BNP.eq {SNSequate}

Bayesian non-parametric model for test equating

Description

This function implements the Bayesian nonparametric approach for test equating as described in Gonzalez, Barrientos and Quintana (2015) <doi:10.1016/j.csda.2015.03.012>. The main idea consists of introducing covariate dependent Bayesian nonparametric models for a collection of covariate-dependent equating transformations

\left\{ \boldsymbol{\varphi}_{\boldsymbol{z}_f, \boldsymbol{z}_t} (\cdot): \boldsymbol{z}_f, \boldsymbol{z}_t \in \mathcal{L} \right\}

Usage

BNP.eq(scores_x, scores_y, range_scores = NULL, design = "EG",
  covariates = NULL, prior = NULL, mcmc = NULL, normalize = TRUE)

Arguments

scores_x

Vector. Scores of form X.

scores_y

Vector. Scores of form Y.

range_scores

Vector of length 2. Represent the minimum and maximum scores in the test.

design

Character. Only supports 'EG' design now.

covariates

Data.frame. A data frame with factors, containing covariates for test X and Y, stacked in that order.

prior

List. Prior information for BNP model. For more information see DPpackage.

mcmc

List. MCMC information for BNP model. For more information see DPpackage.

normalize

Logical. Whether normalize or not the response variable. This is due to Berstein's polynomials. Default is TRUE.

Details

The Bayesian nonparametric (BNP) approach starts by focusing on spaces of distribution functions, so that uncertainty is expressed on F itself. The prior distribution p(F) is defined on the space F of all distribution functions defined on X . If X is an infinite set then F is infinite-dimensional, and the corresponding prior model p(F) on F is termed nonparametric. The prior probability model is also referred to as a random probability measure (RPM), and it essentially corresponds to a distribution on the space of all distributions on the set X . Thus Bayesian nonparametric models are probability models defined on a function space.

Value

A 'BNP.eq' object, which is list containing the following items:

Y Response variable.

X Design Matrix.

fit DPpackage object. Fitted model with raw samples.

max_score Maximum score of test.

patterns A matrix describing the different patterns formed from the factors in the covariables.

patterns_freq The normalized frequency of each pattern.

Author(s)

Daniel Leon [e-mail], Felipe Barrientos [e-mail].

References

Gonzalez, J., Barrientos, A., and Quintana, F. (2015). Bayesian Nonparametric Estimation of Test Equating Functions with Covariates. Computational Statistics and Data Analysis, 89, 222-244.