This function computes the probability of a correct response for multiple items given a set of theta values using the 1PL, 2PL, or 3PL item response models.
Arguments
- theta
A numeric vector of ability values (latent traits).
- a
A numeric vector of item discrimination (slope) parameters.
- b
A numeric vector of item difficulty parameters.
- g
A numeric vector of item guessing parameters. Not required for 1PL or 2PL models.
- D
A scaling constant used in IRT models to make the logistic function closely approximate the normal ogive function. A value of 1.7 is commonly used for this purpose. Default is 1.
Value
A matrix of response probabilities, where rows represent ability values (theta) and columns represent items.
Details
If g is not specified, the function assumes a guessing parameter of 0 for all items,
corresponding to the 1PL or 2PL model. The function automatically adjusts the model
form based on the presence of g.
Author
Hwanggyu Lim hglim83@gmail.com
Examples
## Example 1: theta and item parameters for 3PL model
drm(c(-0.1, 0.0, 1.5), a = c(1, 2), b = c(0, 1), g = c(0.2, 0.1), D = 1)
#> [,1] [,2]
#> [1,] 0.5800167 0.1897754
#> [2,] 0.6000000 0.2072826
#> [3,] 0.8540596 0.7579527
## Example 2: single theta value with 2PL item parameters
drm(0.0, a = c(1, 2), b = c(0, 1), D = 1)
#> [,1] [,2]
#> [1,] 0.5 0.1192029
## Example 3: multiple theta values with a single item (3PL model)
drm(c(-0.1, 0.0, 1.5), a = 1, b = 1, g = 0.2, D = 1)
#> [,1]
#> [1,] 0.3997919
#> [2,] 0.4151531
#> [3,] 0.6979675