Bivariate least squares linear regression: towards a unified analytic formalism

Concerning bivariate least squares linear regression, the classical approach pursued for functional models in earlier attempts is reviewed using a new formalism in terms of deviation (matrix) traces. Within the framework of classical error models, the dependent variable relates to the independent variable according to the usual additive model. Linear models of regression lines are considered in the general case of correlated errors in X and in Y for heteroscedastic data. The special case of (C) generalized orthogonal regression is considered in detail together with well known subcases. In the limit of homoscedastic data, the results determined for functional models are compared with their counterparts related to extreme structural models. While regression line slope and intercept estimators for functional and structural models necessarily coincide, the contrary holds for related variance estimators even if the residuals obey a Gaussian distribution, with a single exception. An example of astronomical application is considered, concerning the [O/H]-[Fe/H] empirical relations deduced from five samples related to different stars and/or different methods of oxygen abundance determination. For selected samples and assigned methods, different regression models yield consistent results within the errors for both heteroscedastic and homoscedastic data. Conversely, samples related to different methods produce discrepant results, due to the presence of (still undetected) systematic errors, which implies no definitive statement can be made at present. A comparison is also made between different expressions of regression line slope and intercept variance estimators, where fractional discrepancies are found to be not exceeding a few percent, which grows up to about 20% in presence of large dispersion data.Comment: 56 pages, 2 tables, and 2 figures. New Astronomy, accepte

Visual Causality: Investigating Graph Layouts for Understanding Causal Processes

Causal diagrams provide a graphical formalism indicating how statistical models can be used to study causal processes. Despite the extensive research on the efficacy of aesthetic graphic layouts, the causal inference domain has not benefited from the results of this research. In this paper, we investigate the performance of graph visualisations for supporting users’ understanding of causal graphs. Two studies were conducted to compare graph visualisations for understanding causation and identifying confounding variables in a causal graph. The first study results suggest that while adjacency matrix layouts are better for understanding direct causation, node-link diagrams are better for understanding mediated causation along causal paths. The second study revealed that node-link layouts, and in particular layouts created by a radial algorithm, are more effective for identifying confounder and collider variables

Searching for phenotypic causal networks involving complex traits: an application to European quail

<p>Abstract</p> <p>Background</p> <p>Structural equation models (SEM) are used to model multiple traits and the casual links among them. The number of different causal structures that can be used to fit a SEM is typically very large, even when only a few traits are studied. In recent applications of SEM in quantitative genetics mixed model settings, causal structures were pre-selected based on prior beliefs alone. Alternatively, there are algorithms that search for structures that are compatible with the joint distribution of the data. However, such a search cannot be performed directly on the joint distribution of the phenotypes since causal relationships are possibly masked by genetic covariances. In this context, the application of the Inductive Causation (IC) algorithm to the joint distribution of phenotypes conditional to unobservable genetic effects has been proposed.</p> <p>Methods</p> <p>Here, we applied this approach to five traits in European quail: birth weight (BW), weight at 35 days of age (W35), age at first egg (AFE), average egg weight from 77 to 110 days of age (AEW), and number of eggs laid in the same period (NE). We have focused the discussion on the challenges and difficulties resulting from applying this method to field data. Statistical decisions regarding partial correlations were based on different Highest Posterior Density (HPD) interval contents and models based on the selected causal structures were compared using the Deviance Information Criterion (DIC). In addition, we used temporal information to perform additional edge orienting, overriding the algorithm output when necessary.</p> <p>Results</p> <p>As a result, the final causal structure consisted of two separated substructures: BW→AEW and W35→AFE→NE, where an arrow represents a direct effect. Comparison between a SEM with the selected structure and a Multiple Trait Animal Model using DIC indicated that the SEM is more plausible.</p> <p>Conclusions</p> <p>Coupling prior knowledge with the output provided by the IC algorithm allowed further learning regarding phenotypic causal structures when compared to standard mixed effects SEM applications.</p

Causal Network Accounts Of Ill-being: Depression & Digital Well-being

Depression is a common and devastating instance of ill-being which deserves an account. Moreover, the ill-being of depression is impacted by digital technology: some uses of digital technology increase such ill-being while other uses of digital technology increase well-being. So a good account of ill-being would explicate the antecedents of depressive symptoms and their relief, digitally and otherwise. This paper borrows a causal network account of well-being and applies it to ill-being, particularly depression. Causal networks are found to provide a principled, coherent, intuitively plausible, and empirically adequate account of cases of depression in every-day and digital contexts. Causal network accounts of ill-being also offer philosophical, scientific, and practical utility. Insofar as other accounts of ill-being cannot offer these advantages, we should prefer causal network accounts of ill-being

MicroRNA Predictors of Longevity in Caenorhabditis elegans

Neither genetic nor environmental factors fully account for variability in individual longevity: genetically identical invertebrates in homogenous environments often experience no less variability in lifespan than outbred human populations. Such variability is often assumed to result from stochasticity in damage accumulation over time; however, the identification of early-life gene expression states that predict future longevity would suggest that lifespan is least in part epigenetically determined. Such “biomarkers of aging,” genetic or otherwise, nevertheless remain rare. In this work, we sought early-life differences in organismal robustness in unperturbed individuals and examined the utility of microRNAs, known regulators of lifespan, development, and robustness, as aging biomarkers. We quantitatively examined Caenorhabditis elegans reared individually in a novel apparatus and observed throughout their lives. Early-to-mid–adulthood measures of homeostatic ability jointly predict 62% of longevity variability. Though correlated, markers of growth/muscle maintenance and of metabolic by-products (“age pigments”) report independently on lifespan, suggesting that graceful aging is not a single process. We further identified three microRNAs in which early-adulthood expression patterns individually predict up to 47% of lifespan differences. Though expression of each increases throughout this time, mir-71 and mir-246 correlate with lifespan, while mir-239 anti-correlates. Two of these three microRNA “biomarkers of aging” act upstream in insulin/IGF-1–like signaling (IIS) and other known longevity pathways, thus we infer that these microRNAs not only report on but also likely determine longevity. Thus, fluctuations in early-life IIS, due to variation in these microRNAs and from other causes, may determine individual lifespan

Choosing and refusing: doxastic voluntarism and folk psychology

A standard view in contemporary philosophy is that belief is involuntary, either as a matter of conceptual necessity or as a contingent fact of human psychology. We present seven experiments on patterns in ordinary folk-psychological judgments about belief. The results provide strong evidence that voluntary belief is conceptually possible and, granted minimal charitable assumptions about folk-psychological competence, provide some evidence that voluntary belief is psychologically possible. We also consider two hypotheses in an attempt to understand why many philosophers have been tempted to view belief as involuntary: that belief is a prototype concept and that belief is a dual character concept. Altogether, our findings contribute to longstanding philosophical debates about the relationship between the will and the intellect, while also advancing scientific understanding of important social judgments

Self-Rated Health in the Baltic Countries, 1994–1999

Numerous studies have examined the explanations of mortality fluctuations in the former USSR during the last decade of the twentieth century-a time of considerable political and socio-economic changes-but fewer studies have considered the health of these populations during this period. Using individual data from the Norbalt surveys held in 1994 and 1999 in the three Baltic countries, we examine the determinants of self-rated health in the three countries and for the two periods, by way of Bayesian structural equation modelling and directed acyclic graphs. The model takes into account, as possible determinants, alcohol consumption, physical health, psychological distress, education, locus of control, and social support. A major result is the remarkable stability of the model's parameters whatever the country, year, gender, ethnicity, or age-group. Particular attention is given to the role of alcohol consumption and to the association observed between better self-assessed health and higher drinking. © 2010 Springer Science+Business Media B.V