Flexible Bayesian Models for Inferences from Coarsened, Group-Level Achievement Data

Autor/inn/en	Lockwood, J. R.; Castellano, Katherine E.; Shear, Benjamin R.
Titel	Flexible Bayesian Models for Inferences from Coarsened, Group-Level Achievement Data
Quelle	In: Journal of Educational and Behavioral Statistics, 43 (2018) 6, S.663-692 (30 Seiten)Infoseite zur Zeitschrift PDF als Volltext (1); PDF als Volltext kostenfreie Datei (2) Verfügbarkeit
Zusatzinformation	Weitere Informationen
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1076-9986
DOI	10.3102/1076998618795124
Schlagwörter	Bayesian Statistics; Mathematical Models; Statistical Inference; Computation; Academic Achievement; Regression (Statistics); Maximum Likelihood Statistics; Monte Carlo Methods; Young Children; Longitudinal Studies + Suchen Sie Ihr Suchwort? Mathematical model; Mathematisches Modell; Inferential statistics; Schließende Statistik; Schulleistung; Regression; Regressionsanalyse; Monte-Carlo-Methode; Frühe Kindheit; Longitudinal study; Longitudinal method; Longitudinal methods; Längsschnittuntersuchung
Abstract	This article proposes a flexible extension of the Fay--Herriot model for making inferences from coarsened, group-level achievement data, for example, school-level data consisting of numbers of students falling into various ordinal performance categories. The model builds on the heteroskedastic ordered probit (HETOP) framework advocated by Reardon, Shear, Castellano, and Ho by allowing group parameters to be modeled with regressions on group-level covariates, and residuals modeled using the flexible exponential family of distributions recommended by Efron. We demonstrate that the alternative modeling framework, termed the "Fay-Herriot heteroskedastic ordered probit" (FH-HETOP) model, is useful for mitigating some of the challenges with direct maximum likelihood estimators from the HETOP model. We conduct a simulation study to compare the costs and benefits of several methods for using the FH-HETOP model to estimate group parameters and functions of them, including posterior means, constrained Bayes estimators, and the "triple goal" estimators of Shen and Louis. We also provide an application of the FH-HETOP model to math proficiency data from the Early Childhood Longitudinal Study. Code for estimating the FH-HETOP model and conducting supporting calculations is provided in a new package for the R environment. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01