Rirt (version 0.0.2)

estimate_gpcm: Estimation of the Generalizaed Partial Credit Model

Description

Estimate the GPCM using the joint or marginal maximum likelihood estimation

model_gpcm_eap scores response vectors using the EAP method

model_gpcm_map scores response vectors using the MAP method

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

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

Usage

model_gpcm_eap(u, a, b, d, D = 1.702, priors = c(0, 1),
  bounds_t = c(-4, 4))
model_gpcm_map(u, a, b, d, D = 1.702, priors = c(0, 1),
  bounds_t = c(-4, 4), iter = 30, 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(u_ix, dvp)
model_gpcm_jmle(u, t = NA, a = NA, b = NA, d = 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),
  bounds_d = c(-4, 4), priors = list(t = c(0, 1)), decay = 1,
  verbose = FALSE, true_params = NULL)
model_gpcm_dv_mmle(u_ix, quad, pdv)
model_gpcm_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), bounds_d = 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_gpcm_fitplot(u, t, a, b, d, D = 1.702, d0 = NULL, index = NULL,
  intervals = seq(-3, 3, 0.5))

Arguments

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

priors

a list of prior distributions

bounds_t

bounds of ability parameters

iter

the maximum iterations

conv

the convergence criterion of 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 iterations of newton-raphson

scale

the scale of theta parameters

bounds_a

bounds of discrimination parameters

bounds_b

bounds of location parameters

bounds_d

bounds of category 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'

d0

insert an initial category value

index

the indices of items being plotted

intervals

intervals on the x-axis

Value

model_gpcm_eap returns theta estimates and standard errors in a list

model_gpcm_map returns theta estimates in a list

model_gpcm_jmle returns estimated t, a, b, d parameters in a list

model_gpcm_mmle returns estimated t, a, b, d parameters in a list

model_gpcm_fitplot returns a ggplot object

Examples

# NOT RUN {
with(model_gpcm_gendata(10, 40, 3), 
     cbind(true=t, est=model_gpcm_eap(u, a, b, d)$t))
with(model_gpcm_gendata(10, 40, 3), 
     cbind(true=t, est=model_gpcm_map(u, a, b, d)$t))
# }
# NOT RUN {
# generate data
x <- model_gpcm_gendata(1000, 40, 3)
# free calibration, 40 iterations
y <- model_gpcm_jmle(x$u, true_params=x, iter=40, verbose=TRUE)
# }
# NOT RUN {
# generate data
x <- model_gpcm_gendata(1000, 40, 3)
# free estimation, 40 iterations
y <- model_gpcm_mmle(x$u, true_params=x, iter=40, verbose=TRUE)
# }
# NOT RUN {
with(model_gpcm_gendata(1000, 20, 3), 
     model_gpcm_fitplot(u, t, a, b, d, index=c(1, 3, 5)))
# }