The analysis of repeated measures or panel data allows control of some of the biases which plague other observational studies, particularly unmeasured confounding. When this bias is suspected, and the research question is: 'Does a change in an exposure cause a change in the outcome?', a fixed effects approach can reduce the impact of confounding by time-invariant factors, such as the unmeasured characteristics of individuals. Epidemiologists familiar with using mixed models may initially presume that specifying a random effect (intercept) for every individual in the study is an appropriate method. However, this method uses information from both the within-individual/unit exposure-outcome association and the between-individual/unit exposure-outcome association. Variation between individuals may introduce confounding bias into mixed model estimates, if unmeasured time-invariant factors are associated with both the exposure and the outcome. Fixed effects estimators rely only on variation within individuals and hence are not affected by confounding from unmeasured time-invariant factors. The reduction in bias using a fixed effects model may come at the expense of precision, particularly if there is little change in exposures over time. Neither fixed effects nor mixed models control for unmeasured time-varying confounding or reverse causation.
We study the basic Laplacian on Riemannian foliations by writing the basic Laplacian in terms of the orthogonal projection from square-integrable forms to basic square-integrable forms. Using a geometric interpretation of this projection, we relate the ordinary Laplacian to the basic Laplacian. Among other results, we show the existence of the basic heat kernel and establish estimates for the eigenvalues of the basic Laplacian.
The classical twin method - comprising comparisons of monozygotic (MZ) and dizygotic (DZ) twins - in the domain of cognitive abilities and attainments has led to wide acceptance of results suggesting a large amount of additive genetic variance, with far-reaching implications both for the nature of future studies on the causes of cognitive variance and for intervention policies, as in education. However, this interpretation is only valid if the method observes a number of conditions, which have to hold. Here, we show that the most crucial of these, namely, the equal environments assumption (EEA), may not hold. Consequently, differences in twin correlations might be at least partly explained by treatment effects from parents, teachers, peers, and so on. In addition, well-known interactions at various levels confound the model of simple additive effects on which the classical twin method is predicated and results are interpreted. For example, at a socio-cognitive level, DZ twins may respond to treatments differently from MZ twins. This interaction may further explain MZ-DZ correlation differences. There is abundant evidence for such interactive effects in published twin data. We suggest that there is a need for a more thorough examination of these problems.
In this paper, we prove the invariance of the spectrum of the basic Dirac operator defined on a Riemannian foliation (M, ℱ) with respect to a change of bundle‐like metric. We then establish new estimates for its eigenvalues on spin flows in terms of the O’Neill tensor and the first eigenvalue of the Dirac operator on M. We discuss examples and also define a new version of the basic Laplacian whose spectrum does not depend on the choice of bundle‐like metric.
As we approach the centenary of the first practical intelligence test, there is still little scientific agreement about how human intelligence should be described, whether IQ tests actually measure it, and if they don't, what they actually do measure. The controversies and debates that result are well known. This paper brings together results and theory rarely considered (at least in conjunction with one another) in the IQ literature. It suggests that all of the population variance in IQ scores can be described in terms of a nexus of sociocognitive-affective factors that differentially prepares individuals for the cognitive, affective and performance demands of the test—in effect that the test is a measure of social class background, and not one of the ability for complex cognition as such. The rest of the paper shows how such factors can explain the correlational evidence usually thought to validate IQ tests, including associations with educational attainments, occupational performance and elementary cognitive tasks, as well as the intercorrelations among tests themselves.
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