Package 'GMLTM' reference manual

Title:	Generalized Multicomponent Latent Trait Model for Diagnosis
Description:	Provides Bayesian estimation of Item Response Theory models that decompose item difficulty into cognitive operations or rules. Implements the Linear Logistic Test Model (LLTM; Fischer (1973) <doi:10.1016/0001-6918(73)90003-6>), the Multicomponent Latent Trait Model for Diagnosis (MLTM-D; Embretson and Yang (2013) <doi:10.1007/s11336-012-9296-y>), and the Generalized Multicomponent Latent Trait Model for Diagnosis (GMLTM-D; Ramirez et al. (2024) <doi:10.3390/jintelligence12070067>). All models are estimated via Hamiltonian Monte Carlo using 'Stan' through the 'rstan' interface. Includes tools for model validation, reliability estimation, and visualization of item characteristic curves. Supports user-defined prior distributions for all model parameters.
Authors:	Eduar Ramirez [aut, cre], Marcos Jimenez [aut], Vithor R. Franco [aut], Jesus Alvarado [aut]
Maintainer:	Eduar Ramirez <[email protected]>
License:	GPL (>= 3)
Version:	0.1.0
Built:	2026-06-30 16:47:51 UTC
Source:	https://github.com/cran/GMLTM

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
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

Check Data Quality for Reliability Analysis

Description

Verifies if the data is suitable for robust reliability analysis.

Usage

check_reliability_data_quality(fit)
check_reliability_data_quality(fit)

Arguments

fit

Fitted model

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

Arguments

cond_rel_obj

An object of class conditional_reliability_tif returned by conditional_reliability_tif.

theta_points

Numeric vector of theta values at which to compare components. Default is c(-1, 0, 1).

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.

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)
compute_model_validation(fit)

Arguments

fit

A fitted GMLTM model or a list of fitted models.

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)

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)

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

Arguments

fit

Fitted model with $\alpha$ , $\beta$ , guessing parameters

theta_range

Vector of $\theta$ values where to evaluate reliability

component

Integer or character. Specific component to analyze

n_samples

Integer. Number of posterior samples to use

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)
demo_reliability_analysis(fit)

Arguments

fit

Fitted model

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)


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

Arguments

fit

A fitted GMLTM, MLTM, or LLTM model object containing posterior samples of theta parameters.

include_conditional

Logical. Whether to compute conditional reliability estimates across ability levels. Default is FALSE for speed.

include_hierarchical

Logical. Whether to compute hierarchical reliability for the general factor. Default is TRUE.

include_comparisons

Logical. Whether to perform Bayesian comparisons between components. Default is TRUE.

n_samples

Integer. Number of posterior samples to use (for speed control). If NULL, uses all available samples.

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)
export_reliability_results(reliability_obj, file_name = NULL)

Arguments

reliability_obj

Object of class enhanced_mltm_reliability

file_name

File name (optional)

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
)
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

Q

A binary matrix of items by rules (original Q-matrix). Each row represents an item and each column represents a rule. Values should be 0 or 1.

M_list

A list where each element contains the indices of rules that belong to the same component/dimension. For example, list(c(1,2,3), c(4,5)) indicates that rules 1,2,3 belong to component 1 and rules 4,5 belong to component 2.

max_condition_index

Numeric. Maximum acceptable condition index. Default is 30. Values above this threshold indicate severe collinearity.

min_eigenvalue

Numeric. Minimum acceptable eigenvalue. Default is 0.1. Values below this threshold may indicate linear dependence.

plot_diagnostics

Logical. Whether to generate diagnostic plots. Default is TRUE.

verbose

Logical. Whether to print detailed diagnostic information. Default is TRUE.

save_to_global

Logical. Whether to save results to global environment. Default is TRUE.

Details

The function performs the following steps:

Validates input parameters
Generates interaction terms for rules within the same component
Performs collinearity diagnostics using multiple methods
Attempts to resolve severe collinearity by removing problematic interactions
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:

Q_extended

The extended Q-matrix with interaction terms

M_list_extended

Updated component list including interaction terms

diagnostics

List with collinearity diagnostics

removed_interactions

Vector of removed interaction names (if any)

plots

List of diagnostic plots (if plot_diagnostics = TRUE)

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


# 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

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)),
  ...
)
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

data

An $n \times p$ matrix or data.frame of binary responses (rows = subjects, columns = items).

Q

A $p \times K$ matrix specifying which cognitive rules each item requires (Q-matrix).

components

A named list grouping rules into components. Each element is a numeric vector of rule indices belonging to that component. Example: list(global = c(1,2,3), local = c(4,5)).

iters

Number of post-warmup MCMC iterations per chain. Default is 2000.

chains

Number of Markov chains. Default is 2.

iter_warmup

Number of warmup iterations per chain. Default is 1000.

quantiles

Numeric vector of probabilities for posterior quantiles. Default is c(0.025, 0.50, 0.975).

cores

Number of CPU cores for parallel chains. Default is parallel::detectCores() - 1.

priors

A named list of prior hyperparameters with elements theta, eta, alpha, and c. For Normal parameters supply mu and sigma; for the guessing parameter supply shape1 and shape2 (Beta prior). Unspecified elements retain defaults.

...

Additional arguments passed to rstan::sampling().

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)


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)

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

Arguments

fit

A fitted GMLTM, MLTM, or LLTM model object.

include_conditional_tif

Logical. Whether to compute conditional TIF-based reliability. Default is TRUE.

theta_range

Numeric vector of theta values for conditional reliability evaluation. Default is seq(-3, 3, 0.1).

...

Additional arguments passed to enhanced_mltm_reliability.

Value

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

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)),
  ...
)
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

data

An $n \times p$ matrix or data.frame of binary responses (rows = subjects, columns = items).

Q

A $p \times K$ matrix specifying which cognitive rules each item requires (Q-matrix).

iters

Number of post-warmup MCMC iterations per chain. Default is 2000.

chains

Number of Markov chains. Default is 2.

iter_warmup

Number of warmup iterations per chain. Default is 1000.

quantiles

Numeric vector of probabilities for posterior quantiles. Default is c(0.025, 0.50, 0.975).

cores

Number of CPU cores for parallel chains. Default is parallel::detectCores() - 1.

priors

A named list of prior hyperparameters. Each element is a named list with mu and sigma. Available parameters: theta (ability, Normal prior) and eta (rule difficulty, Normal prior). Unspecified elements retain defaults. Example: priors = list(eta = list(sigma = 3)).

...

Additional arguments passed to rstan::sampling().

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)


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)

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)
marginal_Pchecks(fit, interval = 0.95)

Arguments

fit

MLTM object containing model results.

interval

Probability associated with the credibility intervals (default = 0.95).

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.

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)),
  ...
)
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

data

An $n \times p$ matrix or data.frame of binary responses (rows = subjects, columns = items).

Q

A $p \times K$ matrix specifying which cognitive rules each item requires (Q-matrix).

components

A named list grouping rules into components. Each element is a numeric vector of rule indices belonging to that component. Example: list(global = c(1,2,3), local = c(4,5)).

iters

Number of post-warmup MCMC iterations per chain. Default is 2000.

chains

Number of Markov chains. Default is 2.

iter_warmup

Number of warmup iterations per chain. Default is 1000.

quantiles

Numeric vector of probabilities for posterior quantiles. Default is c(0.025, 0.50, 0.975).

cores

Number of CPU cores for parallel chains. Default is parallel::detectCores() - 1.

priors

A named list of prior hyperparameters with elements theta, eta, and alpha. Each is a list with mu and sigma. alpha uses a half-Normal prior (truncated at 0). Unspecified elements retain defaults.

...

Additional arguments passed to rstan::sampling().

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)


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)

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

Arguments

results

An object of class conditional_reliability_tif.

plot_type

Character. Type of plot: "reliability", "information", or "both". Default is "both".

include_ci

Logical. Whether to include credible interval bands. Default TRUE.

color_scheme

Character. Color scheme for plots. Default "blue".

save_plots

Logical. Whether to save plots to disk. Default FALSE.

output_dir

Character. Directory for saved plots. Default NULL (no files written). Only creates directory and saves when both save_plots = TRUE and output_dir is non-NULL.

...

Additional arguments passed to plot_conditional_reliability.

Value

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

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

Arguments

results

An object of class conditional_reliability_tif.

include_ci

Logical. Whether to include credible interval bands. Default TRUE.

show_optimal_points

Logical. Whether to mark optimal theta points. Default TRUE.

add_reference_lines

Logical. Whether to add horizontal reference lines at 0.7, 0.8, 0.9. Default TRUE.

color_palette

Character. RColorBrewer palette name for component colors. Default "Set2".

save_plot

Logical. Whether to save the plot. Default FALSE.

filename

Character. Output filename if save_plot = TRUE. Default NULL (no file written). Only writes when both save_plot = TRUE and filename is non-NULL.

...

Additional graphical arguments.

Value

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

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,
  ...
)
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

results

Object of class conditional_reliability_tif

component

Integer or character. Component to plot (NULL for first component)

plot_type

Character. Type of plot: "reliability", "information", "both", "comparison"

include_ci

Logical. Include confidence intervals

ci_level

Numeric. Confidence level (0.90 or 0.95)

color_scheme

Character. Color scheme: "blue", "viridis", "custom"

add_reference_lines

Logical. Add reference lines for reliability levels

save_plot

Logical. Save plot to file

filename

Character. Filename if saving plot. Default NULL (no file written). Only writes when both save_plot = TRUE and filename is non-NULL.

...

Additional plotting parameters

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.

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

Arguments

fit

A fitted GMLTM model object containing EAP parameter estimates.

Q

The Q-matrix indicating the association between items and rules.

components

A list where each element is a vector of rule indices per component.

page

Integer specifying which page of items to display.

n_items_per_page

Number of items to include per page. Default is 9.

ncol

Number of columns in the layout grid. Default is 3.

nrow

Number of rows in the layout grid. Default is 3.

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)


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)
plot_ICC_individual(fit, Q, components)

Arguments

fit

A fitted GMLTM model object.

Q

The Q-matrix for rule-item associations.

components

A list indicating rule groupings per component.

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]])


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 Method for conditional_reliability_tif Objects

Description

Plot Method for conditional_reliability_tif Objects

Usage

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

Arguments

x

An object of class conditional_reliability_tif.

...

Additional arguments passed to plot_conditional_reliability.

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

Arguments

x

Object of class enhanced_mltm_reliability.

type

Character. Type of plot: "marginal", "conditional", "comparison".

component

Integer or character. Specific component for conditional plots.

...

Additional plotting parameters.

Value

Invisibly returns NULL. Called for its side effects.

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

Arguments

fit

A fitted MLTM object containing model results.

nsim

Number of simulated posterior samples (default = 100).

interval

Probability associated with the credibility intervals (default = 0.95).

...

Additional graphical parameters to customize the plot.

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)


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

Arguments

x

An object of class "enhanced_mltm_reliability".

digits

Integer. Number of decimal places to display. Default is 3.

...

Currently unused.

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

Arguments

x

An object of class "reliability_data_quality".

...

Currently unused.

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

Arguments

x

An object of class "reliability_profile".

...

Currently unused.

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)
quick_reliability_check(fit, n_samples_quick = 500)

Arguments

fit

Fitted model object.

n_samples_quick

Integer. Number of samples for quick analysis (default 500).

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)


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)
reliability(fit)

Arguments

fit

MLTM object.

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

Quick Reliability Profile Analysis

Description

Provides a quick overview of reliability characteristics for each component.

Usage

reliability_profile(cond_rel_obj)
reliability_profile(cond_rel_obj)

Arguments

cond_rel_obj

An object of class conditional_reliability_tif returned by conditional_reliability_tif.

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

Arguments

object

An object of class conditional_reliability_tif.

digits

Integer. Number of decimal places to display. Default is 3.

...

Currently unused.

Value

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

Package 'GMLTM'

Help Index

Analogy items dataset

Description

Usage

Format

Source

References

Check Data Quality for Reliability Analysis

Description

Usage

Arguments

Value

Compare Conditional Reliability Between Components at Specific Theta Values

Description

Usage

Arguments

Value

Compute LOO and WAIC for GMLTM models

Description

Usage

Arguments

Value

References

Examples

Conditional Reliability based on Test Information Function (TIF)

Description

Usage

Arguments

Value

Step-by-step Usage Example

Description

Usage

Arguments

Value

Examples

Enhanced Reliability Analysis for GMLTM-D Models

Description

Usage

Arguments

Value

Export Reliability Results

Description

Usage

Arguments

Value

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

Description

Usage

Arguments

Details

Value

References

Examples

The Generalized Multicomponent Latent Trait Model for Diagnosis

Description

Usage

Arguments

Details

Value

References

Examples

Integration with Enhanced Reliability Analysis

Description

Usage

Arguments

Value

The Linear Logistic Test Model

Description

Usage

Arguments

Details

Value

References

Examples

Marginal Proportions Predictive Checks

Description

Usage

Arguments

Details