estimate_gpcm: Estimate Generalizaed Partial Credit Model
In xluo11/xxIRT: Item Response Theory and Computer-Based Testing

Estimate the GPCM using the maximum likelihood estimation

model_gpcm_eap_scoring scores response vectors using the EAP method

model_gpcm_map_scoring scores response vectors using maximum a posteriori

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

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

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

model_gpcm_map_scoring(u, a, b, d, D = 1.702, prior = NULL,
  bound = c(-3, 3), nr_iter = 30, nr_conv = 0.001)

model_gpcm_dv_Pt(t, a, b, d, D)

model_gpcm_dv_Pa(t, a, b, d, D)

model_gpcm_dv_Pb(t, a, b, d, D)

model_gpcm_dv_Pd(t, a, b, d, D)

model_gpcm_dv_jmle(ix, dvp)

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

model_gpcm_dv_mmle(u_ix, quad, pdv)

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

model_gpcm_fitplot(u, t, a, b, d, D = 1.702, insert_d0 = NULL,
  index = NULL, intervals = seq(-3, 3, 0.5), show_points = TRUE)

`u`	the 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)
`d`	category parameters, 2d matrix (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)
`ix`	the 3d indices
`dvp`	the derivatives of P
`iter`	the maximum iterations
`conv`	the convergence criterion of the -2 log-likelihood
`scale`	the scale of theta parameters
`bounds_t`	bounds of ability parameters
`bounds_a`	bounds of discrimination parameters
`bounds_b`	bounds of location parameters
`bounds_d`	bounds of category 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
`quad_degree`	the number of quadrature points
`scoring`	the scoring method: 'eap' or 'map'
`insert_d0`	insert an initial category value
`index`	the indices of items being plotted
`intervals`	intervals on the x-axis
`show_points`	TRUE to show points

with(model_gpcm_gendata(10, 40, 3), cbind(true=t, est=model_gpcm_eap_scoring(u, a, b, d)$t))
with(model_gpcm_gendata(10, 40, 3), cbind(true=t, est=model_gpcm_map_scoring(u, a, b, d)$t))
## Not run: 
# generate data
x <- model_gpcm_gendata(1000, 40, 3)
# free calibration
y <- model_gpcm_estimate_jmle(x$u, true_params=x)
# no priors
y <- model_gpcm_estimate_jmle(x$u, priors=NULL, true_params=x)

## End(Not run)
## Not run: 
# generate data
x <- model_gpcm_gendata(1000, 40, 3)
# free estimation
y <- model_gpcm_estimate_mmle(x$u, true_params=x)
# no priors
y <- model_gpcm_estimate_mmle(x$u, priors=NULL, true_params=x)

## End(Not run)
with(model_gpcm_gendata(1000, 20, 3), model_gpcm_fitplot(u, t, a, b, d, index=c(1, 3, 5)))