model_3pl: 3-parameter-logistic model
In xluo11/xxIRT: Item Response Theory and Computer-Based Testing

Routine functions 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, param = 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), 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),
  show_mle = FALSE)

`t`	ability parameters, 1d vector
`a`	discrimination parameters, 1d vector
`b`	difficulty parameters, 1d vector
`c`	guessing parameters, 1d vector
`D`	the scaling constant, 1.702 by default
`u`	observed responses, 2d matrix
`log`	True to return log-likelihood
`param`	the parameter of the new scale: 't' or 'b'
`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
`missing`	the proportion or number of missing responses
`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
`show_mle`	TRUE to print maximum likelihood estimates

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, show_mle=TRUE))