irt.eq | R Documentation |
Implements methods to perform Test Equating over IRT models.
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)
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 θ 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 |
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 θ is equivalent to the true score on another form associated with that θ.
"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\midθ), and then integrate out the θ parameter. Afterwards, an Equipercentile Equating process is done over the estimated distributions.
An object of the clas irt.eq
is returned. Depending on the method used, the outputs are:
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.
A list(n_items, f_hat, g_hat, e_Y_x) containing the number of items, the estimated distributions and the equated values.
Daniel Acuna Leon. dnacuna@uc.cl
Kolen, M. J., and Brennan, R. L. (2014). Test Equating, Scaling, and Linking: Methods and Practices, Third Edition. Springer Science & Business Media.
irt.link
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)
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