equateIRT (version 2.0)

est3pl: Item Parameter Estimates and Covariance Matrices of a Three-Parameter Logistic Model

Description

This dataset includes item parameter estimates and covariance matrices of a three-parameter logistic model applied to 5 simulated datasets with common items. See details for more information on the linkage plan.

Usage

data(est3pl)

Format

A list of length 2 with components:

coef

a list of length 5 containing the matrices of item parameter estimates. Each matrix presents 3 columns; the first column contains guessing parameters, the second column contains difficulty parameters and the third column contains discrimination parameters. See details for information on the parameterization used. Names of rows correspond to the names of the items.

var

a list of length 5 containing the covariance matrices of item parameter estimates.

Details

Every form is composed by 20 items and presents 10 items in common with adjacent forms. Furthermore, forms 1 and 5 present 10 common items. Use linkp to obtain a matrix with elements equal to the number of common items between different forms.

Item parameters are given under the parameterization used in the ltm package. Under this parameterization, the three-parameter logistic model is as follows $$\pi_i = c_i + (1 - c_i) \frac{\exp(\beta_{1i} + \beta_{2i} z)}{1 + \exp(\beta_{1i} + \beta_{2i} z)},$$ where $\pi_i$ denotes the conditional probability of responding correctly to the $i$th item given $z$, $c_i$ denotes the guessing parameter, $\beta_{1i}$ is the easiness parameter, $\beta_{2i}$ is the discrimination parameter, and $z$ denotes the latent ability. Furthermore, the guessing parameters are given under this parameterization $$c_i = \frac{\exp(c_i^*)}{1+\exp(c_i^*)}. $$

See Also

linkp, modIRT

Examples

data(est3pl)
est3pl$coef
est3pl$var
linkp(coef = est3pl$coef)