Augmented-limited regression models with an application to the study of the risk perceived using continuous scales
| Autor: | Jorge Luis Bazán, Juvêncio S. Nobre, Ana Roberta dos Santos Silva, Caio Lucidius Naberezny Azevedo |
|---|---|
| Rok vydání: | 2022 |
| Předmět: |
Statistics and Probability
021103 operations research Psychometrics 0211 other engineering and technologies food and beverages Regression analysis 02 engineering and technology Articles 01 natural sciences 010104 statistics & probability Frequentist inference Diagnostic analysis Unit interval (data transmission) Statistics SIMULAÇÃO (ESTATÍSTICA) 0101 mathematics Statistics Probability and Uncertainty Mathematics |
| Zdroj: | J Appl Stat Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual) Universidade de São Paulo (USP) instacron:USP |
| ISSN: | 0266-4763 |
| Popis: | Studies of risk perceived using continuous scales of [0,100] were recently introduced in psychometrics, which can be transformed to the unit interval, but the presence of zeros or ones are commonly observed. Motivated by this, we introduce a full inferential set of tools that allows for augmented and limited data modeling. We considered parameter estimation, residual analysis, influence diagnostic and model selection for zero-and/or-one augmented beta rectangular (ZOABR) regression models and their particular nested models, which is based on a new parameterization of the beta rectangular distribution. Different from other alternatives, we performed maximum-likelihood estimation using a combination of the EM algorithm (for the continuous part) and Fisher scoring algorithm (for the discrete part). Also, we perform an additional step, by considering other link functions, besides the usual logistic link, for modeling the response mean. By considering randomized quantile residuals, (local) influence diagnostics and model selection tools, we identified that the ZOABR regression model is the best one. We also conducted extensive simulations studies, which indicate that all developed tools work properly. Finally, we discuss the use of this type of models to treat psychometric data. It is worthwhile to mention that applications of the developed methods go beyond to Psychometric data. Indeed, they can be useful when the response variable in bounded, including or not the respective limits. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|