A Study of Lack-of-Fit Diagnostics for Models Fit to Cross-Classified Binary Variables

Maduranga Dassanayake; Mark Reiser

doi:10.1007/978-3-031-30164-3_11

A Study of Lack-of-Fit Diagnostics for Models Fit to Cross-Classified Binary Variables

Maduranga Dassanayake, Mark Reiser

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

In this paper, an extended version of the GFfit statistic is compared to other lack-of-fit diagnostics for models fit to cross-classified binary variables. The extended GFfit statistic is obtained by decomposing the Pearson statistic from the full table into orthogonal components defined on marginal distributions. The extended version of the statistic, GFfit⊥(ij), can be applied to a variety of models for cross-classified tables. Simulation results show that GFfit⊥(ij) has good Type I error performance even if the joint frequencies are very sparse. Asymptotic power calculations and simulation results show that GFfit⊥(ij) has higher power for detecting the source of lack of fit compared to other diagnostics on bivariate marginal tables for binary variables.

Original language	English (US)
Title of host publication	Statistical Models and Methods for Data Science
Editors	Leonardo Grilli, Monia Lupparelli, Carla Rampichini, Emilia Rocco, Maurizio Vichi
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	133-145
Number of pages	13
ISBN (Print)	9783031301636
DOIs	https://doi.org/10.1007/978-3-031-30164-3_11
State	Published - 2023
Event	13th Scientific Meeting of the Classification and Data Analysis Group of the Italian Statistical Society, CLADAG 2021 - Virtual, Online Duration: Sep 9 2021 → Sep 11 2021

Publication series

Name	Studies in Classification, Data Analysis, and Knowledge Organization
ISSN (Print)	1431-8814
ISSN (Electronic)	2198-3321

Conference

Conference	13th Scientific Meeting of the Classification and Data Analysis Group of the Italian Statistical Society, CLADAG 2021
City	Virtual, Online
Period	9/9/21 → 9/11/21

Keywords

IRT model
Multinomial distribution
Orthogonal components
Pearson Chi-square

ASJC Scopus subject areas

Computer Science Applications
Information Systems
Information Systems and Management
Analysis

Access to Document

10.1007/978-3-031-30164-3_11

Cite this

Dassanayake, M., & Reiser, M. (2023). A Study of Lack-of-Fit Diagnostics for Models Fit to Cross-Classified Binary Variables. In L. Grilli, M. Lupparelli, C. Rampichini, E. Rocco, & M. Vichi (Eds.), Statistical Models and Methods for Data Science (pp. 133-145). (Studies in Classification, Data Analysis, and Knowledge Organization). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-30164-3_11

A Study of Lack-of-Fit Diagnostics for Models Fit to Cross-Classified Binary Variables. / Dassanayake, Maduranga; Reiser, Mark.
Statistical Models and Methods for Data Science. ed. / Leonardo Grilli; Monia Lupparelli; Carla Rampichini; Emilia Rocco; Maurizio Vichi. Springer Science and Business Media Deutschland GmbH, 2023. p. 133-145 (Studies in Classification, Data Analysis, and Knowledge Organization).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Dassanayake, M & Reiser, M 2023, A Study of Lack-of-Fit Diagnostics for Models Fit to Cross-Classified Binary Variables. in L Grilli, M Lupparelli, C Rampichini, E Rocco & M Vichi (eds), Statistical Models and Methods for Data Science. Studies in Classification, Data Analysis, and Knowledge Organization, Springer Science and Business Media Deutschland GmbH, pp. 133-145, 13th Scientific Meeting of the Classification and Data Analysis Group of the Italian Statistical Society, CLADAG 2021, Virtual, Online, 9/9/21. https://doi.org/10.1007/978-3-031-30164-3_11

Dassanayake M, Reiser M. A Study of Lack-of-Fit Diagnostics for Models Fit to Cross-Classified Binary Variables. In Grilli L, Lupparelli M, Rampichini C, Rocco E, Vichi M, editors, Statistical Models and Methods for Data Science. Springer Science and Business Media Deutschland GmbH. 2023. p. 133-145. (Studies in Classification, Data Analysis, and Knowledge Organization). doi: 10.1007/978-3-031-30164-3_11

Dassanayake, Maduranga ; Reiser, Mark. / A Study of Lack-of-Fit Diagnostics for Models Fit to Cross-Classified Binary Variables. Statistical Models and Methods for Data Science. editor / Leonardo Grilli ; Monia Lupparelli ; Carla Rampichini ; Emilia Rocco ; Maurizio Vichi. Springer Science and Business Media Deutschland GmbH, 2023. pp. 133-145 (Studies in Classification, Data Analysis, and Knowledge Organization).

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abstract = "In this paper, an extended version of the GFfit statistic is compared to other lack-of-fit diagnostics for models fit to cross-classified binary variables. The extended GFfit statistic is obtained by decomposing the Pearson statistic from the full table into orthogonal components defined on marginal distributions. The extended version of the statistic, GFfit⊥(ij), can be applied to a variety of models for cross-classified tables. Simulation results show that GFfit⊥(ij) has good Type I error performance even if the joint frequencies are very sparse. Asymptotic power calculations and simulation results show that GFfit⊥(ij) has higher power for detecting the source of lack of fit compared to other diagnostics on bivariate marginal tables for binary variables.",

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AB - In this paper, an extended version of the GFfit statistic is compared to other lack-of-fit diagnostics for models fit to cross-classified binary variables. The extended GFfit statistic is obtained by decomposing the Pearson statistic from the full table into orthogonal components defined on marginal distributions. The extended version of the statistic, GFfit⊥(ij), can be applied to a variety of models for cross-classified tables. Simulation results show that GFfit⊥(ij) has good Type I error performance even if the joint frequencies are very sparse. Asymptotic power calculations and simulation results show that GFfit⊥(ij) has higher power for detecting the source of lack of fit compared to other diagnostics on bivariate marginal tables for binary variables.

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A Study of Lack-of-Fit Diagnostics for Models Fit to Cross-Classified Binary Variables

Abstract

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Conference

Keywords

ASJC Scopus subject areas

Access to Document

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