As is well known, implication is transitive but probabilistic support is not. Eells and Sober, followed by Shogenji, showed that screening off is a sufficient constraint for the transitivity of ...probabilistic support. Moreover, this screening off condition can be weakened without sacrificing transitivity, as was demonstrated by Suppes and later by Roche. In this paper we introduce an even weaker sufficient condition for the transitivity of probabilistic support, in fact one that can be made as weak as one wishes. We explain that this condition has an interesting property: it shows that transitivity is retained even though the Simpson paradox reigns. We further show that by adding a certain restriction the condition can be turned into one that is both sufficient and necessary for transitivity.
The Yule-Simpson paradox refers to the fact that outcomes of comparisons between groups are reversed when groups are combined. Using Essential Sciences Indicators, a part of InCites (Clarivate), data ...for countries, it is shown that although the Yule-Simpson phenomenon in citation analysis and research evaluation is not common, it isn’t extremely rare either. The Yule-Simpson paradox is a phenomenon one should be aware of, otherwise one may encounter unforeseen surprises in scientometric studies.
Causal effect evaluation and causal network learning are two main research areas in causal inference. For causal effect evaluation, we review the two problems of confounders and surrogates. The ...Yule-Simpson paradox is the idea that the association between two variables may be changed dramatically due to ignoring confounders. We review criteria for confounders and methods of adjustment for observed and unobserved confounders. The surrogate paradox occurs when a treatment has a positive causal effect on a surrogate endpoint, which, in turn, has a positive causal effect on a true endpoint, but the treatment may have a negative causal effect on the true endpoint. Some of the existing criteria for surrogates are subject to the surrogate paradox, and we review criteria for consistent surrogates to avoid the surrogate paradox. Causal networks are used to depict the causal relationships among multiple variables. Rather than discovering a global causal network, researchers are often interested in discovering the causes and effects of a given variable. We review some algorithms for local structure learning of causal networks centering around a given variable.
The current study exhibits a new implication of the Yule-Simpson paradox with public policy repercussions. We construct Laffer curves of local property tax collection based on aggregated data and ...group division to residential land uses in Jerusalem. Results indicate that based on aggregated (dis-aggregated) data, the location of owner-occupiers and renters who pay a relatively high rate tariff will be on the upward-sloping (downward-sloping) part of the Laffer curve. Consequently, statistical test outcomes support Laffer's controversial claim that for the few upper-brackets taxpayers, an efficient collection is associated with tax reduction rather than tax increase.
Dysbiosis, developed upon antibiotic administration, results in loss of diversity and shifts in the abundance of gut microbes. Doxycycline is a tetracycline antibiotic widely used for malaria ...prophylaxis in travelers. We prospectively studied changes in the fecal microbiota of 15 French soldiers after a 4-month mission to Mali with doxycycline malaria prophylaxis, compared to changes in the microbiota of 28 soldiers deployed to Iraq and Lebanon without doxycycline. Stool samples were collected with clinical data before and after missions, and 16S rRNA sequenced on MiSeq targeting the V3-V4 region. Doxycycline exposure resulted in increased alpha-biodiversity and no significant beta-dissimilarities. It led to expansion in Bacteroides, with a reduction in Bifidobacterium and Lactobacillus, as in the group deployed without doxycycline. Doxycycline did not alter the community structure and was specifically associated with a reduction in Escherichia and expression of Rothia. Differences in the microbiota existed at baseline between military units but not within the studied groups. This group-effect highlighted the risk of a Simpson paradox in microbiome studies.
We say that the signs of association measures among three variables {X, Y, Z} are transitive if a positive association measure between X and Y and a positive association measure between Y and Z imply ...a positive association measure between X and Z. We introduce four association measures with different stringencies, and discuss conditions for the transitivity of the signs of these association measures. When the variables follow exponential family distributions, the conditions become simpler and more interpretable. Applying our results to two data sets from an observational study and a randomized experiment, we demonstrate that the results can help us draw conclusions about the signs of the association measures between X and Z based only on separate studies about {X, Y} and {Y, Z}.
On stochastic dependence Meyer, Joerg M.
Teaching statistics,
03/2018, Letnik:
40, Številka:
1
Journal Article
Recenzirano
Summary
The contrary of stochastic independence splits up into two cases: pairs of events being favourable or being unfavourable. Examples show that both notions have quite unexpected properties, ...some of them being opposite to intuition. For example, transitivity does not hold. Stochastic dependence is also useful to explain cases of Simpson's paradox.
The Yule-Simpson paradox notes that an association between random variables can be reversed when averaged over a background variable. Cox and Wermuth introduced the concept of distribution dependence ...between two random variables X and Y, and gave two dependence conditions, each of which guarantees that reversal of qualitatively similar conditional dependences cannot occur after marginalizing over the background variable. Ma, Xie and Geng studied the uniform collapsibility of distribution dependence over a background variable founder stronger homogeneity condition. Collapsibility ensures that associations are the same for conditional and marginal models. In this article, we use the notion of average collapsibility, which requires only the conditional effects average over the background variable to the corresponding marginal effect and investigate its conditions for distribution dependence and for quantile regression coefficients.
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