model_3pl function

3-parameter-logistic model

Common computations and operations for the 3PL model

model_3pl_prob(t, a, b, c, D = 1.702)

model_3pl_info(t, a, b, c, D = 1.702)

model_3pl_lh(u, t, a, b, c, D = 1.702, log = FALSE)

model_3pl_rescale(t, a, b, c, scale = c("t", "b"), mean = 0, sd = 1)

model_3pl_gendata(n_p, n_i, t = NULL, a = NULL, b = NULL, c = NULL,
  D = 1.702, t_dist = c(0, 1), a_dist = c(-0.1, 0.2), b_dist = c(0,
  0.7), c_dist = c(5, 46), t_bounds = c(-3, 3), a_bounds = c(0.01,
  2.5), b_bounds = c(-3, 3), c_bounds = c(0, 0.5), missing = NULL,
  ...)

model_3pl_plot(a, b, c, D = 1.702, type = c("prob", "info"),
  total = FALSE, xaxis = seq(-4, 4, 0.1))

model_3pl_plot_loglh(u, a, b, c, D = 1.702, xaxis = seq(-4, 4, 0.1),
  verbose = FALSE)

Arguments

• t: ability parameters, 1d vector
• a: discrimination parameters, 1d vector
• b: difficulty parameters, 1d vector
• c: guessing parameters, 1d vector
• D: the scaling constant, default=1.702
• u: observed responses, 2d matrix
• log: True to return log-likelihood
• scale: the scale, 't' for theta or 'b' for b-parameters
• mean: the mean of the new scale
• sd: the standard deviation of the new scale
• n_p: the number of people to be generated
• n_i: the number of items to be generated
• t_dist: parameters of the normal distribution used to generate t-parameters
• a_dist: parameters of the lognormal distribution used to generate a-parameters
• b_dist: parameters of the normal distribution used to generate b-parameters
• c_dist: parameters of the beta distribution used to generate c-parameters
• t_bounds: bounds of the ability parameters
• a_bounds: bounds of the discrimination parameters
• b_bounds: bounds of the difficulty parameters
• c_bounds: bounds of the guessing parameters
• missing: the proportion or number of missing responses
• ...: additional arguments
• type: the type of plot: 'prob' for item characteristic curve (ICC) and 'info' for item information function curve (IIFC)
• total: TRUE to sum values over items
• xaxis: the values of x-axis
• verbose: TRUE to print rough maximum likelihood estimates

Returns

model_3pl_prob returns the resulting probabilities in a matrix

model_3pl_info returns the resulting information in a matrix

model_3pl_lh returns the resulting likelihood in a matrix

model_3pl_rescale returns t, a, b, c parameters on the new scale

model_3pl_gendata returns the generated response matrix and parameters in a list

model_3pl_plot returns a ggplot object

model_3pl_plot_loglh returns a ggplot object

Examples

with(model_3pl_gendata(10, 5), model_3pl_prob(t, a, b, c))
with(model_3pl_gendata(10, 5), model_3pl_info(t, a, b, c))
with(model_3pl_gendata(10, 5), model_3pl_lh(u, t, a, b, c))
model_3pl_gendata(10, 5)
model_3pl_gendata(10, 5, a=1, c=0, missing=.1)
with(model_3pl_gendata(10, 5), model_3pl_plot(a, b, c, type="prob"))
with(model_3pl_gendata(10, 5), model_3pl_plot(a, b, c, type="info", total=TRUE))
with(model_3pl_gendata(5, 50), model_3pl_plot_loglh(u, a, b, c))