BNP.eq: Bayesian non-parametric model for test equating

In jagonzalb/SNSequate: Standard and Nonstandard Statistical Models and Methods for Test Equating

Description

The Bayesian nonparametric (BNP) approach (Ghoshand Ramamoorthi, 2003; Hjort et al., 2010) 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 (Muller and Quintana, 2004).

Gonzalez et al. (2015) proposed a Bayesian non-parametric approach for equating. The main idea consists of introducing covariate dependent BNP models for a collection of covariate-dependent equating transformations

≤ft\{ \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.
mcmc	List. MCMC information for BNP model.
normalize	Logical. Whether normalize or not the response variable. This is due to Berstein's polynomials. Default is TRUE.

Details

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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 A. [e-mail], Felipe Barrientos [e-mail].

References

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jagonzalb/SNSequate documentation built on May 18, 2019, 9:07 a.m.