guess

Estimate learning from paired pre-test and post-test knowledge responses while accounting for lucky guesses and explicit “don’t know” responses.

Choose A Model

The package exposes separate models for separate estimands. Choose the model before interpreting its output.

estimate_logit_score(), cross_sectional_learning(), and cross_sectional_learning_score() are descriptive score baselines. They do not fit Rasch or IRT models, and the bounded score is not a calibrated probability of learning.

Installation

install.packages("guess")

# Development version
devtools::install_github("finite-sample/guess")

Data Contract

Pass matching data frames with one row per person and one column per item. Pre-test and post-test columns must have the same unique names. Valid response codes are:

Use na_as = "missing" when NA records a structural failure, such as an item that was not shown or a response lost to a technical error. Incomplete pre/post pairs are then omitted by default. Set missing_action = "error" to reject them instead.

fit <- item_lca_fit(pre_test, post_test, na_as = "missing")

fit <- item_lca_fit(
  pre_test,
  post_test,
  na_as = "missing",
  missing_action = "error"
)

Explicit "d" and "DK" values remain observed responses under either setting. Structural missingness is not treated as a latent response class.

Item-Level Learning

item_lca_fit() is the direct entry point for the model in Cor and Sood (2016). It fits every item separately from its paired response transitions.

library(guess)

item_sim <- simulate_lca(
  n = 1500,
  n_items = 4,
  gg = 0.40,
  gk = 0.30,
  kk = 0.30,
  gamma = c(0.15, 0.25, 0.35, 0.45),
  seed = 123
)

item_fit <- item_lca_fit(item_sim$pre, item_sim$post)
item_fit$learning
item_fit$params

For binary responses, the parameter rows are:

multi_transmat() and lca_cor() expose the same workflow in two steps when you already work with transition counts.

transitions <- multi_transmat(item_sim$pre, item_sim$post)
count_fit <- lca_cor(transitions)

Person-Level Learning

person_item_lca_fit() jointly uses all repeated items. It estimates shared class proportions, item-specific guessing rates, and one posterior trajectory for each person.

person_sim <- simulate_lca(
  n = 1500,
  n_items = 5,
  gg = 0.35,
  gk = 0.35,
  kk = 0.30,
  gamma = 0.25,
  seed = 456,
  return_classes = TRUE
)

person_fit <- person_item_lca_fit(person_sim$pre, person_sim$post)
person_fit$class_priors
person_fit$gamma

posterior <- posterior_class_probs(person_fit)
p_learned <- posterior_learned(person_fit)

This model is useful only when one common trajectory across items is substantively defensible. It does not allow the same person to know one item, learn another, and remain ignorant on a third. Use item_lca_fit() when the item-specific learning proportions are the target.

The person model currently supports binary responses but not the explicit DK model.

Don’t-Know Responses

Observed DK responses select the nine-cell model. Its latent transition parameters are gg, gk, gd, kk, dg, dk, and dd, plus gamma. Learning is gk + dk: learning from a guessing state plus learning from an observed don’t-know state.

dk_sim <- simulate_lca_dk(
  n = 1800,
  n_items = 3,
  gg = 0.25,
  gk = 0.15,
  gd = 0.10,
  kk = 0.15,
  dg = 0.10,
  dk = 0.10,
  dd = 0.15,
  gamma = 0.25,
  seed = 789
)

dk_fit <- item_lca_fit(dk_sim$pre, dk_sim$post)
dk_fit$learning
dk_fit$params

Assumptions

The latent class correction relies on assumptions that should be reported with the estimate:

1. People do not lose item knowledge over the interval. Know-to-guess and know-to-DK transitions are fixed to zero.
2. A person who knows an item answers it correctly. The current model has no slip parameter.
3. An item’s guessing probability is stable across waves.
4. Structural missingness is ignorable when incomplete pairs are omitted.
5. The item-wise model treats items independently. The person model instead imposes one shared trajectory across items.

A correct-to-incorrect response is therefore attributed to guessing rather than knowledge loss. That restriction identifies the learning parameters and should be tested through sensitivity analysis when the interval is long or the content can be forgotten.

Diagnostics

The binary item model is saturated, so it has no residual degrees of freedom for a goodness-of-fit test. The DK model has one over-identifying restriction, and fit_model() reports its Pearson test.

fit_stats <- fit_model(
  dk_sim$pre,
  dk_sim$post,
  g = dk_fit$params["gamma", ],
  est_param = dk_fit$params[-nrow(dk_fit$params), ],
  force9 = TRUE
)

Use held-out likelihood and perplexity to compare predictive performance.

transitions <- multi_transmat(item_sim$pre, item_sim$post)
perplexity_items(item_fit, transitions)
perplexity_individuals(item_fit, item_sim$pre, item_sim$post)
cv_items(transitions, k = 4, seed = 321)
cv_individuals(item_sim$pre, item_sim$post, k = 5, seed = 321)

Validate recovery under sample sizes, item counts, class proportions, and guessing rates that resemble the intended application.

recovery <- validate_recovery(
  c(gg = 0.40, gk = 0.30, kk = 0.30, gamma = 0.25),
  n = 500,
  n_items = 4,
  n_sims = 100,
  seed = 654
)
recovery

Longitudinal IRT

The package does not yet fit a longitudinal IRT model. The planned model will estimate a population ability gain directly, constrain latent mastery to be nondecreasing over the study interval, and retain item-specific guessing. It will be exported separately only after simulation establishes identification, parameter recovery, interval coverage, and agreement with standard longitudinal IRT fits in compatible limiting cases.

Documentation

vignette("using_guess", package = "guess")
vignette("model_validation", package = "guess")

Reference

Cor, K., and G. Sood. 2016. “Guessing and Forgetting: A Latent Class Model for Measuring Learning.” Political Analysis 24(2): 226-242.

License

MIT