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Journals / Anadolu Üniversitesi Bilim ve Teknoloji Dergisi :A-Uygulamalı Bilimler ve Mühendislik / 2004 / Cilt: 5 - Sayı: 2

Poissin regresyon modelinde gizli süreç

Latent process in a Poisson regression model

Burcu H. ÜÇER
Cengiz ÇELİKOĞLU
Pages
259–267
Publication Date
2022-10-11
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

As an illustration, monthly number of deathes who were infected by pulmonary tuberculosis for the years 1996 to 2002 in Izmir are investigated as a parameter-driven model and the asymptotic properties of the regression coef-ficients are investigated, then a suitable model is constructed for forecasting.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, time series of Poisson count model was investigated.
📊
Key Findings & Data:In real situations, mean-variance equality, which is the basic property of Poisson data, cannot be provided.
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Conclusion & Impact:As an illustration, monthly number of deathes who were infected by pulmonary tuberculosis for the years 1996 to 2002 in Izmir are investigated as a parameter-driven model and the asymptotic properties of the regression coef-ficients are investigated, then a suitable model is constructed for forecasting.
🔬Design:Modeling & Simulation
📍Scope:2002 Verileri
⚙️Variables:Domain Parameters

Abstract

In this study, time series of Poisson count model was investigated. In real situations, mean-variance equality, which is the basic property of Poisson data, cannot be provided. Generally, in such data variance exceeds mean, this is called overdispersion. When the overdisperison is detected, then there may be autocorrelation in latent process for Poisson regression model. Correlation is assumed to result from a latent process which is added to the linear predictor in a Poisson regression model. A quasi-likelihood approach is used as a parameter estimation technique. Tests for the presence of the latent process and autocorrelation of the latent process are examined. Asymptotic properties of the regression coefficients are investigated by using a simulation study. As an illustration, monthly number of deathes who were infected by pulmonary tuberculosis for the years 1996 to 2002 in Izmir are investigated as a parameter-driven model and the asymptotic properties of the regression coef-ficients are investigated, then a suitable model is constructed for forecasting.

Özet

Bu çalışmada, Poisson sayımlarının zaman serisi modeli incelendi. Poisson dağılan bir verinin temel özelliklerinden olan ortalama-varyans eşitliği uygulamada sağlanamaz. Genellikle, aşırı yayılım olarak adlandırılan varyans değerinin ortalamayı aştığı durum söz konusu olur. Aşırı yayılımın söz konusu olduğu durumda, Poisson regresyon modeli için gizli süreçte otokorelasyonun varlığından söz edilebilir. Poisson regresyon modelinde doğrusal tahmin ediciye eklenen gizli süreçten kaynaklanan bir korelasyon durumunun olduğu varsayılır. Bu durumda yarı-olabilirlilik yöntemi, parametre tahmin yöntemi olarak kullanılabilir. Gizli sürecin varlığının testi ve gizli sürecin otokorelasyon yapısı bu çalışmada incelenmiştir. Aynı zamanda regresyon katsayılarının asimptotik özellikleri yapılan simulasyon çalışmasıyla araştırılmıştır. Yapılan uygulamada, 1996'dan 2002'ye kadar İzmir'deki akciğer tüberkülozu ölümleri aylık olarak incelenmiştir. Yapılan çözümleme sonucunda katsayıların asimptotik özellikleri saptanarak uygun bir model oluşturulmaya çalışılmıştır.

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Cite This Article

ÜÇER, B. H., ÇELİKOĞLU, C. (2022). Poissin regresyon modelinde gizli süreç. Anadolu Üniversitesi Bilim ve Teknoloji Dergisi :A-Uygulamalı Bilimler ve Mühendislik, Cilt: 5 - Sayı: 2, 259–267. https://ajindex.com/articles/438449

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