estimate_3pl function

Estimation of the 3PL model

Estimate the 3PL model using the joint or marginal maximum likelihood estimation methods

model_3pl_eap scores response vectors using the EAP method

model_3pl_map scores response vectors using the MAP method

model_3pl_jmle estimates the item and ability parameters using the joint maximum likelihood estimation (JMLE) method

model_3pl_mmle estimates the item parameters using the marginal maximum likelihood estimation (MMLE) method

model_3pl_eap(u, a, b, c, D = 1.702, priors = c(0, 1),
  bounds_t = c(-4, 4))

model_3pl_map(u, a, b, c, D = 1.702, priors = c(0, 1),
  bounds_t = c(-4, 4), iter = 30, conv = 0.001)

model_3pl_dv_Pt(t, a, b, c, D)

model_3pl_dv_Pa(t, a, b, c, D)

model_3pl_dv_Pb(t, a, b, c, D)

model_3pl_dv_Pc(t, a, b, c, D)

model_3pl_dv_jmle(pdv_fn, u, t, a, b, c, D)

model_3pl_jmle(u, t = NA, a = NA, b = NA, c = NA, D = 1.702,
  iter = 100, conv = 0.001, nr_iter = 10, scale = c(0, 1),
  bounds_t = c(-4, 4), bounds_a = c(0.01, 2.5), bounds_b = c(-4, 4),
  bounds_c = c(0, 0.4), priors = list(t = c(0, 1)), decay = 1,
  verbose = FALSE, true_params = NULL)

model_3pl_dv_mmle(pdv_fn, u, quad, a, b, c, D)

model_3pl_mmle(u, t = NA, a = NA, b = NA, c = NA, D = 1.702,
  iter = 100, conv = 0.001, nr_iter = 10, bounds_t = c(-4, 4),
  bounds_a = c(0.01, 2.5), bounds_b = c(-4, 4), bounds_c = c(0, 0.4),
  priors = list(t = c(0, 1)), decay = 1, quad = "11",
  score_fn = c("eap", "map"), verbose = FALSE, true_params = NULL)

model_3pl_fitplot(u, t, a, b, c, D = 1.702, index = NULL,
  intervals = seq(-3, 3, 0.5))

Arguments

• u: observed response matrix, 2d matrix
• a: discrimination parameters, 1d vector (fixed value) or NA (freely estimate)
• b: difficulty parameters, 1d vector (fixed value) or NA (freely estimate)
• c: pseudo-guessing parameters, 1d vector (fixed value) or NA (freely estimate)
• D: the scaling constant, 1.702 by default
• priors: prior distributions, a list
• bounds_t: the bounds of ability parameters
• iter: the maximum iterations, default=100
• conv: the convergence criterion
• t: ability parameters, 1d vector (fixed value) or NA (freely estimate)
• pdv_fn: the function to compute derivatives of P w.r.t the estimating parameters
• nr_iter: the maximum newton-raphson iterations, default=10
• scale: the mean and SD of the theta scale, default=c(0,1) in JMLE
• bounds_a: the bounds of discrimination parameters
• bounds_b: the bounds of difficulty parameters
• bounds_c: the bounds of guessing parameters
• decay: decay rate, default=1
• verbose: TRUE to print details for debugging
• true_params: a list of true parameters for evaluating the parameter recovery
• quad: the number of quadrature points
• score_fn: the scoring function: 'eap' or 'map'
• index: the indices of items being plotted
• intervals: intervals on the x-axis

Returns

model_3pl_eap returns theta estimates and standard errors in a list

model_3pl_map returns theta estimates in a list

model_3pl_jmle returns estimated t, a, b, c parameters in a list

model_3pl_mmle returns estimated t, a, b, c parameters in a list

model_3pl_fitplot returns a ggplot object

Examples

with(model_3pl_gendata(10, 40), 
    cbind(true=t, est=model_3pl_eap(u, a, b, c)$t))
with(model_3pl_gendata(10, 40), 
     cbind(true=t, est=model_3pl_map(u, a, b, c)$t))

# generate data
x <- model_3pl_gendata(2000, 40)
# free estimation, 40 iterations
y <- model_3pl_jmle(x$u, true_params=x, iter=40, verbose=TRUE)
# fix c-parameters, 40 iterations
y <- model_3pl_jmle(x$u, c=0, true_params=x, iter=40)

# generate data
x <- model_3pl_gendata(2000, 40)
# free estimation, 40 iterations
y <- model_3pl_mmle(x$u, true_params=x, iter=40, verbose=TRUE)

with(model_3pl_gendata(1000, 20), 
     model_3pl_fitplot(u, t, a, b, c, index=c(1, 3, 5)))