estimate_gpcm function

Estimation of the Generalizaed Partial Credit Model

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

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

Returns

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

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))

# 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)

# 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)

with(model_gpcm_gendata(1000, 20, 3), 
     model_gpcm_fitplot(u, t, a, b, d, index=c(1, 3, 5)))