cogirt: Cognitive Testing Using Item Response Theory

Description

Psychometrically analyze latent individual differences related to tasks, interventions, or maturational/aging effects in the context of experimental or longitudinal cognitive research using methods first described by Thomas et al. (2020) doi:10.1177/0013164420919898.

Author(s)

Maintainer: Michael Thomas michael.l.thomas@colostate.edu

Administer Cognitive Tests Using Computerized Adaptive Testing

Description

This function accepts an RDA file or a list containing selected objects and returns omega estimates, the standard error of omega, and the optimal next condition to administer for single-subject computerized adaptive testing. Adaptive testing is guided by D-optimality (see Segall, 2009).

Usage

cog_cat(rda = NULL, obj_fun = NULL, int_par = NULL)

Arguments

Value

A list with elements for omega parameter estimates (omega1), standard error of the estimates (se_omega), and the next condition to administer (next_condition).

References

Segall, D. O. (2009). Principles of Multidimensional Adaptive Testing. In W. J. van der Linden & C. A. W. Glas (Eds.), Elements of Adaptive Testing (pp. 57-75). https://doi.org/10.1007/978-0-387-85461-8_3

Examples

rda = ex5
rda$y[which(!rda$condition %in% c(3))] <- NA
cog_cat(rda = rda, obj_fun = dich_response_model, int_par = 1)

Perform Simulated Computerized Adaptive Testing

Description

This function performs simulated adapting testing using the D-optimality criterion (Segall, 2009) which allows the user to focus on a subset of intentional abilities (or traits).

Usage

cog_cat_sim(
  data = NULL,
  model = NULL,
  guessing = NULL,
  contrast_codes = NULL,
  num_conditions = NULL,
  num_contrasts = NULL,
  constraints = NULL,
  key = NULL,
  omega = NULL,
  item_disc = NULL,
  item_int = NULL,
  conditions = NULL,
  int_par = NULL,
  start_conditions = NULL,
  max_conditions = Inf,
  omit_conditions = NULL,
  min_se = -Inf,
  link = "probit",
  verbose = TRUE
)

Arguments

Value

A list with elements with the model used (model), true omega parameters (omega), various simulation parameters, final omega estimates (omega1) and information matrices (info1_omega), ongoing estimates of omega (ongoing_omega_est) and standard error of the estimates (ongoing_se_omega), and completed conditions (completed_conditions).

References

Segall, D. O. (2009). Principles of Multidimensional Adaptive Testing. In W. J. van der Linden & C. A. W. Glas (Eds.), Elements of Adaptive Testing (pp. 57-75). https://doi.org/10.1007/978-0-387-85461-8_3

Examples

sim_res <- cog_cat_sim(data = ex3$y, model = 'sdt', guessing = NULL,
                       contrast_codes = "contr.poly", num_conditions = 10,
                       num_contrasts = 2, constraints = NULL, key = ex3$key,
                       omega = ex3$omega, item_disc = ex3$lambda,
                       item_int = ex3$nu, conditions = ex3$condition,
                       int_par = c(1, 2), start_conditions = 3,
                       max_conditions = 3, link = "probit")
summary(sim_res)
plot(sim_res)

Fit Item Response Theory Models with Optional Contrast Effects

Description

This function estimates item response theory (IRT) model parameters. Users can optionally estimate person parameters that account for experimental or longitudinal contrast effects.

Usage

cog_irt(
  data = NULL,
  model = NULL,
  guessing = NULL,
  contrast_codes = NULL,
  num_conditions = NULL,
  num_contrasts = NULL,
  constraints = NULL,
  key = NULL,
  link = "probit",
  verbose = TRUE,
  ...
)

Arguments

Value

A list with elements for all parameters estimated (omega1, nu1, and/or lambda1), information values for all parameters estimated (info1_omega, info1_nu, and/or info1_lambda), the model log-likelihood value (log_lik), and the total number of estimated parameters (par) in the model.

Dimensions

I = Number of items per condition; J = Number of conditions or time points; K = Number of examinees; M Number of ability (or trait) dimensions; N Number of contrast effects (including intercept).

References

Embretson S. E., & Reise S. P. (2000). Item response theory for psychologists. Mahwah, N.J.: L. Erlbaum Associates.

Thomas, M. L., Brown, G. G., Patt, V. M., & Duffy, J. R. (2021). Latent variable modeling and adaptive testing for experimental cognitive psychopathology research. Educational and Psychological Measurement, 81(1), 155-181.

Examples

nback_fit_contr <- cog_irt(data = nback$y, model = "sdt",
                           contrast_codes = "contr.poly", key = nback$key,
                           num_conditions = length(unique(nback$condition)),
                           num_contrasts = 2)
plot(nback_fit_contr)

CPT Data

Description

CPT task accuracy data collected from an online experiment. The condition vector indicates backward mask onset (50, 100, 150, or 200 ms).The key indicates whether items are targets (1) or distractors (2).

Usage

cpt

Format

A list with the following elements:

y

Matrix of dichotomous responses.

key

Item key vector where 1 indicates target and 2 indicates distractor (IJ)

condition

Condition vector indiciting distinct conditions or time points.

Derivatives and Information for Lambda

Description

This function calculates the matrix of first partial derivatives, the matrix of second partial derivatives, and matrix of posterior and Fisher information for the posterior distribution with respect to alpha (discrimination) based on the slope-intercept form of the 1-, 2-, or 3-P item response theory model.

Usage

deriv_lambda(
  y = NULL,
  omega = NULL,
  gamma = NULL,
  lambda = NULL,
  zeta = NULL,
  kappa = NULL,
  nu = NULL,
  lambda_mu = NULL,
  lambda_sigma2 = NULL,
  link = NULL
)

Arguments

Value

List with elements fpd (1 by JM vector of first partial derivatives for alpha), spd (JM by JM matrix of second partial derivatives for alpha), post_info (JM by JM posterior information matrix for alpha), and fisher_info (JM by JM Fisher information matrix for alpha). Within each of these elements, there are sub-elements for all IJ items

Dimensions

I = Number of items per condition; J = Number of conditions; K = Number of examinees; M Number of ability (or trait) dimensions; N Number of contrasts (should include intercept).

A Note About Model Notation

The function converts GLLVM notation to the more typical IRT notation used by Segall (1996) for ease of referencing formulas (with the exception of using the slope-intercept form of the item response model).

References

Carlson, J. E. (1987). Multidimensional Item Response Theory Estimation: A computer program (Reprot No. ONR87-2). The American College Testing Program. https://apps.dtic.mil/sti/pdfs/ADA197160.pdf

Segall, D. O. (1996). Multidimensional adaptive testing. Psychometrika, 61(2), 331-354. https://doi.org/10.1007/BF02294343

Segall, D. O. (2009). Principles of Multidimensional Adaptive Testing. In W. J. van der Linden & C. A. W. Glas (Eds.), Elements of Adaptive Testing (pp. 57-75). https://doi.org/10.1007/978-0-387-85461-8_3

Derivatives and Information for Nu

Description

This function calculates the matrix of first partial derivatives, the matrix of second partial derivatives, and matrix of posterior and Fisher information for the posterior distribution with respect to nu (easiness) based on the slope-intercept form of the 1-, 2-, or 3-P item response theory model.

Usage

deriv_nu(
  y = NULL,
  omega = NULL,
  gamma = NULL,
  lambda = NULL,
  zeta = NULL,
  nu = NULL,
  kappa = NULL,
  nu_mu = NULL,
  nu_sigma2 = NULL,
  link = NULL
)

Arguments

Value

List with elements fpd (1 by 1 vector of first partial derivatives for nu), spd (1 by 1 matrix of second partial derivatives for nu), post_info (1 by 1 posterior information matrix for nu), and fisher_info (1 by 1) Fisher information matrix for nu). Within each of these elements, there are sub-elements for all IJ items.

Dimensions

I = Number of items per condition; J = Number of conditions; K = Number of examinees; M Number of ability (or trait) dimensions; N Number of contrasts (should include intercept).

A Note About Model Notation

The function converts GLLVM notation to the more typical IRT notation used by Segall (1996) for ease of referencing formulas (with the exception of using the slope-intercept form of the item response model).

References

Carlson, J. E. (1987). Multidimensional Item Response Theory Estimation: A computer program (Reprot No. ONR87-2). The American College Testing Program. https://apps.dtic.mil/sti/pdfs/ADA197160.pdf

Segall, D. O. (1996). Multidimensional adaptive testing. Psychometrika, 61(2), 331-354. https://doi.org/10.1007/BF02294343

Segall, D. O. (2009). Principles of Multidimensional Adaptive Testing. In W. J. van der Linden & C. A. W. Glas (Eds.), Elements of Adaptive Testing (pp. 57-75). https://doi.org/10.1007/978-0-387-85461-8_3

Derivatives and Information for Omega

Description

This function calculates the matrix of first partial derivatives, the matrix of second partial derivatives, and matrix of posterior and Fisher information for the posterior distribution with respect to omega (ability) based on the slope-intercept form of the 1-, 2-, or 3-parameter item response theory model.

Usage

deriv_omega(
  y = NULL,
  omega = NULL,
  gamma = NULL,
  lambda = NULL,
  zeta = NULL,
  nu = NULL,
  kappa = NULL,
  omega_mu = NULL,
  omega_sigma2 = NULL,
  zeta_mu = NULL,
  zeta_sigma2 = NULL,
  est_zeta = TRUE,
  link = NULL
)

Arguments

Value

List with elements fpd (1 by MN vector of first partial derivatives for omega), spd (MN by MN matrix of second partial derivatives for omega), post_info (MN by MN posterior information matrix for omega), and fisher_info (MN by MN Fisher information matrix for omega). Within each of these elements, there are sub-elements for all K examinees.

Dimensions

I = Number of items per condition; J = Number of conditions; K = Number of examinees; M Number of ability (or trait) dimensions; N Number of contrasts (should include intercept).

A Note About Model Notation

The function converts GLLVM notation to the more typical IRT notation used by Segall (1996) for ease of referencing formulas (with the exception of using the slope-intercept form of the item response model).

References

Segall, D. O. (1996). Multidimensional adaptive testing. Psychometrika, 61(2), 331-354. https://doi.org/10.1007/BF02294343

Segall, D. O. (2009). Principles of Multidimensional Adaptive Testing. In W. J. van der Linden & C. A. W. Glas (Eds.), Elements of Adaptive Testing (pp. 57-75). https://doi.org/10.1007/978-0-387-85461-8_3

Dichotomous Response Model

Description

This function calculates predictions and log-likelihood values for a dichotomous response model framed using generalized latent variable modeling (GLVM; Skrondal & Rabe-Hesketh, 2004).

Usage

dich_response_model(
  y = NULL,
  omega = NULL,
  gamma = NULL,
  lambda = NULL,
  zeta = NULL,
  nu = NULL,
  kappa = NULL,
  link = NULL
)

Arguments

Value

p = response probability matrix (K by IJ); yhatstar = latent response variate matrix (K by IJ); loglikelihood = model log-likelihood (scalar).

Dimensions

I = Number of items per condition; J = Number of conditions; K = Number of examinees; M Number of ability (or trait) dimensions; N Number of contrasts (should include intercept).

References

Skrondal, A., & Rabe-Hesketh, S. (2004). Generalized latent variable modeling: Multilevel, longitudinal, and structural equation models. Boca Raton: Chapman & Hall/CRC.

Simulate Dichotomous Response Model

Description

This function calculates the matrix of first partial derivatives, the matrix of second partial derivatives, and the information matrix for the posterior distribution with respect to theta (ability) based on theslope-intercept form of the item response theory model.

Usage

dich_response_sim(
  I = NULL,
  J = NULL,
  K = NULL,
  M = NULL,
  N = NULL,
  omega = NULL,
  omega_mu = NULL,
  omega_sigma2 = NULL,
  gamma = NULL,
  lambda = NULL,
  lambda_mu = NULL,
  lambda_sigma2 = NULL,
  nu = NULL,
  nu_mu = NULL,
  nu_sigma2 = NULL,
  zeta = NULL,
  zeta_mu = NULL,
  zeta_sigma2 = NULL,
  kappa = NULL,
  key = NULL,
  link = "probit"
)

Arguments

Value

y = simulated response matrix; yhatstar = simulated latent response probability matrix; [simulation_parameters]

References

Skrondal, A., & Rabe-Hesketh, S. (2004). Generalized latent variable modeling: Multilevel, longitudinal, and structural equation models. Boca Raton: Chapman & Hall/CRC.

Thomas, M. L., Brown, G. G., Gur, R. C., Moore, T. M., Patt, V. M., Risbrough, V. B., & Baker, D. G. (2018). A signal detection-item response theory model for evaluating neuropsychological measures. Journal of Clinical and Experimental Neuropsychology, 40(8), 745-760.

Examples

# Example 1

I <- 100
J <- 1
K <- 250
M <- 1
N <- 1
omega_mu <- matrix(data = 0, nrow = 1, ncol = M * N)
omega_sigma2 <- diag(x = 1, nrow = M * N)
gamma <- diag(x = 1, nrow = J * M, ncol = M * N)
lambda_mu <- matrix(data = 1, nrow = 1, ncol = M)
lambda_sigma2 <- diag(x = 0.25, nrow = M)
zeta_mu <- matrix(data = rep(x = 0, times = M * J), nrow = 1, ncol = J * M)
zeta_sigma2 <- diag(x = 0, nrow = J * M, ncol = J * M)
nu_mu <- matrix(data = 0, nrow = 1, ncol = 1)
nu_sigma2 <- matrix(data = 1, nrow = 1, ncol = 1)
set.seed(624)
ex1 <- dich_response_sim(I = I, J = J, K = K, M = M, N = N,
                         omega_mu = omega_mu, omega_sigma2 = omega_sigma2,
                         gamma = gamma, lambda_mu = lambda_mu,
                         lambda_sigma2 = lambda_sigma2, nu_mu = nu_mu,
                         nu_sigma2 = nu_sigma2, zeta_mu = zeta_mu,
                         zeta_sigma2 = zeta_sigma2)

# Example 2

I <- 100
J <- 1
K <- 50
M <- 2
N <- 1
omega_mu <- matrix(data = c(3.50, 1.00), nrow = 1, ncol = M * N)
omega_sigma2 <- diag(x = c(0.90, 0.30), nrow = M * N)
gamma <- diag(x = 1, nrow = J * M, ncol = M * N)
key <- rbinom(n = I * J, size = 1, prob = .7) + 1
measure_weights <-
  matrix(data = c(0.5, -1.0, 0.5, 1.0), nrow = 2, ncol = M, byrow = TRUE)
lambda <- matrix(data = 0, nrow = I * J, ncol = J * M)
for(j in 1:J) {
  lambda[(1 + (j - 1) * I):(j * I), (1 + (j - 1) * M):(j * M)] <-
    measure_weights[key, ][(1 + (j - 1) * I):(j * I), ]
}
zeta_mu <- matrix(data = rep(x = 0, times = M * J), nrow = 1, ncol = J * M)
zeta_sigma2 <- diag(x = 0, nrow = J * M, ncol = J * M)
nu_mu <- matrix(data = 0, nrow = 1, ncol = 1)
nu_sigma2 <- matrix(data = .2, nrow = 1, ncol = 1)
set.seed(624)
ex2 <- dich_response_sim(I = I, J = J, K = K, M = M, N = N,
                         omega_mu = omega_mu, omega_sigma2 = omega_sigma2,
                         gamma = gamma, lambda = lambda, nu_mu = nu_mu,
                         nu_sigma2 = nu_sigma2, zeta_mu = zeta_mu,
                         zeta_sigma2 = zeta_sigma2, key = key)

# Example 3

I <- 20
J <- 10
K <- 50
M <- 2
N <- 2
omega_mu <- matrix(data = c(2.50, -2.00, 0.50, 0.00), nrow = 1, ncol = M * N)
omega_sigma2 <- diag(x = c(0.90, 0.70, 0.30, 0.10), nrow = M * N)
contrast_codes <- cbind(1, contr.poly(n = J))[, 1:N]
gamma <- matrix(data = 0, nrow = J * M, ncol = M * N)
for(j in 1:J) {
  for(m in 1:M) {
    gamma[(m + M * (j - 1)), (((m - 1) * N + 1):((m - 1) * N + N))] <-
      contrast_codes[j, ]
  }
}
key <- rbinom(n = I * J, size = 1, prob = .7) + 1
measure_weights <-
  matrix(data = c(0.5, -1.0, 0.5, 1.0), nrow = 2, ncol = M, byrow = TRUE)
lambda <- matrix(data = 0, nrow = I * J, ncol = J * M)
for(j in 1:J) {
  lambda[(1 + (j - 1) * I):(j * I), (1 + (j - 1) * M):(j * M)] <-
    measure_weights[key, ][(1 + (j - 1) * I):(j * I), ]
}
zeta_mu <- matrix(data = rep(x = 0, times = M * J), nrow = 1, ncol = J * M)
zeta_sigma2 <- diag(x = 0.2, nrow = J * M, ncol = J * M)
nu_mu <- matrix(data = c(0.00), nrow = 1, ncol = 1)
nu_sigma2 <- matrix(data = c(0.20), nrow = 1, ncol = 1)
set.seed(624)
ex3 <- dich_response_sim(I = I, J = J, K = K, M = M, N = N,
                         omega_mu = omega_mu, omega_sigma2 = omega_sigma2,
                         gamma = gamma, lambda = lambda, nu_mu = nu_mu,
                         nu_sigma2 = nu_sigma2, zeta_mu = zeta_mu,
                         zeta_sigma2 = zeta_sigma2, key = key)

# Example 4

I <- 25
J <- 2
K <- 200
M <- 1
N <- 2
omega_mu <- matrix(data = c(1, -2), nrow = 1, ncol = M * N)
omega_sigma2 <- diag(x = c(1.00, 0.25), nrow = M * N)
contrast_codes <- cbind(1, contr.treatment(n = J))[, 1:N]
gamma <- matrix(data = 0, nrow = J * M, ncol = M * N)
for(j in 1:J) {
  for(m in 1:M) {
    gamma[(m + M * (j - 1)), (((m - 1) * N + 1):((m - 1) * N + N))] <-
    contrast_codes[j, ]
  }
}
lambda <- matrix(data = 0, nrow = I * J, ncol = J * M)
lam_vals <- rnorm(I, 1.5, .23)
for (j in 1:J) {
  lambda[(1 + (j - 1) * I):(j * I), (1 + (j - 1) * M):(j * M)] <- lam_vals
}
zeta_mu <- matrix(data = rep(x = 0, times = M * J), nrow = 1, ncol = J * M)
zeta_sigma2 <- diag(x = 0.2, nrow = J * M, ncol = J * M)
nu <- matrix(data = rnorm(n = I, mean = 0, sd = 2), nrow = I * J, ncol = 1)
set.seed(624)
ex4 <- dich_response_sim(I = I, J = J, K = K, M = M, N = N,
                         omega_mu = omega_mu, omega_sigma2 = omega_sigma2,
                         gamma = gamma, lambda = lambda, nu = nu,
                         zeta_mu = zeta_mu, zeta_sigma2 = zeta_sigma2)

# Example 5

I <- 20
J <- 10
K <- 1
M <- 2
N <- 2
omega_mu <- matrix(data = c(2.50, -2.00, 0.50, 0.00), nrow = 1, ncol = M * N)
omega_sigma2 <- diag(x = c(0.90, 0.70, 0.30, 0.10), nrow = M * N)
contrast_codes <- cbind(1, contr.poly(n = J))[, 1:N]
gamma <- matrix(data = 0, nrow = J * M, ncol = M * N)
for(j in 1:J) {
  for(m in 1:M) {
    gamma[(m + M * (j - 1)), (((m - 1) * N + 1):((m - 1) * N + N))] <-
      contrast_codes[j, ]
  }
}
key <- rbinom(n = I * J, size = 1, prob = .7) + 1
measure_weights <-
  matrix(data = c(0.5, -1.0, 0.5, 1.0), nrow = 2, ncol = M, byrow = TRUE)
lambda <- matrix(data = 0, nrow = I * J, ncol = J * M)
for(j in 1:J) {
  lambda[(1 + (j - 1) * I):(j * I), (1 + (j - 1) * M):(j * M)] <-
    measure_weights[key, ][(1 + (j - 1) * I):(j * I), ]
}
zeta_mu <- matrix(data = rep(x = 0, times = M * J), nrow = 1, ncol = J * M)
zeta_sigma2 <- diag(x = 0.2, nrow = J * M, ncol = J * M)
nu_mu <- matrix(data = c(0.00), nrow = 1, ncol = 1)
nu_sigma2 <- matrix(data = c(0.20), nrow = 1, ncol = 1)
set.seed(624)
ex5 <- dich_response_sim(I = I, J = J, K = K, M = M, N = N,
                         omega_mu = omega_mu, omega_sigma2 = omega_sigma2,
                         gamma = gamma, lambda = lambda, nu_mu = nu_mu,
                         nu_sigma2 = nu_sigma2, zeta_mu = zeta_mu,
                         zeta_sigma2 = zeta_sigma2, key = key)

Simulated Data for a Unidimensional Two-Parameter Item Response Model

Description

Data and parameters were simulated based on example 1 provided for the sim_dich_response.R function.

Usage

ex1

Format

A list with the following elements:

y

Matrix of dichotomous responses.

ystar

Matrix of latent response variates.

omega

Subject-level effects of the experimental manipulation.

omega_mu

Vector of means for the subject-level effects of the experimental manipulation (1 by K * M).

omega_sigma2

Covariance matrix for the subject-level effects of the experimental manipulation (K * M by K * M).

gamma

Contrast codes matrix.

lambda

Matrix of item slope parameters.

lambda_mu

Vector of means for the item slope parameters (1 by JM).

lambda_sigma2

Covariance matrix for the item slope parameters (JM by JM).

nu

Mean of the item intercept parameters (scalar).

nu_mu

Mean of the item intercept parameters (scalar).

nu_sigma2

Variance of the item intercept parameters (scalar).

zeta

Condition-level prediction errors.

zeta_mu

Vector of means for the condition-level prediction errors (1 by J * M).

zeta_sigma2

Covariance matrix for the condition-level prediction errors (J * M by J * M).

kappa

Item guessing matrix (K by IJ).

condition

Condition vector indiciting distinct conditions or time points.

key

Item key vector where 1 indicates target and 2 indicates distractor (IJ)

...

Simulated Data for a Signal Detection Weighted IRT Model

Description

Data and parameters were simulated based on example 2 provided for the sim_dich_response.R function.

Usage

ex2

Format

A list with the following elements:

y

Matrix of dichotomous responses.

ystar

Matrix of latent response variates.

omega

Subject-level effects of the experimental manipulation.

omega_mu

Vector of means for the subject-level effects of the experimental manipulation (1 by K * M).

omega_sigma2

Covariance matrix for the subject-level effects of the experimental manipulation (K * M by K * M).

gamma

Contrast codes matrix.

lambda

Matrix of item slope parameters.

lambda_mu

Vector of means for the item slope parameters (1 by JM).

lambda_sigma2

Covariance matrix for the item slope parameters (JM by JM).

nu

Mean of the item intercept parameters (scalar).

nu_mu

Mean of the item intercept parameters (scalar).

nu_sigma2

Variance of the item intercept parameters (scalar).

zeta

Condition-level prediction errors.

zeta_mu

Vector of means for the condition-level prediction errors (1 by J * M).

zeta_sigma2

Covariance matrix for the condition-level prediction errors (J * M by J * M).

kappa

Item guessing matrix (K by IJ).

condition

Condition vector indiciting distinct conditions or time points.

key

Item key vector where 1 indicates target and 2 indicates distractor (IJ)

...

Simulated Data for a Signal Detection Weighted IRT Model with an Experimental Design

Description

Data and parameters were simulated based on example 3 provided for the sim_dich_response.R function.

Usage

ex3

Format

A list with the following elements:

y

Matrix of dichotomous responses.

ystar

Matrix of latent response variates.

omega

Subject-level effects of the experimental manipulation.

omega_mu

Vector of means for the subject-level effects of the experimental manipulation (1 by K * M).

omega_sigma2

Covariance matrix for the subject-level effects of the experimental manipulation (K * M by K * M).

gamma

Contrast codes matrix.

lambda

Matrix of item slope parameters.

lambda_mu

Vector of means for the item slope parameters (1 by JM).

lambda_sigma2

Covariance matrix for the item slope parameters (JM by JM).

nu

Mean of the item intercept parameters (scalar).

nu_mu

Mean of the item intercept parameters (scalar).

nu_sigma2

Variance of the item intercept parameters (scalar).

zeta

Condition-level prediction errors.

zeta_mu

Vector of means for the condition-level prediction errors (1 by J * M).

zeta_sigma2

Covariance matrix for the condition-level prediction errors (J * M by J * M).

kappa

Item guessing matrix (K by IJ).

condition

Condition vector indiciting distinct conditions or time points.

key

Item key vector where 1 indicates target and 2 indicates distractor (IJ)

...

Simulated Data for a Unidimensional Two-Parameter Item Response Model with Two Measurement Occasions

Description

Data and parameters were simulated based on example 4 provided for the sim_dich_response.R function.

Usage

ex4

Format

A list with the following elements:

y

Matrix of dichotomous responses.

ystar

Matrix of latent response variates.

omega

Subject-level effects of the experimental manipulation.

omega_mu

Vector of means for the subject-level effects of the experimental manipulation (1 by K * M).

omega_sigma2

Covariance matrix for the subject-level effects of the experimental manipulation (K * M by K * M).

gamma

Contrast codes matrix.

lambda

Matrix of item slope parameters.

lambda_mu

Vector of means for the item slope parameters (1 by JM).

lambda_sigma2

Covariance matrix for the item slope parameters (JM by JM).

nu

Mean of the item intercept parameters (scalar).

nu_mu

Mean of the item intercept parameters (scalar).

nu_sigma2

Variance of the item intercept parameters (scalar).

zeta

Condition-level prediction errors.

zeta_mu

Vector of means for the condition-level prediction errors (1 by J * M).

zeta_sigma2

Covariance matrix for the condition-level prediction errors (J * M by J * M).

kappa

Item guessing matrix (K by IJ).

condition

Condition vector indiciting distinct conditions or time points.

key

Item key vector where 1 indicates target and 2 indicates distractor (IJ)

...

Simulated Single Subject Data for a Signal Detection Weighted IRT Model with an Experimental Design

Description

Data and parameters were simulated based on example 5 provided for the sim_dich_response.R function.

Usage

ex5

Format

A list with the following elements:

y

Matrix of dichotomous responses.

ystar

Matrix of latent response variates.

omega

Subject-level effects of the experimental manipulation.

omega_mu

Vector of means for the subject-level effects of the experimental manipulation (1 by K * M).

omega_sigma2

Covariance matrix for the subject-level effects of the experimental manipulation (K * M by K * M).

gamma

Contrast codes matrix.

lambda

Matrix of item slope parameters.

lambda_mu

Vector of means for the item slope parameters (1 by JM).

lambda_sigma2

Covariance matrix for the item slope parameters (JM by JM).

nu

Mean of the item intercept parameters (scalar).

nu_mu

Mean of the item intercept parameters (scalar).

nu_sigma2

Variance of the item intercept parameters (scalar).

zeta

Condition-level prediction errors.

zeta_mu

Vector of means for the condition-level prediction errors (1 by J * M).

zeta_sigma2

Covariance matrix for the condition-level prediction errors (J * M by J * M).

kappa

Item guessing matrix (K by IJ).

condition

Condition vector indiciting distinct conditions or time points.

key

Item key vector where 1 indicates target and 2 indicates distractor (IJ)

...

Flanker Data

Description

Flanker task accuracy data collected from an online experiment. The condition vector indicates level of congruency ("congruent, incongruent_part, incongruent_all, neutral).

Usage

flanker

Format

A list with the following elements:

y

Matrix of dichotomous responses.

condition

Condition vector indiciting distinct conditions or time points.

Method of anova for cogirt S3

Description

This function compares fit of models produced by cogirt.

Usage

lrt(object, ...)

Arguments

Value

An object of class "anova".

MHMC Parameter Estimates for Multiple Chains

Description

This function calculates MHMC parameter estimates for multiple chains. See documentation for mhmc_sc.R for more information.

Usage

mhmc_mc(
  chains = NULL,
  y = y,
  obj_fun = NULL,
  link = NULL,
  est_omega = TRUE,
  est_lambda = TRUE,
  est_zeta = TRUE,
  est_nu = TRUE,
  omega0 = NULL,
  gamma0 = NULL,
  lambda0 = NULL,
  zeta0 = NULL,
  nu0 = NULL,
  kappa0 = NULL,
  omega_mu = NULL,
  omega_sigma2 = NULL,
  lambda_mu = NULL,
  lambda_sigma2 = NULL,
  zeta_mu = NULL,
  zeta_sigma2 = NULL,
  nu_mu = NULL,
  nu_sigma2 = NULL,
  burn = NULL,
  thin = NULL,
  min_tune = NULL,
  tune_int = NULL,
  max_tune = NULL,
  niter = NULL,
  psrf = FALSE
)

Arguments

Value

List with elements omega_draws (draws from every saved iteration of the MHMC sampler), omegaEAP (expected a posteriori estimates for omega), omegaPSD (posterior standard deviation estimates for omega), omega_psrf (potential scale reduction factor for omega), nuEAP (expected a posteriori estimates for nu), nuPSD (posterior standard deviation estimates for nu), nu_psrf (potential scale reduction factor for nu), zetaEAP (expected a posteriori estimates for zeta), zetaPSD (posterior standard deviation estimates for zeta), zeta_psrf (potential scale reduction factor for zeta).

MHMC Parameter Estimates for Single Chain

Description

This function uses the Metropolis-Hastings algorithm for a single chain to calculate parameter estimates using the Markov Chain Monte Carlo method. The method implemented follows Patz and Junker (1999). The approach to tuning the scale and covariance matrix follows BDA and SAS 9.2 User Guide, 2nd Ed. "The MCMC Procedure: Tuning the Proposal Distribution".

Usage

mhmc_sc(
  y = y,
  obj_fun = NULL,
  link = NULL,
  est_omega = TRUE,
  est_lambda = TRUE,
  est_zeta = TRUE,
  est_nu = TRUE,
  omega0 = NULL,
  gamma0 = NULL,
  lambda0 = NULL,
  zeta0 = NULL,
  nu0 = NULL,
  kappa0 = NULL,
  omega_mu = NULL,
  omega_sigma2 = NULL,
  lambda_mu = NULL,
  lambda_sigma2 = NULL,
  zeta_mu = NULL,
  zeta_sigma2 = NULL,
  nu_mu = NULL,
  nu_sigma2 = NULL,
  burn = NULL,
  thin = NULL,
  min_tune = NULL,
  tune_int = NULL,
  max_tune = NULL,
  niter = NULL,
  weight = 1,
  verbose = FALSE
)

Arguments

Value

List with elements omega_draws (list of (niter - burn) / thin draws for K by MN omega matrix), lambda_draws (list of (niter - burn) / thin draws for IJ by JM lambda matrix), zeta_draws (list of (niter - burn) / thin draws for K by JM zeta matrix), nu_draws (list of (niter - burn) / thin draws for IJ by 1 nu matrix), cand_o_var (list of K final MN by MN candidate proposal covariance matrices for omega for each examinee), cand_l_var (list of IJ final JM by JM candidate proposal covariance matrices for lambda for each item), cand_z_var (list of final JM by JM candidate proposal covariance matrices for zeta for all examinees), and cand_n_var (list of IJ final scalar candidate proposal variances for nu for all items).

References

Patz, R. J., & Junker, B. W. (1999). A Straightforward Approach to Markov Chain Monte Carlo Methods for Item Response Models. Journal of Educational and Behavioral Statistics, 24(2), 146.

MHRM Parameter Estimates for Multiple Chains

Description

This function calculates mhrm parameter estimates for multiple chains.

Usage

mhrm(
  y = y,
  obj_fun = NULL,
  link = NULL,
  est_omega = TRUE,
  est_lambda = TRUE,
  est_zeta = TRUE,
  est_nu = TRUE,
  omega0 = NULL,
  gamma0 = NULL,
  lambda0 = NULL,
  zeta0 = NULL,
  nu0 = NULL,
  kappa0 = NULL,
  omega_mu = NULL,
  omega_sigma2 = NULL,
  lambda_mu = NULL,
  lambda_sigma2 = NULL,
  zeta_mu = NULL,
  zeta_sigma2 = NULL,
  nu_mu = NULL,
  nu_sigma2 = NULL,
  constraints = NULL,
  J = NULL,
  M = NULL,
  N = NULL,
  verbose = TRUE,
  ...
)

Arguments

Value

List with elements for all parameters estimated, information values for all parameters estimated, and the model log-likelihood value.

References

Cai, L. (2010). High-dimensional exploratory item factor analysis by a Metropolis-Hastings Robbins-Monro algorithm. Psychometrika, 75(1), 33-57.

Cai, L. (2010). Metropolis-Hastings Robbins-Monro algorithm for confirmatory item factor analysis. Journal of Educational and Behavioral Statistics, 35(3), 307-335.

N-Back Data

Description

N-Back task accuracy data collected from an online experiment. The condition vector indicates working memory load level (1-back, 2-back, 3-back, or 4-back). The key indicates whether items are targets (1) or distractors (2).

Usage

nback

Format

A list with the following elements:

y

Matrix of dichotomous responses.

key

Item key vector where 1 indicates target and 2 indicates distractor (IJ)

condition

Condition vector indiciting distinct conditions or time points.

Method of Plot for Simulated Adaptive Testing Using cogirt S3

Description

This function produces plots for standard errors for cog_cat_sim results

Usage

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

Arguments

Value

This function returns a base R plot displayed in the graphics device. It does not return any value to the R environment.

Method of Plot for cogirt S3

Description

This function produces plots for parameter estimates produced for various cogirt models.

Usage

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

Arguments

Value

This function returns a base R plot displayed in the graphics device. It does not return any value to the R environment.

PLT Data

Description

Probabilistic Learning Task (SOPT) accuracy data collected from an online experiment. The condition vector indicates feedback consistency (90 70 vector indicates which side was rewarded.

Usage

plt

Format

A list with the following elements:

y

Matrix of dichotomous responses.

targ

Item targ left vs. right vector (IJ)

fdbk

Item fdbk left vs. right vector (IJ)

condition

Condition vector indiciting distinct conditions or time points.

SOPT Data

Description

Self-Ordered Pointing Task (SOPT) accuracy data collected from an online experiment. The condition vector indicates working memory load level (3, 6, 9, or 12 items).

Usage

sopt

Format

A list with the following elements:

y

Matrix of dichotomous responses.

condition

Condition vector indiciting distinct conditions or time points.

Sternberg Data

Description

Sternberg task accuracy data collected from an online experiment. The condition vector indicates working memory load level (2, 4, 6, 8, 10, or 12 items).The key indicates whether items are targets (1) or distractors (2).

Usage

sternberg

Format

A list with the following elements:

y

Matrix of dichotomous responses.

key

Item key vector where 1 indicates target and 2 indicates distractor (IJ)

condition

Condition vector indiciting distinct conditions or time points.

Method of Summary for cog_cat_sim S3

Description

This function provides summary statistics for simulated computerized adaptive testing.

Usage

## S3 method for class 'cog_cat_sim'
summary(object, ...)

Arguments

Value

This function does not return a value to the R environment. Instead, it prints a comprehensive summary of the simulated computerized adaptive testing results to the console. The output includes model name and simulation settings as well as summary statistics for each parameter of interest. The function is intended for interactive use.

Method of Summary for cog_irt S3

Description

This function provides summary statistics for cogirt models.

Usage

## S3 method for class 'cog_irt'
summary(object, ...)

Arguments

Value

This function does not return a value to the R environment. Instead, it prints a detailed summary of the specified IRT model to the console. The output includes the type of IRT model (e.g., One-Parameter, Two-Parameter, etc.), the number of subjects and items in the dataset, the log-likelihood of the model, and summary statistics (mean, standard deviation, median standard error, and reliability) for estimated parameters. The function is intended for interactive use to review the results of the fitted model.