Penalized Likelihood Methods for Modeling Count Data

[2109.14010] Penalized Likelihood Methods for Modeling Count Data Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Statistics > Methodology arXiv:2109.14010 (stat) [Submitted on 28 Sep 2021 ( v1 ), last revised 12 May 2022 (this version, v4)] Title: Penalized Likelihood Methods for Modeling Count Data Authors: Minh Thu Bui , Cornelis J. Potgieter , Akihito Kamata View a PDF of the paper titled Penalized Likelihood Methods for Modeling Count Data, by Minh Thu Bui and 2 other authors View PDF HTML (experimental) Abstract: The paper considers parameter estimation in count data models using penalized likelihood methods. The motivating data consists of multiple independent count variables with a moderate sample size per variable. The data were collected during the assessment of oral reading fluency (ORF) in school-aged children. A sample of fourth-grade students were given one of ten available passages to read with these differing in length and difficulty. The observed number of words read incorrectly (WRI) is used to measure ORF. Three models are considered for WRI scores, namely the binomial, the zero-inflated binomial, and the beta-binomial. We aim to efficiently estimate passage difficulty, a quantity expressed as a function of the underlying model parameters. Two types of penalty functions are considered for penalized likelihood with respective goals of shrinking parameter estimates closer to zero or closer to one another. A simulation study evaluates the efficacy of the shrinkage estimates using Mean Square Error (MSE) as metric. Big reductions in MSE relative to unpenalized maximum likelihood are observed. The paper concludes with an analysis of the motivating ORF data. Subjects: Methodology (stat.ME) ; Applications (stat.AP) Cite as: arXiv:2109.14010 [stat.ME] (or arXiv:2109.14010v4 [stat.ME] for this version) https://doi.org/10.48550/arXiv.2109.14010 Focus to learn more arXiv-issued DOI via DataCite Related DOI : https://doi.org/10.1080/02664763.2022.2103101 Focus to learn more DOI(s) linking to related resources Submission history From: Minh Thu Bui [ view email ] [v1] Tue, 28 Sep 2021 19:57:22 UTC (119 KB) [v2] Fri, 12 Nov 2021 18:31:17 UTC (278 KB) [v3] Tue, 8 Mar 2022 21:48:23 UTC (282 KB) [v4] Thu, 12 May 2022 23:22:40 UTC (435 KB) Full-text links: Access Paper: View a PDF of the paper titled Penalized Likelihood Methods for Modeling Count Data, by Minh Thu Bui and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: stat.ME < prev | next > new | recent | 2021-09 Change to browse by: stat stat.AP References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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