irt.eq {SNSequate}

IRT methods for Test Equating

Description

Implements methods to perform Test Equating over IRT models.

Usage

irt.eq(n_items, param_x, param_y, theta_points=NULL, weights=NULL, n_points=10, w=1, 
      A=NULL, B=NULL, link=NULL, method_link=NULL, common=NULL,  method="TS", D=1.7)

Arguments

n_items

Number of items of the test

param_x

Estimated parameters for IRT model on test X. This list must have the following structure: list(a, b, c), where each parameter is a vector with the respective estimate for each subject. If you want to perform other models (i.e. Rasch), replace according with a vector of zeros.

param_y

Estimated parameters for IRT model on test Y. This list must have the following structure: list(a, b, c), where each parameter is a vector with the respective estimate for each subject. If you want to perform other models (i.e. Rasch), replace according with a vector of zeros.

method

A string, either "TS" or "OS". Each one stands for "True Score Equating" and "Observed score equating". Notice that OS requires the additional arguments "theta_points" and "weigths".

theta_points

For "OS" only. Points over a grid of possible values of \theta to integrate out the ability term.

weights

For "OS" only. Weigths for integrate out the ability term. If is NULL, the method assumes the distribution of ability is characterized by a finite number of abilities (Kolen and Brennan 2013, pg 199).

n_points

In case theta_ponints is not provided, is the length of the grid for the gaussian quadrature.

A, B

Scaling parameters. In the case they are not provided, they will be calculated depending on the next described inputs.

link

An irt.link object.

method_link

Method used to estimate A and B. Default is "mean/sigma". Others are "mean/mean", "Haebara" and "Stocklord". For more information see irt.link

common

Common items to estimate A and B. Default asume all items are common.

w

Weight of the synthetic population.

D

Sclaing constant

Details

This function implements two methods to perform Test Equating over Item Response Theory models (Kolen and Brennan 2013).

"True Score Equating" relate number-correct scores on Form X and Form Y. Assumes that the true score associated with each \theta is equivalent to the true score on another form associated with that \theta.

"Observed Score Equating" uses the IRT model to produce an estimated distribution of observed number-correct scores on each form. Using the compound binomial distribution (Lord and Wingersky 1984) to find the conditional distributions f(x\mid\theta), and then integrate out the \theta parameter. Afterwards, an Equipercentile Equating process is done over the estimated distributions.

Value

An object of the clas irt.eq is returned. Depending on the method used, the outputs are:

True Score Equating

A list(n_items, theta_equivalent, tau_y) containing the number of items, the theta equivalent values on Form X to Form Y and the equivalent scores.

Observed Score Equating

A list(n_items, f_hat, g_hat, e_Y_x) containing the number of items, the estimated distributions and the equated values.

Author(s)

Daniel Acuna Leon. [e-mail]

References

Kolen, M. J., and Brennan, R. L. (2014). Test Equating, Scaling, and Linking: Methods and Practices, Third Edition. Springer Science & Business Media.

See Also

irt.link

Examples

data(KB36_t)
dfo <- KB36_t

param_x <- list(a=dfo[,3],b=dfo[,4],c=dfo[,5])
param_y <- list(a=dfo[,7],b=dfo[,8],c=dfo[,9])

theta_points=c(-5.2086,-4.163,-3.1175,-2.072,-1.0269,0.0184,
               1.0635,2.109,3.1546,4.2001)
weights=c(0.000101,0.00276,0.03021,0.142,0.3149,0.3158,
         0.1542,0.03596,0.003925,0.000186)


irt.eq(36, param_x, param_y, method="TS", A=1, B=0)
irt.eq(36, param_x, param_y, theta_points, weights, method="OS", A=1, B=0)