Pub Date : 2025-01-24DOI: 10.1007/s10182-024-00518-x
Huihui Sun, Qiang Liu, Yuying Jiang
This paper considers a partially linear model in which the covariates of parametric part are measured with normal distributed errors. A newly robust corrected empirical likelihood procedure based on the corrected score function is proposed to attenuate the effects of measurement errors as well as outliers. What’s more, profit from the QR decomposition technique, the parametric and nonparametric components of the models can be estimated separately. The asymptotic properties of the proposed robust corrected empirical likelihood approach are established under some regularity conditions. Simulation studies are demonstrated to show that our proposed method performs well in finite samples. Boston housing price data are applied to illustrate the proposed estimation procedure.
{"title":"Robust corrected empirical likelihood for partially linear measurement error models","authors":"Huihui Sun, Qiang Liu, Yuying Jiang","doi":"10.1007/s10182-024-00518-x","DOIUrl":"10.1007/s10182-024-00518-x","url":null,"abstract":"<div><p>This paper considers a partially linear model in which the covariates of parametric part are measured with normal distributed errors. A newly robust corrected empirical likelihood procedure based on the corrected score function is proposed to attenuate the effects of measurement errors as well as outliers. What’s more, profit from the QR decomposition technique, the parametric and nonparametric components of the models can be estimated separately. The asymptotic properties of the proposed robust corrected empirical likelihood approach are established under some regularity conditions. Simulation studies are demonstrated to show that our proposed method performs well in finite samples. Boston housing price data are applied to illustrate the proposed estimation procedure.</p></div>","PeriodicalId":55446,"journal":{"name":"Asta-Advances in Statistical Analysis","volume":"109 2","pages":"337 - 361"},"PeriodicalIF":1.4,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145168072","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-24DOI: 10.1007/s10182-025-00523-8
Jan Beran, Frieder Droullier
We consider random coefficient INAR(1) processes with a strongly dependent latent random coefficient process. It is shown that, in spite of its conditional Markovian structure, the unconditional process exhibits long-range dependence. Short-term prediction and estimation of parameters involved in the prediction are considered. Asymptotic rates of convergence are derived.
{"title":"On random coefficient INAR processes with long memory","authors":"Jan Beran, Frieder Droullier","doi":"10.1007/s10182-025-00523-8","DOIUrl":"10.1007/s10182-025-00523-8","url":null,"abstract":"<div><p>We consider random coefficient INAR(1) processes with a strongly dependent latent random coefficient process. It is shown that, in spite of its conditional Markovian structure, the unconditional process exhibits long-range dependence. Short-term prediction and estimation of parameters involved in the prediction are considered. Asymptotic rates of convergence are derived.</p></div>","PeriodicalId":55446,"journal":{"name":"Asta-Advances in Statistical Analysis","volume":"109 2","pages":"281 - 311"},"PeriodicalIF":1.4,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10182-025-00523-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145168071","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-03DOI: 10.1007/s10182-024-00522-1
Roy Cerqueti, Pierpaolo D’Urso, Raffaele Mattera
The paper discusses the problem of estimating group heterogeneous fixed-effect panel data models under the assumption of fuzzy clustering, that is each unit belongs to all the clusters with a membership degree. To enhance spatial clustering, a spatio-temporal approach is considered. An iterative procedure, alternating panel data estimation and spatio-temporal clustering of the residuals, is proposed. The proposed method can be of relevance to researchers interested in using fuzzy group fixed-effect methods, but want to leverage spatial dimension for clustering units. Two empirical examples, the first on cigarette consumption in the US states and the second on non-life insurance demand in Italy, are presented to illustrate the performance of the proposed approach. The spatial fuzzy GFE model reveals important regional differences in both the US cigarette consumption and non-life insurance determinants in Italy. In the case of the US, we found a distinction in two main clusters, East and West. For the Italy provinces data, we find a distinction in North and South clusters. Regarding the regression results, for cigarette consumption data, different from the previous studies, we find that the smuggling effect is significant only in east regions, thus suggesting localised impacts of bootlegging. In the context of Italian non-life insurance demand, we find that while population density explains insurance consumption in northern provinces, the trust issues in the south explain the lower insurance demand.
{"title":"Fuzzy group fixed-effects estimation with spatial clustering","authors":"Roy Cerqueti, Pierpaolo D’Urso, Raffaele Mattera","doi":"10.1007/s10182-024-00522-1","DOIUrl":"10.1007/s10182-024-00522-1","url":null,"abstract":"<div><p>The paper discusses the problem of estimating group heterogeneous fixed-effect panel data models under the assumption of fuzzy clustering, that is each unit belongs to all the clusters with a membership degree. To enhance spatial clustering, a spatio-temporal approach is considered. An iterative procedure, alternating panel data estimation and spatio-temporal clustering of the residuals, is proposed. The proposed method can be of relevance to researchers interested in using fuzzy group fixed-effect methods, but want to leverage spatial dimension for clustering units. Two empirical examples, the first on cigarette consumption in the US states and the second on non-life insurance demand in Italy, are presented to illustrate the performance of the proposed approach. The spatial fuzzy GFE model reveals important regional differences in both the US cigarette consumption and non-life insurance determinants in Italy. In the case of the US, we found a distinction in two main clusters, East and West. For the Italy provinces data, we find a distinction in North and South clusters. Regarding the regression results, for cigarette consumption data, different from the previous studies, we find that the smuggling effect is significant only in east regions, thus suggesting localised impacts of bootlegging. In the context of Italian non-life insurance demand, we find that while population density explains insurance consumption in northern provinces, the trust issues in the south explain the lower insurance demand.</p></div>","PeriodicalId":55446,"journal":{"name":"Asta-Advances in Statistical Analysis","volume":"109 4","pages":"721 - 752"},"PeriodicalIF":1.4,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145915720","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-30DOI: 10.1007/s10182-024-00520-3
Codruta Mare, Stefana Belbe, Norbert Petrovici
This study investigates the spatial clustering and spillover effects of COVID-19 vaccine uptake in Romania, focusing on the municipality-level distribution of vaccine acceptance and hesitancy while considering the factors that influence it. The research uses the Spatial Durbin Error Model (SDEM) and identifies spatial clusterization, as well as significant contagion and diffusion processes in the vaccination behaviour conditioned by socioeconomic factors, labour market characteristics, social and religious attitudes, urban, and health indicators. We find evidence in favour of spatial spillover effects of the poverty rate, opposition to same-sex marriage, COVID-19 infection rate, peri-urban towns, and denser cities. Our findings contribute to the literature of the spatial distribution and determinants of vaccine uptake and carry practical implications for policy makers offering evidence-based insights that can inform targeted strategies and interventions to enhance vaccine acceptance and address hesitancy in specific locations.
{"title":"Exploring the spatial clustering and spillover effects of COVID-19 vaccination uptake in Romania: an analysis at municipality level","authors":"Codruta Mare, Stefana Belbe, Norbert Petrovici","doi":"10.1007/s10182-024-00520-3","DOIUrl":"10.1007/s10182-024-00520-3","url":null,"abstract":"<div><p>This study investigates the spatial clustering and spillover effects of COVID-19 vaccine uptake in Romania, focusing on the municipality-level distribution of vaccine acceptance and hesitancy while considering the factors that influence it. The research uses the Spatial Durbin Error Model (SDEM) and identifies spatial clusterization, as well as significant contagion and diffusion processes in the vaccination behaviour conditioned by socioeconomic factors, labour market characteristics, social and religious attitudes, urban, and health indicators. We find evidence in favour of spatial spillover effects of the poverty rate, opposition to same-sex marriage, COVID-19 infection rate, peri-urban towns, and denser cities. Our findings contribute to the literature of the spatial distribution and determinants of vaccine uptake and carry practical implications for policy makers offering evidence-based insights that can inform targeted strategies and interventions to enhance vaccine acceptance and address hesitancy in specific locations.</p></div>","PeriodicalId":55446,"journal":{"name":"Asta-Advances in Statistical Analysis","volume":"109 4","pages":"667 - 688"},"PeriodicalIF":1.4,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10182-024-00520-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145915718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-28DOI: 10.1007/s10182-024-00521-2
Osman Doğan, Ye Yang, Süleyman Taşpınar
In this paper, we propose an integrated modified harmonic mean estimator (IHME) for nested and non-nested model selection problems in spatial panel data models with entity and time fixed effects. We formulate the IHME based on the integrated likelihood functions obtained by analytically integrating out the high-dimensional entity and time fixed effects from the complete likelihood functions. To investigate the finite sample properties of the IHME, we design a comprehensive simulation study that allows for both nested and non-nested model selection exercises in some popular spatial panel data models. Our simulation results show that the IHME has excellent finite sample performance and outperforms some competing estimators in terms of precision. We provide an empirical application on the US house price changes to show the usefulness of the proposed IHME in a model selection exercise.
{"title":"Integrated modified harmonic mean method for spatial panel data models","authors":"Osman Doğan, Ye Yang, Süleyman Taşpınar","doi":"10.1007/s10182-024-00521-2","DOIUrl":"10.1007/s10182-024-00521-2","url":null,"abstract":"<div><p>In this paper, we propose an integrated modified harmonic mean estimator (IHME) for nested and non-nested model selection problems in spatial panel data models with entity and time fixed effects. We formulate the IHME based on the integrated likelihood functions obtained by analytically integrating out the high-dimensional entity and time fixed effects from the complete likelihood functions. To investigate the finite sample properties of the IHME, we design a comprehensive simulation study that allows for both nested and non-nested model selection exercises in some popular spatial panel data models. Our simulation results show that the IHME has excellent finite sample performance and outperforms some competing estimators in terms of precision. We provide an empirical application on the US house price changes to show the usefulness of the proposed IHME in a model selection exercise.</p></div>","PeriodicalId":55446,"journal":{"name":"Asta-Advances in Statistical Analysis","volume":"109 4","pages":"689 - 719"},"PeriodicalIF":1.4,"publicationDate":"2024-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145915719","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-21DOI: 10.1007/s10182-024-00519-w
Antonello Maruotti, Pierfrancesco Alaimo Di Loro, Cathleen Johnson
The primary purpose of this paper is to assess households’ burden due to out-of-pocket healthcare expenditures. These payments are modeled on a representative sample of 25668 Italian households as the fraction of out-of-pocket healthcare expenditures over the households’ capacity to pay. For this purpose, we propose extending the analysis of the so-called catastrophic payments by looking at the entire distribution of this ratio. We introduce a novel finite mixture regression able to capture different levels of heterogeneity in the data. By using such a model specification, the fairness of the Italian National Health Service and its determinants are investigated.
{"title":"Beyond catastrophic payments: modeling household health expenditure shares with endogenous selection","authors":"Antonello Maruotti, Pierfrancesco Alaimo Di Loro, Cathleen Johnson","doi":"10.1007/s10182-024-00519-w","DOIUrl":"10.1007/s10182-024-00519-w","url":null,"abstract":"<div><p>The primary purpose of this paper is to assess households’ burden due to out-of-pocket healthcare expenditures. These payments are modeled on a representative sample of 25668 Italian households as the fraction of out-of-pocket healthcare expenditures over the households’ capacity to pay. For this purpose, we propose extending the analysis of the so-called catastrophic payments by looking at the entire distribution of this ratio. We introduce a novel finite mixture regression able to capture different levels of heterogeneity in the data. By using such a model specification, the fairness of the Italian National Health Service and its determinants are investigated.</p></div>","PeriodicalId":55446,"journal":{"name":"Asta-Advances in Statistical Analysis","volume":"109 2","pages":"363 - 386"},"PeriodicalIF":1.4,"publicationDate":"2024-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145167896","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-14DOI: 10.1007/s10182-024-00517-y
Scott H. Koeneman, Joseph E. Cavanaugh
In this work, the distributional properties of the goodness-of-fit term in likelihood-based information criteria are explored. These properties are then leveraged to construct a novel goodness-of-fit test for normal linear regression models that relies on a nonparametric bootstrap. Several simulation studies are performed to investigate the properties and efficacy of the developed procedure, with these studies demonstrating that the bootstrap test offers distinct advantages as compared to other methods of assessing the goodness-of-fit of a normal linear regression model. Our inferential technique can be employed using the DBModelSelect R package, available freely via the Comprehensive R Archive Network.
{"title":"A novel bootstrap goodness-of-fit test for normal linear regression models","authors":"Scott H. Koeneman, Joseph E. Cavanaugh","doi":"10.1007/s10182-024-00517-y","DOIUrl":"10.1007/s10182-024-00517-y","url":null,"abstract":"<div><p>In this work, the distributional properties of the goodness-of-fit term in likelihood-based information criteria are explored. These properties are then leveraged to construct a novel goodness-of-fit test for normal linear regression models that relies on a nonparametric bootstrap. Several simulation studies are performed to investigate the properties and efficacy of the developed procedure, with these studies demonstrating that the bootstrap test offers distinct advantages as compared to other methods of assessing the goodness-of-fit of a normal linear regression model. Our inferential technique can be employed using the <span>DBModelSelect</span> R package, available freely via the Comprehensive R Archive Network.</p></div>","PeriodicalId":55446,"journal":{"name":"Asta-Advances in Statistical Analysis","volume":"109 3","pages":"443 - 461"},"PeriodicalIF":1.4,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10182-024-00517-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145384849","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-13DOI: 10.1007/s10182-024-00515-0
Dennis Kant, Andreas Pick, Jasper de Winter
This paper compares the ability of several econometric and machine learning methods to nowcast GDP in (pseudo) real-time. The analysis takes the example of Dutch GDP over the period 1992Q1–2018Q4 using a broad data set of monthly indicators. It discusses the forecast accuracy but also analyzes the use of information from the large data set of macroeconomic and financial predictors. We find that, on average, the random forest provides the most accurate forecast and nowcasts, whilst the dynamic factor model provides the most accurate backcasts.
{"title":"Nowcasting GDP using machine learning methods","authors":"Dennis Kant, Andreas Pick, Jasper de Winter","doi":"10.1007/s10182-024-00515-0","DOIUrl":"10.1007/s10182-024-00515-0","url":null,"abstract":"<div><p>This paper compares the ability of several econometric and machine learning methods to nowcast GDP in (pseudo) real-time. The analysis takes the example of Dutch GDP over the period 1992Q1–2018Q4 using a broad data set of monthly indicators. It discusses the forecast accuracy but also analyzes the use of information from the large data set of macroeconomic and financial predictors. We find that, on average, the random forest provides the most accurate forecast and nowcasts, whilst the dynamic factor model provides the most accurate backcasts.</p></div>","PeriodicalId":55446,"journal":{"name":"Asta-Advances in Statistical Analysis","volume":"109 1","pages":"1 - 24"},"PeriodicalIF":1.4,"publicationDate":"2024-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10182-024-00515-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143530002","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-09DOI: 10.1007/s10182-024-00516-z
Seonghun Cho, Minsup Shin, Young Hyun Cho, Johan Lim
This research proposes a method to test and estimate change points in the covariance structure of high-dimensional multivariate series data. Our method uses the trace of the beta matrix, known as Pillai’s statistics, to test the change in covariance matrix at each time point. We study the asymptotic normality of Pillai’s statistics for testing the equality of two covariance matrices when both sample size and dimension increase at the same rate. We test the existence of a single change point in a given time period using Cauchy combination test, the test using an weighted sum of Cauchy transformed p-values, and estimate the change point as the point whose statistic is the greatest. To test and estimate multiple change points, we use the idea of the wild binary segmentation and repeatedly apply the procedure for a single change point to each segmented period until no significant change point exists. We numerically provide the size and power of our method. We finally apply our procedure to finding abnormal behavior in the investment of a private equity fund.
本研究提出了一种测试和估计高维多变量序列数据协方差结构变化点的方法。我们的方法使用贝塔矩阵的迹,即 Pillai 统计量,来检验每个时间点协方差矩阵的变化。我们研究了 Pillai 统计量的渐近正态性,以检验样本量和维度以相同速度增加时两个协方差矩阵的相等性。我们使用考奇组合检验(该检验使用考奇转换 p 值的加权和)来检验给定时间段内是否存在单个变化点,并将统计量最大的点作为变化点。为了检验和估计多个变化点,我们采用了二元狂分段的思想,对每个分段时期重复应用单个变化点的程序,直到不存在显著变化点为止。我们用数字说明了我们方法的规模和威力。最后,我们将我们的程序应用于发现私募股权基金投资中的异常行为。
{"title":"Change point detection in high dimensional covariance matrix using Pillai’s statistics","authors":"Seonghun Cho, Minsup Shin, Young Hyun Cho, Johan Lim","doi":"10.1007/s10182-024-00516-z","DOIUrl":"10.1007/s10182-024-00516-z","url":null,"abstract":"<div><p>This research proposes a method to test and estimate change points in the covariance structure of high-dimensional multivariate series data. Our method uses the trace of the beta matrix, known as Pillai’s statistics, to test the change in covariance matrix at each time point. We study the asymptotic normality of Pillai’s statistics for testing the equality of two covariance matrices when both sample size and dimension increase at the same rate. We test the existence of a single change point in a given time period using Cauchy combination test, the test using an weighted sum of Cauchy transformed <i>p</i>-values, and estimate the change point as the point whose statistic is the greatest. To test and estimate multiple change points, we use the idea of the wild binary segmentation and repeatedly apply the procedure for a single change point to each segmented period until no significant change point exists. We numerically provide the size and power of our method. We finally apply our procedure to finding abnormal behavior in the investment of a private equity fund.</p></div>","PeriodicalId":55446,"journal":{"name":"Asta-Advances in Statistical Analysis","volume":"109 1","pages":"53 - 84"},"PeriodicalIF":1.4,"publicationDate":"2024-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10182-024-00516-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143530001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Questionnaires are useful tool for exploring respondents’ perceptions through ratings, assumed to result from a latent decision process (DP). The DP varies when respondents rate on Likert or Semantic Differential scales. A possible paradigm to formalize the DP is based on the presence of a feeling and an uncertainty latent component, originally proposed as the foundations of the CUB (Combination of Uniform and shifted Binomial) class. It can be assumed that with Likert scales, respondents begin reasoning from the bottom, progressing upwards based on their sensations. Conversely, Semantic Differential scale users are assumed to start from the middle and move either upward or downward. The CUM (Combination of Uniform and Multinomial), a new model in the CUB class, derived from this DP, analyzes rating data on a Semantic Differential scale. This paper defines the concept of local and global unidirectional equivalence and studies, from an analytical point of view, the conditions under which CUB and CUM models generate identical theoretical probabilities, in order to enhance the interpretative understanding of the models.
问卷是有用的工具,探索受访者的看法通过评级,假设结果从一个潜在的决策过程(DP)。当被调查者在李克特或语义差异量表上评分时,DP会有所不同。将DP形式化的一个可能范例是基于感觉和不确定性潜在成分的存在,最初被提议作为CUB(统一和转移二项组合)类的基础。可以假设,在李克特量表中,被调查者从底部开始推理,根据他们的感觉向上发展。相反,假设语义差异量表的用户从中间开始,向上或向下移动。在此基础上衍生出了CUB类中的新模型CUM (combined of Uniform and Multinomial),该模型在语义差异尺度上分析评级数据。本文定义了局部和全局单向等价的概念,并从分析的角度研究了CUB和CUM模型产生相同理论概率的条件,以增强对模型的解释性理解。
{"title":"On the equivalence of two mixture models for rating data","authors":"Matteo Ventura, Ambra Macis, Marica Manisera, Paola Zuccolotto","doi":"10.1007/s10182-024-00513-2","DOIUrl":"10.1007/s10182-024-00513-2","url":null,"abstract":"<div><p>Questionnaires are useful tool for exploring respondents’ perceptions through ratings, assumed to result from a latent decision process (DP). The DP varies when respondents rate on Likert or Semantic Differential scales. A possible paradigm to formalize the DP is based on the presence of a feeling and an uncertainty latent component, originally proposed as the foundations of the CUB (Combination of Uniform and shifted Binomial) class. It can be assumed that with Likert scales, respondents begin reasoning from the bottom, progressing upwards based on their sensations. Conversely, Semantic Differential scale users are assumed to start from the middle and move either upward or downward. The CUM (Combination of Uniform and Multinomial), a new model in the CUB class, derived from this DP, analyzes rating data on a Semantic Differential scale. This paper defines the concept of local and global unidirectional equivalence and studies, from an analytical point of view, the conditions under which CUB and CUM models generate identical theoretical probabilities, in order to enhance the interpretative understanding of the models.</p></div>","PeriodicalId":55446,"journal":{"name":"Asta-Advances in Statistical Analysis","volume":"109 2","pages":"387 - 411"},"PeriodicalIF":1.4,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145170213","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}