence_states(two_state, method = "viterbi"))
compare_sequence_hmms(one_state = one_state, two_state = two_state)

Assemble report-ready evidence

case_evidence <- list(
  preparation_status = case_prepared$status,
  preparation_decisions = case_prepared$decisions,
  state_summary = state_summary$overall,
  motif_summary = case_motif_filter$motifs,
  consensus = format_consensus_sequence(
    case_consensus,
    include_agreement = TRUE
  ),
  group_state_contrasts = case_comparison$state_contrasts,
  distance_summary = summarise_sequence_distance(case_distance)$overall,
  cluster_validation = case_cluster_validation$overall,
  representatives = case_representatives,
  network = case_network,
  centrality = case_centrality,
  hmm_comparison = compare_sequence_hmms(
    one_state = one_state,
    two_state = two_state
  )
)

names(case_evidence)

Interpretation boundary

The workflow documents recurring paths, aligned-position support, descriptive condition contrasts, dissimilarity, clustering reproducibility, transition structure, recent-context probabilities, and latent statistical summaries. None of these outputs independently identifies attention, preference, comprehension, emotion, cognition, intention, diagnosis, deception, or causal mechanisms. Such interpretation requires an appropriate design, external measurement, and independent validation.

gp3sequences documentation built on Aug. 23, 2026, 5:10 p.m.