estimate_3pl: Estimate 3-parameter-logistic model
In xxIRT: Item Response Theory and Computer-Based Testing in R

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)

`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

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)))