Time-Varying Condition Comparisons
In gp3sequences: Transparent Analysis of Ordered Categorical Sequences

knitr::opts_chunk$set(collapse = TRUE, comment = "#>")
library(gp3sequences)

Model target

fit_time_varying_sequence_model() estimates the probability of a declared state or transition over aligned sequence time. It uses group-specific smooths and can include a participant random-effect smooth. The model concerns a predeclared structural outcome, not an unobserved psychological state.

Synthetic repeated sequences

set.seed(1)
participants <- paste0("p", 1:24)
x <- do.call(
  rbind,
  lapply(seq_along(participants), function(i) {
    time <- 1:12
    group <- if (i <= 12L) "control" else "treatment"
    linear <-
      -0.4 +
      0.06 * time +
      0.35 * (group == "treatment") * sin(time / 3)

    data.frame(
      participant_id = participants[i],
      sequence_id = participants[i],
      sequence_order = time,
      group = group,
      state = ifelse(
        stats::runif(length(time)) < stats::plogis(linear),
        "A",
        "B"
      ),
      stringsAsFactors = FALSE
    )
  })
)

Fit and inspect

if (requireNamespace("mgcv", quietly = TRUE)) {
  model <- fit_time_varying_sequence_model(
    x,
    group_col = "group",
    participant_id_col = "participant_id",
    target_state = "A",
    k = 5L
  )
  model_summary <- summarise_time_varying_sequence_model(model)
  model_summary$metadata
  model_summary$parametric_terms
  model_summary$smooth_terms
}

Predictions

if (requireNamespace("mgcv", quietly = TRUE)) {
  predictions <- predict_time_varying_sequence_model(
    model,
    time = seq(1, 12, length.out = 60L),
    level = 0.95
  )
  head(predictions)
}

if (requireNamespace("mgcv", quietly = TRUE)) {
  plot_time_varying_sequence_model(model)
}

Transition outcomes

Use outcome = "transition" together with from_state and to_state to model a predeclared transition. The time coordinate refers to the origin position.

Interpretation

Pointwise intervals describe uncertainty conditional on the fitted model. A time-varying association is not automatically a causal condition effect. Causal language requires valid assignment, implementation, estimand definition, and an analysis aligned with the experimental design.