Technical Comment on "Policy impacts of statistical uncertainty and privacy".

Steed et al. (1) illustrates the crucial impact that the quality of official statistical data products may exert on the accuracy, stability, and equity of policy decisions on which they are based. The authors remind us that data, however responsibly curated, can be fallible. With this comment, we underscore the importance of conducting principled quality assessment of official statistical data products. We observe that the quality assessment procedure employed by Steed et al. needs improvement, due to (i) the inadmissibility of the estimator used, and (ii) the inconsistent probability model it induces on the joint space of the estimator and the observed data. We discuss the design of alternative statistical methods to conduct principled quality assessments for official statistical data products, showcasing two simulation-based methods for admissible minimax shrinkage estimation via multilevel empirical Bayesian modeling. For policymakers and stakeholders to accurately gauge the context-specific usability of data, the assessment should take into account both uncertainty sources inherent to the data and the downstream use cases, such as policy decisions based on those data products.

BFF: Bayesian, Fiducial, and Frequentist Analysis of Cognitive Engagement among Cognitively Impaired Older Adults.

Engagement in cognitively demanding activities is beneficial to preserving cognitive health. Our goal was to demonstrate the utility of frequentist, Bayesian, and fiducial statistical methods for evaluating the robustness of effects in identifying factors that contribute to cognitive engagement for older adults experiencing cognitive decline. We collected a total of 504 observations across two longitudinal waves of data from 28 cognitively impaired older adults. Participants' systolic blood pressure responsivity, an index of cognitive engagement, was continuously sampled during cognitive testing. Participants reported on physical and mental health challenges and provided hair samples to assess chronic stress at each wave. Using the three statistical paradigms, we compared results from six model testing levels and longitudinal changes in health and stress predicting changes in cognitive engagement. Findings were mostly consistent across the three paradigms, providing additional confidence in determining effects. We extend selective engagement theory to cognitive impairment, noting that health challenges and stress appear to be important moderators. Further, we emphasize the utility of the Bayesian and fiducial paradigms for use with relatively small sample sizes because they are not based on asymptotic distributions. In particular, the fiducial paradigm is a useful tool because it provides more information than p values without the need to specify prior distributions, which may unduly influence the results based on a small sample. We provide the R code used to develop and implement all models.

Covariance estimation via fiducial inference.

As a classical problem, covariance estimation has drawn much attention from the statistical community for decades. Much work has been done under the frequentist and the Bayesian frameworks. Aiming to quantify the uncertainty of the estimators without having to choose a prior, we have developed a fiducial approach to the estimation of covariance matrix. Built upon the Fiducial Berstein-von Mises Theorem (Sonderegger and Hannig 2014), we show that the fiducial distribution of the covariate matrix is consistent under our framework. Consequently, the samples generated from this fiducial distribution are good estimators to the true covariance matrix, which enable us to define a meaningful confidence region for the covariance matrix. Lastly, we also show that the fiducial approach can be a powerful tool for identifying clique structures in covariance matrices.

JOINT AND INDIVIDUAL ANALYSIS OF BREAST CANCER HISTOLOGIC IMAGES AND GENOMIC COVARIATES.

The two main approaches in the study of breast cancer are histopathology (analyzing visual characteristics of tumors) and genomics. While both histopathology and genomics are fundamental to cancer research, the connections between these fields have been relatively superficial. We bridge this gap by investigating the Carolina Breast Cancer Study through the development of an integrative, exploratory analysis framework. Our analysis gives insights - some known, some novel - that are engaging to both pathologists and geneticists. Our analysis framework is based on Angle-based Joint and Individual Variation Explained (AJIVE) for statistical data integration and exploits Convolutional Neural Networks (CNNs) as a powerful, automatic method for image feature extraction. CNNs raise interpretability issues that we address by developing novel methods to explore visual modes of variation captured by statistical algorithms (e.g. PCA or AJIVE) applied to CNN features.

BFF: Bayesian, Fiducial, Frequentist Analysis of Age Effects in Daily Diary Data.

OBJECTIVES: We apply new statistical models to daily diary data to advance both methodological and conceptual goals. We examine age effects in within-person slopes in daily diary data and introduce Generalized Fiducial Inference (GFI), which provides a compromise between frequentist and Bayesian inference. We use daily stressor exposure data across six domains to generate within-person emotional reactivity slopes with daily negative affect. We test for systematic age differences and similarities in these reactivity slopes, which are inconsistent in previous research. METHOD: One hundred and eleven older (aged 60-90) and 108 younger (aged 18-36) adults responded to daily stressor and negative affect questions each day for eight consecutive days, resulting in 1,438 total days. Daily stressor domains included arguments, avoided arguments, work/volunteer stressors, home stressors, network stressors, and health-related stressors. RESULTS: Using Bayesian, GFI, and frequentist paradigms, we compared results for the six stressor domains with a focus on interpreting age effects in within-person reactivity. Multilevel models suggested null age effects in emotional reactivity across each of the paradigms within the domains of avoided arguments, work/volunteer stressors, home stressors, and health-related stressors. However, the models diverged with respect to null age effects in emotional reactivity to arguments and network stressors. DISCUSSION: The three paradigms converged on null age effects in reactivity for four of the six stressor domains. GFI is a useful tool that provides additional information when making determinations regarding null age effects in within-person slopes. We provide the code for readers to apply these models to their own data.

Second-Order Probability Matching Priors for the Person Parameter in Unidimensional IRT Models.

In applications of item response theory (IRT), it is often of interest to compute confidence intervals (CIs) for person parameters with prescribed frequentist coverage. The ubiquitous use of short tests in social science research and practices calls for a refinement of standard interval estimation procedures based on asymptotic normality, such as the Wald and Bayesian CIs, which only maintain desirable coverage when the test is sufficiently long. In the current paper, we propose a simple construction of second-order probability matching priors for the person parameter in unidimensional IRT models, which in turn yields CIs with accurate coverage even when the test is composed of a few items. The probability matching property is established based on an expansion of the posterior distribution function and a shrinkage argument. CIs based on the proposed prior can be efficiently computed for a variety of unidimensional IRT models. A real data example with a mixed-format test and a simulation study are presented to compare the proposed method against several existing asymptotic CIs.

A novel scale-space approach for multinormality testing and the k-sample problem in the high dimension low sample size scenario.

Two classical multivariate statistical problems, testing of multivariate normality and the k-sample problem, are explored by a novel analysis on several resolutions simultaneously. The presented methods do not invert any estimated covariance matrix. Thereby, the methods work in the High Dimension Low Sample Size situation, i.e. when n ≤ p. The output, a significance map, is produced by doing a one-dimensional test for all possible resolution/position pairs. The significance map shows for which resolution/position pairs the null hypothesis is rejected. For the testing of multinormality, the Anderson-Darling test is utilized to detect potential departures from multinormality at different combinations of resolutions and positions. In the k-sample case, it is tested whether k data sets can be said to originate from the same unspecified discrete or continuous multivariate distribution. This is done by testing the k vectors corresponding to the same resolution/position pair of the k different data sets through the k-sample Anderson-Darling test. Successful demonstrations of the new methodology on artificial and real data sets are presented, and a feature selection scheme is demonstrated.

Generalized Fiducial Inference for Logistic Graded Response Models.

Samejima's graded response model (GRM) has gained popularity in the analyses of ordinal response data in psychological, educational, and health-related assessment. Obtaining high-quality point and interval estimates for GRM parameters attracts a great deal of attention in the literature. In the current work, we derive generalized fiducial inference (GFI) for a family of multidimensional graded response model, implement a Gibbs sampler to perform fiducial estimation, and compare its finite-sample performance with several commonly used likelihood-based and Bayesian approaches via three simulation studies. It is found that the proposed method is able to yield reliable inference even in the presence of small sample size and extreme generating parameter values, outperforming the other candidate methods under investigation. The use of GFI as a convenient tool to quantify sampling variability in various inferential procedures is illustrated by an empirical data analysis using the patient-reported emotional distress data.

Generalized Fiducial Inference for Binary Logistic Item Response Models.

Generalized fiducial inference (GFI) has been proposed as an alternative to likelihood-based and Bayesian inference in mainstream statistics. Confidence intervals (CIs) can be constructed from a fiducial distribution on the parameter space in a fashion similar to those used with a Bayesian posterior distribution. However, no prior distribution needs to be specified, which renders GFI more suitable when no a priori information about model parameters is available. In the current paper, we apply GFI to a family of binary logistic item response theory models, which includes the two-parameter logistic (2PL), bifactor and exploratory item factor models as special cases. Asymptotic properties of the resulting fiducial distribution are discussed. Random draws from the fiducial distribution can be obtained by the proposed Markov chain Monte Carlo sampling algorithm. We investigate the finite-sample performance of our fiducial percentile CI and two commonly used Wald-type CIs associated with maximum likelihood (ML) estimation via Monte Carlo simulation. The use of GFI in high-dimensional exploratory item factor analysis was illustrated by the analysis of a set of the Eysenck Personality Questionnaire data.