Package {GMLTM}

The Generalized Multicomponent Latent Trait Model for Diagnosis

Description

Estimate the parameters of the GMLTM-D via Bayesian Hamiltonian Monte Carlo.

Usage

GMLTM(
  data,
  Q,
  components,
  iters = 2000,
  chains = 2,
  iter_warmup = 1000,
  quantiles = c(0.025, 0.5, 0.975),
  cores = parallel::detectCores() - 1,
  priors = list(theta = list(mu = 0, sigma = 1), eta = list(mu = 0, sigma = 1), alpha =
    list(mu = 0, sigma = 1), c = list(shape1 = 3, shape2 = 20)),
  ...
)

Arguments

Details

GMLTM estimates the Generalized Multicomponent Latent Trait Model for Diagnosis (GMLTM-D; Ramirez et al., 2024) in its Bayesian version. This model analyses items composed of cognitive rules or operations, incorporating three IRT parameters. Rules can be grouped into distinct components.

Prior distributions: Ability (\theta) and rule difficulty (\eta) receive Normal priors. Discrimination (\alpha) receives a half-Normal prior. Guessing (c) receives a Beta prior.

Value

A list of class "GMLTM" with elements:

EAP

Posterior mean estimates: theta, alpha, eta, beta, guessing.

quantiles

Posterior credible intervals for each parameter.

posterior

Full posterior samples and derived quantities.

fit

The stanfit object from rstan::sampling.

data

The original data matrix.

priors

The prior hyperparameters used.

References

Ramirez, E.S.; Jimenez, M.; Franco, V.R.; Alvarado, J.M. (2024). Delving into the Complexity of Analogical Reasoning: A Detailed Exploration with the Generalized Multicomponent Latent Trait Model for Diagnosis. J. Intell., 12, 67. doi:10.3390/jintelligence12070067

Examples

  if (!requireNamespace("rstan", quietly = TRUE)) return()
  data(analogy)
  Q <- structure(
    c(0,0,1,0,1,0,1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,1,
      1,0,0,0,0,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,0,
      1,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,1,0,1,0,1,1,0,1,0,0,0,
      0,0,0,0,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,
      1,0,0,0,1,1,0,1,1,1,1,1,1,1,0,1,1,0,1,1,1,1,0,1),
    dim = c(27L, 5L),
    dimnames = list(NULL, c("rot_fig","rot_trap","reflection",
                            "subt_seg","mov_point")))
  components <- list(global = c(1, 2, 3), local = c(4, 5))
  fit <- GMLTM(analogy, Q, components, iters = 200, iter_warmup = 100, chains = 1)
  fit$EAP$eta
  reliability(fit)

The Linear Logistic Test Model

Description

Estimate the parameters of the LLTM via Bayesian Hamiltonian Monte Carlo.

Usage

LLTM(
  data,
  Q,
  iters = 2000,
  chains = 2,
  iter_warmup = 1000,
  quantiles = c(0.025, 0.5, 0.975),
  cores = parallel::detectCores() - 1,
  priors = list(theta = list(mu = 0, sigma = 1), eta = list(mu = 0, sigma = 1)),
  ...
)

Arguments

Details

LLTM estimates the Bayesian version of the Linear Logistic Test Model (Fischer, 1973), which extends the Rasch model by decomposing item difficulty into cognitive rules. Item difficulty is expressed as \beta_i = \mathbf{q}_i^\top \boldsymbol{\eta}, where \mathbf{q}_i is the i-th row of Q and \boldsymbol{\eta} is the vector of rule difficulty parameters.

Prior distributions: Ability (\theta) and rule difficulty (\eta) receive Normal priors. Prior sensitivity analysis is recommended.

Value

A list of class "LLTM" with elements:

EAP

Posterior mean estimates: theta, eta, beta.

quantiles

Posterior credible intervals for each parameter.

posterior

Full posterior samples and derived quantities.

fit

The stanfit object from rstan::sampling.

data

The original data matrix.

priors

The prior hyperparameters used.

References

Fischer, G. H. (1973). The linear logistic test model as an instrument in educational research. Acta Psychologica, 37(6), 359–374.

Ramirez, E.S.; Jimenez, M.; Franco, V.R.; Alvarado, J.M. (2024). Delving into the Complexity of Analogical Reasoning. J. Intell., 12, 67. doi:10.3390/jintelligence12070067

Examples

  if (!requireNamespace("rstan", quietly = TRUE)) return()
  data(analogy)
  Q <- structure(
    c(0,0,1,0,1,0,1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,1,
      1,0,0,0,0,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,0,
      1,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,1,0,1,0,1,1,0,1,0,0,0,
      0,0,0,0,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,
      1,0,0,0,1,1,0,1,1,1,1,1,1,1,0,1,1,0,1,1,1,1,0,1),
    dim = c(27L, 5L),
    dimnames = list(NULL, c("rot_fig","rot_trap","reflection",
                            "subt_seg","mov_point")))
  fit <- LLTM(analogy, Q, iters = 200, iter_warmup = 100, chains = 1)
  fit$EAP$eta
  reliability(fit)

The Multicomponent Latent Trait Model for Diagnosis

Description

Estimate the parameters of the MLTM-D via Bayesian Hamiltonian Monte Carlo.

Usage

MLTM(
  data,
  Q,
  components,
  iters = 2000,
  chains = 2,
  iter_warmup = 1000,
  quantiles = c(0.025, 0.5, 0.975),
  cores = parallel::detectCores() - 1,
  priors = list(theta = list(mu = 0, sigma = 1), eta = list(mu = 0, sigma = 1), alpha =
    list(mu = 0, sigma = 1)),
  ...
)

Arguments

Details

MLTM estimates the Bayesian version of the Multicomponent Latent Trait Model for Diagnosis (MLTM-D; Embretson & Yang, 2013). This noncompensatory model specifies a hierarchical relationship between components and rules.

Prior distributions: Ability (\theta) and rule difficulty (\eta) receive Normal priors. Discrimination (\alpha) receives a half-Normal prior.

Value

A list of class "MLTM" with elements:

EAP

Posterior mean estimates: theta, alpha, eta, beta.

quantiles

Posterior credible intervals for each parameter.

posterior

Full posterior samples and derived quantities.

fit

The stanfit object from rstan::sampling.

data

The original data matrix.

priors

The prior hyperparameters used.

References

Embretson, S. E., & Yang, X. (2013). A multicomponent latent trait model for diagnosis. Psychometrika, 78, 14–36.

Ramirez, E.S.; Jimenez, M.; Franco, V.R.; Alvarado, J.M. (2024). Delving into the Complexity of Analogical Reasoning. J. Intell., 12, 67. doi:10.3390/jintelligence12070067

Examples

  if (!requireNamespace("rstan", quietly = TRUE)) return()
  data(analogy)
  Q <- structure(
    c(0,0,1,0,1,0,1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,1,
      1,0,0,0,0,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,0,
      1,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,1,0,1,0,1,1,0,1,0,0,0,
      0,0,0,0,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,
      1,0,0,0,1,1,0,1,1,1,1,1,1,1,0,1,1,0,1,1,1,1,0,1),
    dim = c(27L, 5L),
    dimnames = list(NULL, c("rot_fig","rot_trap","reflection",
                            "subt_seg","mov_point")))
  components <- list(global = c(1, 2, 3), local = c(4, 5))
  fit <- MLTM(analogy, Q, components, iters = 200, iter_warmup = 100, chains = 1)
  fit$EAP$eta
  reliability(fit)

Analogy items dataset

Description

Binary item response data from a figural analogies test used to illustrate the LLTM, MLTM-D, and GMLTM-D models.

Usage

analogy

Format

A matrix with 149 rows (subjects) and 27 columns (items), where each cell contains a binary response (0 = incorrect, 1 = correct).

Source

Blum, D., Holling, H., Galibert, M. S., & Forthmann, B. (2016). Task difficulty prediction of figural analogies. Intelligence, 56, 72–81. doi:10.1016/j.intell.2016.03.001

References

Ramirez, E. S., Jimenez, M., Franco, V. R., & Alvarado, J. M. (2024). Delving into the complexity of analogical reasoning: A detailed exploration with the Generalized Multicomponent Latent Trait Model for Diagnosis. Journal of Intelligence, 12, 67. doi:10.3390/jintelligence12070067

Fast Bayesian Marginal Reliability

Description

Optimized computation of marginal reliability with uncertainty quantification.

Usage

bayesian_reliability_fast(theta_samples, EAP_theta)

Arguments

Value

List of reliability estimates per component.

Check Data Quality for Reliability Analysis

Description

Verifies if the data is suitable for robust reliability analysis.

Usage

check_reliability_data_quality(fit)

Arguments

Value

List with data quality diagnostics

Compare Conditional Reliability Between Components at Specific Theta Values

Description

Compare Conditional Reliability Between Components at Specific Theta Values

Usage

compare_conditional_reliability(cond_rel_obj, theta_points = c(-1, 0, 1))

Arguments

Value

Invisibly returns a data frame with columns theta, reliability, and se evaluated at the requested theta_points. Called primarily for its side effect of printing a formatted summary table to the console.

Basic Diagnostics (No External Dependencies)

Description

Computes basic MCMC diagnostics without external packages.

Usage

compute_basic_diagnostics(theta_samples)

Arguments

Value

List of diagnostic statistics.

Compute LOO and WAIC for GMLTM models

Description

This function extracts the log-likelihood from a GMLTM model and computes the Leave-One-Out Cross-Validation (LOO) and the Widely Applicable Information Criterion (WAIC). LOO is a Bayesian model comparison metric based on Pareto-smoothed importance sampling, while WAIC is a fully Bayesian criterion that estimates predictive accuracy.

Usage

compute_model_validation(fit)

Arguments

Value

If a single model is provided, returns a list with LOO and WAIC results. If multiple models are provided, returns a summary table with key LOO and WAIC indices.

References

Vehtari, A., Gelman, A., & Gabry, J. (2017). Practical Bayesian model evaluation using LOO-CV and WAIC. Statistics and Computing, 27(5), 1413–1432. doi:10.1007/s11222-016-9696-4

Examples

  if (!requireNamespace("rstan", quietly = TRUE)) return()
  data(analogy)
  Q <- structure(
    c(0,0,1,0,1,0,1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,1,
      1,0,0,0,0,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,0,
      1,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,1,0,1,0,1,1,0,1,0,0,0,
      0,0,0,0,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,
      1,0,0,0,1,1,0,1,1,1,1,1,1,1,0,1,1,0,1,1,1,1,0,1),
    dim = c(27L, 5L),
    dimnames = list(NULL, c("rot_fig","rot_trap","reflection",
                            "subt_seg","mov_point")))
  components <- list(global = c(1, 2, 3), local = c(4, 5))
  fit1 <- GMLTM(data = analogy, Q = Q, components = components,
                iters = 200, iter_warmup = 100, chains = 1)
  compute_model_validation(fit1)

Fast Conditional Reliability (Simplified)

Description

Simplified conditional reliability using quantile-based approach.

Usage

conditional_reliability_fast(theta_samples, EAP_theta, n_bins = 5)

Arguments

Value

List of conditional reliability by bins.

Conditional Reliability based on Test Information Function (TIF)

Description

Calculates conditional reliability using Test Information Function for 3-parameter MLTM-D models. This approach is more precise than quantile-based partitioning methods.

Usage

conditional_reliability_tif(
  fit,
  theta_range = seq(-3, 3, 0.2),
  component = NULL,
  n_samples = 1000
)

Arguments

Value

A list of class "conditional_reliability_tif" with elements:

theta

Numeric vector of theta values.

reliability

Numeric vector of reliability estimates at each theta value.

information

Numeric vector of test information values at each theta value.

component

Integer indicating the model component.

fit

The original fitted model object.

Step-by-step Usage Example

Description

Demonstration function to show how to use the optimized functions.

Usage

demo_reliability_analysis(fit)

Arguments

Value

Invisibly returns a list with the reliability estimates computed at each step of the analysis. Called primarily for its side effect of printing a step-by-step explanation to the console.

Examples

  if (!requireNamespace("rstan", quietly = TRUE)) return()
  data(analogy)
  Q <- structure(
    c(0,0,1,0,1,0,1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,1,
      1,0,0,0,0,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,0,
      1,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,1,0,1,0,1,1,0,1,0,0,0,
      0,0,0,0,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,
      1,0,0,0,1,1,0,1,1,1,1,1,1,1,0,1,1,0,1,1,1,1,0,1),
    dim = c(27L, 5L),
    dimnames = list(NULL, c("rot_fig","rot_trap","reflection",
                            "subt_seg","mov_point")))
  components <- list(global = c(1, 2, 3), local = c(4, 5))
  fit <- GMLTM(analogy, Q, components, iters = 200, iter_warmup = 100, chains = 1)
  demo_reliability_analysis(fit)

Enhanced Reliability Analysis for GMLTM-D Models

Description

Provides comprehensive reliability analysis for General Multicomponent Latent Trait Models for Diagnosis (GMLTM-D) using Bayesian posterior distributions. Optimized for speed and minimal dependencies.

Usage

enhanced_mltm_reliability(
  fit,
  include_conditional = FALSE,
  include_hierarchical = TRUE,
  include_comparisons = TRUE,
  n_samples = NULL
)

Arguments

Value

An object of class enhanced_mltm_reliability.

Export Reliability Results

Description

Exports results in tabular format for publications.

Usage

export_reliability_results(reliability_obj, file_name = NULL)

Arguments

Value

data.frame with tabulated results

Generate an Extended Q-matrix with Rule Interactions and Collinearity Diagnostics

Description

This function generates interaction terms between rules within the same component, extends the Q-matrix, and evaluates the resulting matrix for collinearity issues using eigenvalues, condition indices, and variance inflation factors (VIF). If severe collinearity is detected, it attempts to iteratively remove problematic interaction terms while keeping the original rules untouched.

Usage

generate_Q_with_interactions(
  Q,
  M_list,
  max_condition_index = 30,
  min_eigenvalue = 0.1,
  plot_diagnostics = TRUE,
  verbose = TRUE,
  save_to_global = TRUE
)

Arguments

Details

The function performs the following steps:

1. Validates input parameters

2. Generates interaction terms for rules within the same component

3. Performs collinearity diagnostics using multiple methods

4. Attempts to resolve severe collinearity by removing problematic interactions

5. Generates diagnostic plots and summaries

Collinearity is assessed using:

• Condition indices (based on eigenvalues of correlation matrix)

• Variance Inflation Factors (VIF)

• Matrix rank assessment

• Eigenvalue analysis

Value

A list containing:

References

Belsley, D. A., Kuh, E., & Welsch, R. E. (1980). Regression diagnostics: Identifying influential data and sources of collinearity. John Wiley & Sons. O'Brien, R. M. (2007). A caution regarding rules of thumb for variance inflation factors. Quality & Quantity, 41(5), 673-690. Hair, J. F., Anderson, R. E., Tatham, R. L., & Black, W. C. (1995). Multivariate data analysis. Prentice Hall.

Examples

# Create a sample Q-matrix (5 items, 4 rules)
Q <- matrix(c(1,1,0,0,0,
              1,0,1,0,0,
              0,1,1,0,0,
              0,0,0,1,1), nrow=5, ncol=4, byrow=FALSE)

# Define components (rules 1-2 in component 1, rules 3-4 in component 2)
M_list <- list(c(1,2), c(3,4))

# Generate extended Q-matrix with interactions
result <- generate_Q_with_interactions(Q, M_list)

# Access results
extended_Q <- result$Q_extended
diagnostics <- result$diagnostics
plots <- result$plots

Fast Hierarchical Reliability

Description

Optimized hierarchical reliability computation.

Usage

hierarchical_reliability_fast(theta_samples)

Arguments

Value

List with component and general factor reliability.

Integration with Enhanced Reliability Analysis

Description

Integrates conditional TIF analysis with existing reliability functions.

Usage

integrate_with_enhanced_reliability(
  fit,
  include_conditional_tif = TRUE,
  theta_range = seq(-3, 3, 0.1),
  ...
)

Arguments

Value

A list combining enhanced reliability results and, optionally, conditional TIF-based reliability.

Marginal Proportions Predictive Checks

Description

Computes and visualizes marginal success proportions, including predicted values, confidence intervals, RMSR, SRMR, and bias estimation.

Usage

marginal_Pchecks(fit, interval = 0.95)

Arguments

Details

marginal_Pchecks calculates marginal prediction intervals and observed success proportions. It prints a table with observed vs. predicted values, generates a forest plot for visualization, and computes key fit indices: RMSR, SRMR, and bias.

Value

A list containing:

• items: A table of fitted values and prediction intervals for each item.

• rmsr: The Root Mean Square Residual (RMSR).

• srmr: The Standardized Root Mean Square Residual (SRMR).

• bias: The difference between the total observed and predicted proportions.

The function also generates:

• A forest plot visualizing prediction intervals and observed success probabilities.

Plot Method for conditional_reliability_tif Objects

Description

Plot Method for conditional_reliability_tif Objects

Usage

## S3 method for class 'conditional_reliability_tif'
plot(x, ...)

Arguments

Value

Invisibly returns NULL. Called for its side effect of producing a reliability and/or information plot via plot_conditional_reliability().

Simple Plot Method (Minimal Dependencies)

Description

Creates basic plots using base R (no ggplot2 dependency).

Usage

## S3 method for class 'enhanced_mltm_reliability'
plot(x, type = "marginal", component = NULL, ...)

Arguments

Value

Invisibly returns NULL. Called for its side effects.

Grouped Item Characteristic Curves (ICC) Plot

Description

Generates Item Characteristic Curves (ICCs) for a group of items displayed in a grid layout with a shared legend.

Usage

plot_ICC_grouped(
  fit,
  Q,
  components,
  page = 1,
  n_items_per_page = 9,
  ncol = 3,
  nrow = 3
)

Arguments

Details

Displays one legend shared across all plots and ensures consistency across theta and probability axes. Ideal for publications or appendices.

Value

A composed ICC grid with one shared legend, plotted to the active device.

References

Ramirez, E.S.; Jimenez, M.; Franco, V.R.; Alvarado, J.M. (2024). Delving into the Complexity of Analogical Reasoning. J. Intell., 12, 67. doi:10.3390/jintelligence12070067

Examples

  if (!requireNamespace("rstan", quietly = TRUE)) return()
  data(analogy)
  Q <- structure(
    c(0,0,1,0,1,0,1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,1,
      1,0,0,0,0,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,0,
      1,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,1,0,1,0,1,1,0,1,0,0,0,
      0,0,0,0,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,
      1,0,0,0,1,1,0,1,1,1,1,1,1,1,0,1,1,0,1,1,1,1,0,1),
    dim = c(27L, 5L),
    dimnames = list(NULL, c("rot_fig","rot_trap","reflection",
                            "subt_seg","mov_point")))
  components <- list(global = c(1, 2, 3), local = c(4, 5))
  fit <- GMLTM(analogy, Q, components, iters = 200, iter_warmup = 100, chains = 1)
  plot_ICC_grouped(fit, Q, components, page = 1)

Individual Item Characteristic Curves (ICC)

Description

Returns a list of individual ICC ggplot2 plots (one per item).

Usage

plot_ICC_individual(fit, Q, components)

Arguments

Value

A list of individual ggplot objects, one per item.

Examples

  if (!requireNamespace("rstan", quietly = TRUE)) return()
  data(analogy)
  Q <- structure(
    c(0,0,1,0,1,0,1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,1,
      1,0,0,0,0,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,0,
      1,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,1,0,1,0,1,1,0,1,0,0,0,
      0,0,0,0,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,
      1,0,0,0,1,1,0,1,1,1,1,1,1,1,0,1,1,0,1,1,1,1,0,1),
    dim = c(27L, 5L),
    dimnames = list(NULL, c("rot_fig","rot_trap","reflection",
                            "subt_seg","mov_point")))
  components <- list(global = c(1, 2, 3), local = c(4, 5))
  fit <- GMLTM(analogy, Q, components, iters = 200, iter_warmup = 100, chains = 1)
  plots <- plot_ICC_individual(fit, Q, components)
  print(plots[[1]])

Plot All Components Separately

Description

Creates individual plots for each component in the analysis.

Usage

plot_all_components(
  results,
  plot_type = "both",
  include_ci = TRUE,
  color_scheme = "blue",
  save_plots = FALSE,
  output_dir = NULL,
  ...
)

Arguments

Value

Invisibly returns NULL. Called for its side effect of producing reliability plots for all model components.

Plot Comparisons (Base R)

Description

Plot Comparisons (Base R)

Usage

plot_comparison_base(comparison_data, ...)

Plot Comparison of Conditional Reliability Between Components

Description

Plot Comparison of Conditional Reliability Between Components

Usage

plot_comparison_conditional(x, include_ci = TRUE, color_scheme = "blue", ...)

Create Comparison Plot of All Components

Description

Creates a single plot comparing conditional reliability across all components.

Usage

plot_components_comparison(
  results,
  include_ci = TRUE,
  show_optimal_points = TRUE,
  add_reference_lines = TRUE,
  color_palette = "Set2",
  save_plot = FALSE,
  filename = NULL,
  ...
)

Arguments

Value

Invisibly returns NULL. Called for its side effect of producing a comparative reliability plot across model components.

Plot Conditional Reliability (Base R)

Description

Plot Conditional Reliability (Base R)

Usage

plot_conditional_base(conditional_data, component = NULL, ...)

Plot Conditional Reliability Results

Description

Creates plots for conditional reliability analysis with multiple visualization options

Usage

plot_conditional_reliability(
  results,
  component = NULL,
  plot_type = "both",
  include_ci = TRUE,
  ci_level = 0.95,
  color_scheme = "blue",
  add_reference_lines = TRUE,
  save_plot = FALSE,
  filename = NULL,
  ...
)

Arguments

Value

Invisibly returns NULL. Called for its side effect of producing one or two plots (reliability curve, test information function, or both) depending on plot_type.

Plot Marginal Reliability (Base R)

Description

Plot Marginal Reliability (Base R)

Usage

plot_marginal_base(marginal_data, ...)

Posterior Predictive Checks (PPC) for Model Fit Evaluation

Description

This function generates posterior predictive checks by plotting the observed and simulated total scores distribution, comparing empirical data against model predictions. It also computes fitted values and prediction intervals.

Usage

ppchecks(fit, nsim = 100, interval = 0.95, ...)

Arguments

Details

The function simulates multiple datasets from the posterior distribution and compares the empirical distribution of total scores with the predicted distribution. It overlays the observed and predicted distributions using a histogram with transparency.

The fitted values, along with their credibility intervals, are computed and returned.

Value

A list containing:

• items: A table of fitted values and prediction intervals for each item.

• subjects: Fitted and observed mean scores per subject.

• ysim: Simulated response matrices.

The function also generates:

• A histogram comparing observed vs. predicted total scores.

References

Ramirez, E.S.; Jimenez, M.; Franco, V.R.; Alvarado, J.M. Delving into the Complexity of Analogical Reasoning: A Detailed Exploration with the Generalized Multicomponent Latent Trait Model for Diagnosis. J. Intell. 2024, 12, 67. https://doi.org/10.3390/jintelligence12070067

Examples

  if (!requireNamespace("rstan", quietly = TRUE)) return()
  data(analogy)
  Q <- structure(
    c(0,0,1,0,1,0,1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,1,
      1,0,0,0,0,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,0,
      1,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,1,0,1,0,1,1,0,1,0,0,0,
      0,0,0,0,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,
      1,0,0,0,1,1,0,1,1,1,1,1,1,1,0,1,1,0,1,1,1,1,0,1),
    dim = c(27L, 5L),
    dimnames = list(NULL, c("rot_fig","rot_trap","reflection",
                            "subt_seg","mov_point")))
  fit <- LLTM(analogy, Q, iters = 200, iter_warmup = 100, chains = 1)
  ppchecks(fit)

Print Method for Enhanced MLTM Reliability

Description

Print Method for Enhanced MLTM Reliability

Usage

## S3 method for class 'enhanced_mltm_reliability'
print(x, digits = 3, ...)

Arguments

Value

Invisibly returns x. Called for its side effect of printing the enhanced reliability analysis results to the console.

Print Method for Data Quality Diagnostics

Description

Print Method for Data Quality Diagnostics

Usage

## S3 method for class 'reliability_data_quality'
print(x, ...)

Arguments

Value

Invisibly returns x. Called for its side effect of printing the data quality diagnostics to the console.

Print Method for Reliability Profile

Description

Print Method for Reliability Profile

Usage

## S3 method for class 'reliability_profile'
print(x, ...)

Arguments

Value

Invisibly returns x. Called for its side effect of printing a formatted reliability profile summary to the console.

Quick Reliability Check

Description

Ultra-fast reliability check for initial assessment.

Usage

quick_reliability_check(fit, n_samples_quick = 500)

Arguments

Value

Named vector of reliability estimates.

Examples

  if (!requireNamespace("rstan", quietly = TRUE)) return()
  data(analogy)
  Q <- structure(
    c(0,0,1,0,1,0,1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,1,
      1,0,0,0,0,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,0,
      1,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,1,0,1,0,1,1,0,1,0,0,0,
      0,0,0,0,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,
      1,0,0,0,1,1,0,1,1,1,1,1,1,1,0,1,1,0,1,1,1,1,0,1),
    dim = c(27L, 5L),
    dimnames = list(NULL, c("rot_fig","rot_trap","reflection",
                            "subt_seg","mov_point")))
  fit <- LLTM(analogy, Q, iters = 200, iter_warmup = 100, chains = 1)
  quick_rel <- quick_reliability_check(fit)
  print(quick_rel)

Marginal reliability

Description

Estimate the the marginal reliability of the GMLTM.

Usage

reliability(fit)

Arguments

Details

reliability estimates a ...

Value

A number denoting the reliability estimate.

References

Ramírez, E.S.; Jiménez, M.; Franco, V.R.; Alvarado, J.M. Delving into the Complexity of Analogical Reasoning: A Detailed Exploration with the Generalized Multicomponent Latent Trait Model for Diagnosis. J. Intell. 2024, 12, 67. https://doi.org/10.3390/jintelligence12070067

Fast Reliability Comparisons

Description

Optimized pairwise comparisons of reliability between components.

Usage

reliability_comparison_fast(marginal_results)

Arguments

Value

List of comparison results.

Quick Reliability Profile Analysis

Description

Provides a quick overview of reliability characteristics for each component.

Usage

reliability_profile(cond_rel_obj)

Arguments

Value

A list of class "reliability_profile" with elements:

summary

Data frame with columns theta, reliability, lower, and upper.

component

Integer indicating which model component was analysed.

Usage Instructions

Description

Prints detailed usage instructions.

Usage

reliability_usage_instructions()

Value

Invisibly returns NULL. Called for its side effect of printing step-by-step usage instructions to the console.

Summary Method for Conditional Reliability Analysis

Description

Summary Method for Conditional Reliability Analysis

Usage

## S3 method for class 'conditional_reliability_tif'
summary(object, digits = 3, ...)

Arguments

Value

Invisibly returns object. Called for its side effect of printing a formatted summary of conditional reliability statistics to the console.