Many population-based surveys have binary responses from a large number of individuals in each household within small areas. One example is the Nepal Living Standards Survey (NLSS II), in which health status binary data (good versus poor) for each individual from sampled households (sub-areas) are available in the sampled wards (small areas). To make an inference for the finite population proportion of individuals in each household, we use the sub-area logistic regression model with reliable auxiliary information. The contribution of this model is twofold. First, we extend an area-level model to a sub-area level model. Second, because there are numerous sub-areas, standard Markov chain Monte Carlo (MCMC) methods to find the joint posterior density are very time-consuming. Therefore, we provide a sampling-based method, the integrated nested normal approximation (INNA), which permits fast computation. Our main goal is to describe this hierarchical Bayesian logistic regression model and to show that the computation is much faster than the exact MCMC method and also reasonably accurate. The performance of our method is studied by using NLSS II data. Our model can borrow strength from both areas and sub-areas to obtain more efficient and precise estimates. The hierarchical structure of our model captures the variation in the binary data reasonably well.
{"title":"Bayesian Logistic Regression Model for Sub-Areas","authors":"Lu Chen, B. Nandram","doi":"10.3390/stats6010013","DOIUrl":"https://doi.org/10.3390/stats6010013","url":null,"abstract":"Many population-based surveys have binary responses from a large number of individuals in each household within small areas. One example is the Nepal Living Standards Survey (NLSS II), in which health status binary data (good versus poor) for each individual from sampled households (sub-areas) are available in the sampled wards (small areas). To make an inference for the finite population proportion of individuals in each household, we use the sub-area logistic regression model with reliable auxiliary information. The contribution of this model is twofold. First, we extend an area-level model to a sub-area level model. Second, because there are numerous sub-areas, standard Markov chain Monte Carlo (MCMC) methods to find the joint posterior density are very time-consuming. Therefore, we provide a sampling-based method, the integrated nested normal approximation (INNA), which permits fast computation. Our main goal is to describe this hierarchical Bayesian logistic regression model and to show that the computation is much faster than the exact MCMC method and also reasonably accurate. The performance of our method is studied by using NLSS II data. Our model can borrow strength from both areas and sub-areas to obtain more efficient and precise estimates. The hierarchical structure of our model captures the variation in the binary data reasonably well.","PeriodicalId":93142,"journal":{"name":"Stats","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41412551","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the social sciences, the performance of two groups is frequently compared based on a cognitive test involving binary items. Item response models are often utilized for comparing the two groups. However, the presence of differential item functioning (DIF) can impact group comparisons. In order to avoid the biased estimation of groups, appropriate statistical methods for handling differential item functioning are required. This article compares the performance-regularized estimation and several robust linking approaches in three simulation studies that address the one-parameter logistic (1PL) and two-parameter logistic (2PL) models, respectively. It turned out that robust linking approaches are at least as effective as the regularized estimation approach in most of the conditions in the simulation studies.
{"title":"Comparing Robust Linking and Regularized Estimation for Linking Two Groups in the 1PL and 2PL Models in the Presence of Sparse Uniform Differential Item Functioning","authors":"A. Robitzsch","doi":"10.3390/stats6010012","DOIUrl":"https://doi.org/10.3390/stats6010012","url":null,"abstract":"In the social sciences, the performance of two groups is frequently compared based on a cognitive test involving binary items. Item response models are often utilized for comparing the two groups. However, the presence of differential item functioning (DIF) can impact group comparisons. In order to avoid the biased estimation of groups, appropriate statistical methods for handling differential item functioning are required. This article compares the performance-regularized estimation and several robust linking approaches in three simulation studies that address the one-parameter logistic (1PL) and two-parameter logistic (2PL) models, respectively. It turned out that robust linking approaches are at least as effective as the regularized estimation approach in most of the conditions in the simulation studies.","PeriodicalId":93142,"journal":{"name":"Stats","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42309810","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yu-Fang Chien, Haiming Zhou, T. Hanson, Theodore C. Lystig
Zellner’s objective g-prior has been widely used in linear regression models due to its simple interpretation and computational tractability in evaluating marginal likelihoods. However, the g-prior further allows portioning the prior variability explained by the linear predictor versus that of pure noise. In this paper, we propose a novel yet remarkably simple g-prior specification when a subject matter expert has information on the marginal distribution of the response yi. The approach is extended for use in mixed models with some surprising but intuitive results. Simulation studies are conducted to compare the model fitting under the proposed g-prior with that under other existing priors.
{"title":"Informative g-Priors for Mixed Models","authors":"Yu-Fang Chien, Haiming Zhou, T. Hanson, Theodore C. Lystig","doi":"10.3390/stats6010011","DOIUrl":"https://doi.org/10.3390/stats6010011","url":null,"abstract":"Zellner’s objective g-prior has been widely used in linear regression models due to its simple interpretation and computational tractability in evaluating marginal likelihoods. However, the g-prior further allows portioning the prior variability explained by the linear predictor versus that of pure noise. In this paper, we propose a novel yet remarkably simple g-prior specification when a subject matter expert has information on the marginal distribution of the response yi. The approach is extended for use in mixed models with some surprising but intuitive results. Simulation studies are conducted to compare the model fitting under the proposed g-prior with that under other existing priors.","PeriodicalId":93142,"journal":{"name":"Stats","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48885348","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Irshad, M. Monisha, C. Chesneau, R. Maya, D. S. Shibu
The zero-truncated Poisson distribution (ZTPD) generates a statistical model that could be appropriate when observations begin once at least one event occurs. The intervened Poisson distribution (IPD) is a substitute for the ZTPD, in which some intervention processes may change the mean of the rare events. These two zero-truncated distributions exhibit underdispersion (i.e., their variance is less than their mean). In this research, we offer an alternative solution for dealing with intervention problems by proposing a generalization of the IPD by a Lagrangian approach called the Lagrangian intervened Poisson distribution (LIPD), which in fact generalizes both the ZTPD and the IPD. As a notable feature, it has the ability to analyze both overdispersed and underdispersed datasets. In addition, the LIPD has a closed-form expression of all of its statistical characteristics, as well as an increasing, decreasing, bathtub-shaped, and upside-down bathtub-shaped hazard rate function. A consequent part is devoted to its statistical application. The maximum likelihood estimation method is considered, and the effectiveness of the estimates is demonstrated through a simulated study. To evaluate the significance of the new parameter in the LIPD, a generalized likelihood ratio test is performed. Subsequently, we present a new count regression model that is suitable for both overdispersed and underdispersed datasets using the mean-parametrized form of the LIPD. Additionally, the LIPD’s relevance and application are shown using real-world datasets.
{"title":"A Novel Flexible Class of Intervened Poisson Distribution by Lagrangian Approach","authors":"M. Irshad, M. Monisha, C. Chesneau, R. Maya, D. S. Shibu","doi":"10.3390/stats6010010","DOIUrl":"https://doi.org/10.3390/stats6010010","url":null,"abstract":"The zero-truncated Poisson distribution (ZTPD) generates a statistical model that could be appropriate when observations begin once at least one event occurs. The intervened Poisson distribution (IPD) is a substitute for the ZTPD, in which some intervention processes may change the mean of the rare events. These two zero-truncated distributions exhibit underdispersion (i.e., their variance is less than their mean). In this research, we offer an alternative solution for dealing with intervention problems by proposing a generalization of the IPD by a Lagrangian approach called the Lagrangian intervened Poisson distribution (LIPD), which in fact generalizes both the ZTPD and the IPD. As a notable feature, it has the ability to analyze both overdispersed and underdispersed datasets. In addition, the LIPD has a closed-form expression of all of its statistical characteristics, as well as an increasing, decreasing, bathtub-shaped, and upside-down bathtub-shaped hazard rate function. A consequent part is devoted to its statistical application. The maximum likelihood estimation method is considered, and the effectiveness of the estimates is demonstrated through a simulated study. To evaluate the significance of the new parameter in the LIPD, a generalized likelihood ratio test is performed. Subsequently, we present a new count regression model that is suitable for both overdispersed and underdispersed datasets using the mean-parametrized form of the LIPD. Additionally, the LIPD’s relevance and application are shown using real-world datasets.","PeriodicalId":93142,"journal":{"name":"Stats","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42405726","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
High-quality academic publishing is built on rigorous peer review [...]
高质量的学术出版建立在严格的同行评审的基础上[…]
{"title":"Acknowledgment to the Reviewers of Stats in 2022","authors":"","doi":"10.3390/stats6010009","DOIUrl":"https://doi.org/10.3390/stats6010009","url":null,"abstract":"High-quality academic publishing is built on rigorous peer review [...]","PeriodicalId":93142,"journal":{"name":"Stats","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135996027","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Point prediction of future record values based on sequences of previous lower or upper records is considered by means of the method of maximum product of spacings, where the underlying distribution is assumed to be a power function distribution and a Pareto distribution, respectively. Moreover, exact and approximate prediction intervals are discussed and compared with regard to their expected lengths and their percentages of coverage. The focus is on deriving explicit expressions in the point and interval prediction procedures. Predictions and forecasts are of interest, e.g., in sports analytics, which is gaining more and more attention in several sports disciplines. Previous works on forecasting athletic records have mainly been based on extreme value theory. The presented statistical prediction methods are exemplarily applied to data from various disciplines of athletics as well as to data from American football based on fantasy football points according to the points per reception scoring scheme. The results are discussed along with basic assumptions and the choice of underlying distributions.
{"title":"Statistical Prediction of Future Sports Records Based on Record Values","authors":"Christina Empacher, U. Kamps, G. Volovskiy","doi":"10.3390/stats6010008","DOIUrl":"https://doi.org/10.3390/stats6010008","url":null,"abstract":"Point prediction of future record values based on sequences of previous lower or upper records is considered by means of the method of maximum product of spacings, where the underlying distribution is assumed to be a power function distribution and a Pareto distribution, respectively. Moreover, exact and approximate prediction intervals are discussed and compared with regard to their expected lengths and their percentages of coverage. The focus is on deriving explicit expressions in the point and interval prediction procedures. Predictions and forecasts are of interest, e.g., in sports analytics, which is gaining more and more attention in several sports disciplines. Previous works on forecasting athletic records have mainly been based on extreme value theory. The presented statistical prediction methods are exemplarily applied to data from various disciplines of athletics as well as to data from American football based on fantasy football points according to the points per reception scoring scheme. The results are discussed along with basic assumptions and the choice of underlying distributions.","PeriodicalId":93142,"journal":{"name":"Stats","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43503521","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This work presents the statistical analysis of a monthly average temperatures time series in several European cities using a state space approach, which considers models with a deterministic seasonal component and a stochastic trend. Temperature rise rates in Europe seem to have increased in the last decades when compared with longer periods. Therefore, change point detection methods, both parametric and non-parametric methods, were applied to the standardized residuals of the state space models (or some other related component) in order to identify these possible changes in the monthly temperature rise rates. All of the used methods have identified at least one change point in each of the temperature time series, particularly in the late 1980s or early 1990s. The differences in the average temperature trend are more evident in Eastern European cities than in Western Europe. The smoother-based t-test framework proposed in this work showed an advantage over the other methods, precisely because it considers the time correlation presented in time series. Moreover, this framework focuses the change point detection on the stochastic trend component.
{"title":"Change Point Detection by State Space Modeling of Long-Term Air Temperature Series in Europe","authors":"Magda Monteiro, M. Costa","doi":"10.3390/stats6010007","DOIUrl":"https://doi.org/10.3390/stats6010007","url":null,"abstract":"This work presents the statistical analysis of a monthly average temperatures time series in several European cities using a state space approach, which considers models with a deterministic seasonal component and a stochastic trend. Temperature rise rates in Europe seem to have increased in the last decades when compared with longer periods. Therefore, change point detection methods, both parametric and non-parametric methods, were applied to the standardized residuals of the state space models (or some other related component) in order to identify these possible changes in the monthly temperature rise rates. All of the used methods have identified at least one change point in each of the temperature time series, particularly in the late 1980s or early 1990s. The differences in the average temperature trend are more evident in Eastern European cities than in Western Europe. The smoother-based t-test framework proposed in this work showed an advantage over the other methods, precisely because it considers the time correlation presented in time series. Moreover, this framework focuses the change point detection on the stochastic trend component.","PeriodicalId":93142,"journal":{"name":"Stats","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43119824","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present REGA, a new adaptive-sampling-based algorithm for the control of finite-horizon Markov decision processes (MDPs) with very large state spaces and small action spaces. We apply a variant of the ϵ-greedy multiarmed bandit algorithm to each stage of the MDP in a recursive manner, thus computing an estimation of the “reward-to-go” value at each stage of the MDP. We provide a finite-time analysis of REGA. In particular, we provide a bound on the probability that the approximation error exceeds a given threshold, where the bound is given in terms of the number of samples collected at each stage of the MDP. We empirically compare REGA against another sampling-based algorithm called RASA by running simulations against the SysAdmin benchmark problem with 210 states. The results show that REGA and RASA achieved similar performance. Moreover, REGA and RASA empirically outperformed an implementation of the algorithm that uses the “original” ϵ-greedy algorithm that commonly appears in the literature.
{"title":"An ϵ-Greedy Multiarmed Bandit Approach to Markov Decision Processes","authors":"Isa Muqattash, Jiaqiao Hu","doi":"10.3390/stats6010006","DOIUrl":"https://doi.org/10.3390/stats6010006","url":null,"abstract":"We present REGA, a new adaptive-sampling-based algorithm for the control of finite-horizon Markov decision processes (MDPs) with very large state spaces and small action spaces. We apply a variant of the ϵ-greedy multiarmed bandit algorithm to each stage of the MDP in a recursive manner, thus computing an estimation of the “reward-to-go” value at each stage of the MDP. We provide a finite-time analysis of REGA. In particular, we provide a bound on the probability that the approximation error exceeds a given threshold, where the bound is given in terms of the number of samples collected at each stage of the MDP. We empirically compare REGA against another sampling-based algorithm called RASA by running simulations against the SysAdmin benchmark problem with 210 states. The results show that REGA and RASA achieved similar performance. Moreover, REGA and RASA empirically outperformed an implementation of the algorithm that uses the “original” ϵ-greedy algorithm that commonly appears in the literature.","PeriodicalId":93142,"journal":{"name":"Stats","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45930650","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Income inequality remains one of the most burning issues discussed in the world. The difficulty of the problem arises from its multiple manifestations at regional and local levels and unique patterns within countries. This paper employs a multilevel approach to identify factors that influence income and wage inequalities at regional and municipal scales in Russia. We carried out the study on data from 2017 municipalities of 75 Russian regions from 2015 to 2019. A Hierarchical Linear Model with Cross-Classified Random Effects (HLMHCM) allowed us to establish that most of the total variances in population income and average wages accounted for the regional scale. Our analysis revealed different variances of income per capita and average wage; we disclosed the reasons for these disparities. We also found a mixed relationship between income inequality and social transfers. These variables influence income growth but change the relationship between income and labour productivity. Our study underlined that the impacts of shares of employees in agriculture and manufacturing should be considered together with labour productivity in these industries.
{"title":"Applying the Multilevel Approach in Estimation of Income Population Differences","authors":"V. Timiryanova, Dina Krasnoselskaya, N. Kuzminykh","doi":"10.3390/stats6010005","DOIUrl":"https://doi.org/10.3390/stats6010005","url":null,"abstract":"Income inequality remains one of the most burning issues discussed in the world. The difficulty of the problem arises from its multiple manifestations at regional and local levels and unique patterns within countries. This paper employs a multilevel approach to identify factors that influence income and wage inequalities at regional and municipal scales in Russia. We carried out the study on data from 2017 municipalities of 75 Russian regions from 2015 to 2019. A Hierarchical Linear Model with Cross-Classified Random Effects (HLMHCM) allowed us to establish that most of the total variances in population income and average wages accounted for the regional scale. Our analysis revealed different variances of income per capita and average wage; we disclosed the reasons for these disparities. We also found a mixed relationship between income inequality and social transfers. These variables influence income growth but change the relationship between income and labour productivity. Our study underlined that the impacts of shares of employees in agriculture and manufacturing should be considered together with labour productivity in these industries.","PeriodicalId":93142,"journal":{"name":"Stats","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43768845","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The properties of non-parametric kernel estimators for probability density function from two special classes are investigated. Each class is parametrized with distribution smoothness parameter. One of the classes was introduced by Rosenblatt, another one is introduced in this paper. For the case of the known smoothness parameter, the rates of mean square convergence of optimal (on the bandwidth) density estimators are found. For the case of unknown smoothness parameter, the estimation procedure of the parameter is developed and almost surely convergency is proved. The convergence rates in the almost sure sense of these estimators are obtained. Adaptive estimators of densities from the given class on the basis of the constructed smoothness parameter estimators are presented. It is shown in examples how parameters of the adaptive density estimation procedures can be chosen. Non-asymptotic and asymptotic properties of these estimators are investigated. Specifically, the upper bounds for the mean square error of the adaptive density estimators for a fixed sample size are found and their strong consistency is proved. The convergence of these estimators in the almost sure sense is established. Simulation results illustrate the realization of the asymptotic behavior when the sample size grows large.
{"title":"Estimating Smoothness and Optimal Bandwidth for Probability Density Functions","authors":"D. Politis, P. Tarassenko, V. Vasiliev","doi":"10.3390/stats6010003","DOIUrl":"https://doi.org/10.3390/stats6010003","url":null,"abstract":"The properties of non-parametric kernel estimators for probability density function from two special classes are investigated. Each class is parametrized with distribution smoothness parameter. One of the classes was introduced by Rosenblatt, another one is introduced in this paper. For the case of the known smoothness parameter, the rates of mean square convergence of optimal (on the bandwidth) density estimators are found. For the case of unknown smoothness parameter, the estimation procedure of the parameter is developed and almost surely convergency is proved. The convergence rates in the almost sure sense of these estimators are obtained. Adaptive estimators of densities from the given class on the basis of the constructed smoothness parameter estimators are presented. It is shown in examples how parameters of the adaptive density estimation procedures can be chosen. Non-asymptotic and asymptotic properties of these estimators are investigated. Specifically, the upper bounds for the mean square error of the adaptive density estimators for a fixed sample size are found and their strong consistency is proved. The convergence of these estimators in the almost sure sense is established. Simulation results illustrate the realization of the asymptotic behavior when the sample size grows large.","PeriodicalId":93142,"journal":{"name":"Stats","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48907693","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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