estimate_3pl function

Estimate 3-parameter-logistic model

Estimate the 3PL model using the maximum likelihood estimation

model_3pl_eap_scoring scores response vectors using the EAP method

model_3pl_map_scoring scores response vectors using the MAP method

model_3pl_dv_jmle calculates the first and second derivatives for the joint maximum likelihood estimation

model_3pl_estimate_jmle estimates the parameters using the joint maximum likelihood estimation (JMLE) method

model_3pl_dv_mmle calculates the first and second derivatives for the marginal maximum likelihood estimation

model_3pl_estimate_mmle estimates the parameters using the marginal maximum likelihood estimation (MMLE) method

model_3pl_eap_scoring(u, a, b, c, D = 1.702, prior = c(0, 1),
  bound = c(-3, 3))

model_3pl_map_scoring(u, a, b, c, D = 1.702, prior = c(0, 1),
  bound = c(-3, 3), nr_iter = 30, nr_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(dv, u)

model_3pl_estimate_jmle(u, t = NA, a = NA, b = NA, c = NA,
  D = 1.702, iter = 100, conv = 1, nr_iter = 10, nr_conv = 0.001,
  scale = c(0, 1), bounds_t = c(-3, 3), bounds_a = c(0.01, 2),
  bounds_b = c(-3, 3), bounds_c = c(0, 0.25), priors = list(t = c(0,
  1), a = c(-0.1, 0.2), b = c(0, 1), c = c(4, 20)), decay = 1,
  debug = FALSE, true_params = NULL)

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

model_3pl_estimate_mmle(u, t = NA, a = NA, b = NA, c = NA,
  D = 1.702, iter = 100, conv = 1, nr_iter = 10, nr_conv = 0.001,
  bounds_t = c(-3, 3), bounds_a = c(0.01, 2), bounds_b = c(-3, 3),
  bounds_c = c(0, 0.25), priors = list(t = c(0, 1), a = c(-0.1, 0.2), b
  = c(0, 1), c = c(4, 20)), decay = 1, quad_degree = "11",
  scoring = c("eap", "map"), debug = FALSE, true_params = NULL)

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

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
• prior: the prior distribution
• nr_iter: the maximum iterations of newton-raphson
• nr_conv: the convegence criterion for newton-raphson
• t: ability parameters, 1d vector (fixed value) or NA (freely estimate)
• iter: the maximum iterations
• conv: the convergence criterion of the -2 log-likelihood
• scale: the meand and SD of the theta scale, N(0, 1) for JMLE by default
• bounds_t: bounds of ability parameters
• bounds_a: bounds of discrimination parameters
• bounds_b: bounds of difficulty parameters
• bounds_c: bounds of guessing parameters
• priors: a list of prior distributions
• decay: decay rate
• debug: TRUE to print debuggin information
• true_params: a list of true parameters for evaluating the estimation accuracy
• pdv_fn: the function to compute derivatives of P w.r.t the estimating parameters
• quad_degree: the number of quadrature points
• scoring: the scoring method: 'eap' or 'map'
• index: the indices of items being plotted
• intervals: intervals on the x-axis
• show_points: TRUE to show points

Examples

with(model_3pl_gendata(10, 40), cbind(true=t, est=model_3pl_eap_scoring(u, a, b, c)$t))
with(model_3pl_gendata(10, 40), cbind(true=t, est=model_3pl_map_scoring(u, a, b, c)$t))
## Not run:

# generate data
x <- model_3pl_gendata(2000, 40)
# free estimation
y <- model_3pl_estimate_jmle(x$u, true_params=x)
# fix c-parameters
y <- model_3pl_estimate_jmle(x$u, c=0, true_params=x)
# no priors
y <- model_3pl_estimate_jmle(x$u, priors=NULL, iter=30, debug=T)
## End(Not run)

## Not run:

# generate data
x <- model_3pl_gendata(2000, 40)
# free estimation
y <- model_3pl_estimate_mmle(x$u, true_params=x)
# fix c-parameters
y <- model_3pl_estimate_mmle(x$u, c=0, true_params=x)
# no priors
y <- model_3pl_estimate_mmle(x$u, priors=NULL, iter=30, debug=T)
## End(Not run)

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