estimate_grm: Estimation of the Graded Response Model
In Rirt: Data Analysis and Parameter Estimation Using Item Response Theory

Description Usage Arguments Value Examples

Estimate the GRM using the joint or marginal maximum likelihood estimation

model_grm_eap scores response vectors using the EAP method

model_grm_map scores response vectors using the MAP method

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

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

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

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

model_grm_dv_Pt(t, a, b, D)

model_grm_dv_Pa(t, a, b, D)

model_grm_dv_Pb(t, a, b, D)

model_grm_dv_jmle(u_ix, dvp)

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

model_grm_dv_mmle(u_ix, quad, pdv)

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

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

`u`	the observed response matrix, 2d matrix
`a`	discrimination parameters, 1d vector (fixed value) or NA (freely estimate)
`b`	difficulty parameters, 2d matrix (fixed value) or NA (freely estimate)
`D`	the scaling constant, 1.702 by default
`priors`	a list of prior distributions
`bounds_t`	bounds of ability parameters
`iter`	the maximum iterations
`conv`	the convergence criterion for the -2 log-likelihood
`t`	ability parameters, 1d vector (fixed value) or NA (freely estimate)
`u_ix`	the 3d indices
`dvp`	the derivatives of P
`nr_iter`	the maximum newton-raphson iterations, default=10
`scale`	the scale of theta parameters
`bounds_a`	bounds of discrimination parameters
`bounds_b`	bounds of location parameters
`decay`	decay rate
`verbose`	TRUE to print debuggin information
`true_params`	a list of true parameters for evaluating the estimation accuracy
`quad_degree`	the number of quadrature points
`score_fn`	the scoring method: 'eap' or 'map'
`index`	the indices of items being plotted
`intervals`	intervals on the x-axis

model_grm_eap returns theta estimates and standard errors in a list

model_grm_map returns theta estimates in a list

model_grm_jmle returns estimated t, a, b parameters in a list

model_grm_mmle returns estimated t, a, b parameters in a list

model_grm_fitplot returns a ggplot object

with(model_grm_gendata(10, 50, 3), 
     cbind(true=t, est=model_grm_eap(u, a, b)$t))
with(model_grm_gendata(10, 50, 3), 
     cbind(true=t, est=model_grm_map(u, a, b)$t))

# generate data
x <- model_grm_gendata(1000, 40, 3)
# free calibration, 40 iterations
y <- model_grm_jmle(x$u, true_params=x, iter=40, verbose=TRUE)


# generate data
x <- model_grm_gendata(1000, 40, 3)
# free estimation, 40 iterations
y <- model_grm_mmle(x$u, true_params=x, iter=40, verbose=TRUE)

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