AbstractIn this paper measures of interrater absolute agreement for quantitative measurements based on the standard deviation are proposed. Such indices allow (i) to overcome the limits affecting the intraclass correlation index; (ii) to measure the interrater agreement on single targets. Estimators of the proposed measures are introduced and their sampling properties are investigated for normal and non-normal data. Simulated data are employed to demonstrate the accuracy and practical utility of the new indices for assessing agreement. Finally, an application to assess the consistency of measurements performed by radiologists evaluating tumor size of lung cancer is presented.

AbstractA family of consistent tests, derived from a characterization of the probability generating function, is proposed for assessing Poissonity against a wide class of count distributions, which includes some of the most frequently adopted alternatives to the Poisson distribution. Actually, the family of test statistics is based on the difference between the plug-in estimator of the Poisson cumulative distribution function and the empirical cumulative distribution function. The test statistics have an intuitive and simple form and are asymptotically normally distributed, allowing a straightforward implementation of the test. The finite sample properties of the test are investigated by means of an extensive simulation study. The test shows satisfactory behaviour compared to other tests with known limit distribution.

AbstractDespite the popularity of feature importance (FI) measures in interpretable machine learning, the statistical adequacy of these methods is rarely discussed. From a statistical perspective, a major distinction is between analysing a variable’s importance before and after adjusting for covariates—i.e., between marginal and conditional measures. Our work draws attention to this rarely acknowledged, yet crucial distinction and showcases its implications. We find that few methods are available for testing conditional FI and practitioners have hitherto been severely restricted in method application due to mismatched data requirements. Most real-world data exhibits complex feature dependencies and incorporates both continuous and categorical features (i.e., mixed data). Both properties are oftentimes neglected by conditional FI measures. To fill this gap, we propose to combine the conditional predictive impact (CPI) framework with sequential knockoff sampling. The CPI enables conditional FI measurement that controls for any feature dependencies by sampling valid knockoffs—hence, generating synthetic data with similar statistical properties—for the data to be analysed. Sequential knockoffs were deliberately designed to handle mixed data and thus allow us to extend the CPI approach to such datasets. We demonstrate through numerous simulations and a real-world example that our proposed workflow controls type I error, achieves high power, and is in-line with results given by other conditional FI measures, whereas marginal FI metrics can result in misleading interpretations. Our findings highlight the necessity of developing statistically adequate, specialized methods for mixed data.

AbstractThis paper proposes an M-quantile regression approach to address the heterogeneity of the housing market in a modern European city. We show how M-quantile modelling is a rich and flexible tool for empirical market price data analysis, allowing us to obtain a robust estimation of the hedonic price function whilst accounting for different sources of heterogeneity in market prices. The suggested methodology can generally be used to analyse nonlinear interactions between prices and predictors. In particular, we develop a spatial semiparametric M-quantile model to capture both the potential nonlinear effects of the cultural environment on pricing and spatial trends. In both cases, nonlinearity is introduced into the model using appropriate bases functions. We show how the implicit price associated with the variable that measures cultural amenities can be determined in this semiparametric framework. Our findings show that the effect of several housing attributes and urban amenities differs significantly across the response distribution, suggesting that buyers of lower-priced properties behave differently than buyers of higher-priced properties.

AbstractMany real-life data sets can be analyzed using linear mixed models (LMMs). Since these are ordinarily based on normality assumptions, under small deviations from the model the inference can be highly unstable when the associated parameters are estimated by classical methods. On the other hand, the density power divergence (DPD) family, which measures the discrepancy between two probability density functions, has been successfully used to build robust estimators with high stability associated with minimal loss in efficiency. Here, we develop the minimum DPD estimator (MDPDE) for independent but non-identically distributed observations for LMMs according to the variance components model. We prove that the theoretical properties hold, including consistency and asymptotic normality of the estimators. The influence function and sensitivity measures are computed to explore the robustness properties. As a data-based choice of the MDPDE tuning parameter $$\alpha$$ α is very important, we propose two candidates as “optimal” choices, where optimality is in the sense of choosing the strongest downweighting that is necessary for the particular data set. We conduct a simulation study comparing the proposed MDPDE, for different values of $$\alpha$$ α , with S-estimators, M-estimators and the classical maximum likelihood estimator, considering different levels of contamination. Finally, we illustrate the performance of our proposal on a real-data example.

AbstractCommunication through websites is often characterised by short texts, made of few words, such as image captions or tweets. This paper explores the class of supervised learning methods for the analysis of short texts, as an alternative to unsupervised methods, widely employed to infer topics from structured texts. The aim is to assess the effectiveness of text data in social sciences, when they are used as explanatory variables in regression models. To this purpose, we compare different variable selection procedures when text regression models are fitted to real, short, text data. We discuss the results obtained by several variants of lasso, screening-based methods and randomisation-based models, such as sure independence screening and stability selection, in terms of number and importance of selected variables, assessed through goodness-of-fit measures, inclusion frequency and model class reliance. Latent Dirichlet allocation results are also considered as a term of comparison. Our perspective is primarily empirical and our starting point is the analysis of two real case studies, though bootstrap replications of each dataset are considered. The first case study aims at explaining price variations based on the information contained in the description of items on sale on e-commerce platforms. The second regards open questions in surveys on satisfaction ratings. The case studies are different in nature and representative of different kinds of short texts, as, in one case, a concise descriptive text is considered, whereas, in the other case, the text expresses an opinion.

While the vaccination campaign against COVID-19 is having its positive impact, we retrospectively analyze the causal impact of some decisions made by the Italian government on the second outbreak of the SARS-CoV-2 pandemic in Italy, when no vaccine was available. First, we analyze the causal impact of reopenings after the first lockdown in 2020. In addition, we also analyze the impact of reopening schools in September 2020. Our results provide an unprecedented opportunity to evaluate the causal relationship between the relaxation of restrictions and the transmission in the community of a highly contagious respiratory virus that causes severe illness in the absence of prophylactic vaccination programs. We present a purely data-analytic approach based on a Bayesian methodology and discuss possible interpretations of the results obtained and implications for policy makers.

AbstractFrom the inventory of the health insurer AOK in 2004, we draw a sample of a quarter million people and follow each person’s health claims continuously until 2013. Our aim is to estimate the effect of a stroke on the dementia onset probability for Germans born in the first half of the 20th century. People deceased before 2004 are randomly left-truncated, and especially their number is unknown. Filtrations, modelling the missing data, enable circumventing the unknown number of truncated persons by using a conditional likelihood. Dementia onset after 2013 is a fixed right-censoring event. For each observed health history, Jacod’s formula yields its conditional likelihood contribution. Asymptotic normality of the estimated intensities is derived, related to a sample size definition including the number of truncated people. The standard error results from the asymptotic normality and is easily computable, despite the unknown sample size. The claims data reveal that after a stroke, with time measured in years, the intensity of dementia onset increases from 0.02 to 0.07. Using the independence of the two estimated intensities, a 95% confidence interval for their difference is [0.053, 0.057]. The effect halves when we extend the analysis to an age-inhomogeneous model, but does not change further when we additionally adjust for multi-morbidity.