Sequences of regressions and their dependences
نویسنده
چکیده
In this paper, we study sequences of regressions in joint or single responses given a set of context variables, where a dependence structure of interest is captured by a regression graph. These graphs have nodes representing random variables and three types of edge. Their set of missing edges defines the independence structure of the graph provided two properties are used that are not common to all probability distributions, named the intersection and the composition property. We derive the additionally needed properties for tracing the effects of single active paths and for excluding any canceling of effects due to several paths connecting the same pair of nodes. For this, we use the notion of a generating process for the joint distribution and derive new properties of an edge matrix calculus for transforming graphs. One key is the M-matrix property of each regularized square edge matrix, others are the proposed notions of traceable regressions and of singleton transitivity.
منابع مشابه
Traceable Regressions
In this paper, we define and study the concept of traceable regressions and apply it to some examples. Traceable regressions are sequences of conditional distributions in joint or single responses for which a corresponding graph captures an independence structure and represents, in addition, conditional dependences that permit the tracing of pathways of dependence. We give the properties needed...
متن کاملCase-control studies for rare diseases: improved estimation of several risks and of feature dependences
To capture the dependences of a disease on several risk factors, a challenge is to combine model-based estimation with evidence-based arguments. Standard case-control methods allow estimation of the dependences of a rare disease on several regressors via logistic regressions. For case-control studies, the sampling design leads to samples from two different populations and for the set of regress...
متن کاملIRF and ISRF Sequences and their Anti-Pedagogical Value
Initiation, Response, and Feedback(IRF) sequences are the most frequent interaction network in any classroom contexts. IRF sequences have been examined profusely in previous studies and were reported to be negatively correlated with participation opportunities (Kasper, 2006; Cazden, 2001; Ellis, 1994).In all these studies, all contingent factors of any classroom context which might influence in...
متن کاملStar graphs induce tetrad correlations: for Gaussian as well as for binary variables
Tetrad correlations were obtained historically for Gaussian distributions when tasks are designed to measure an ability or attitude so that a single unobserved variable may generate the observed, linearly increasing dependences among the tasks. We connect such generating processes to a particular type of directed graph, the star graph, and to the notion of traceable regressions. Tetrad correlat...
متن کاملThermal Effects Study on Stimulated Brillouin Light Scattering in Photonic Crystal Fiber
we investigate the temperature-dependences of the Brillouin frequency shift in three different kind of single-mode fibers using a heterodyne method for sensing temperature. Positive dependences coefficients of 0.77, 0.56 and 1.45MHz/0C are demonstrated for 25 km long single-mode fiber, 10 km long non-zero dispersion shifted fiber and 100 m photonic crystal fiber, respectively. The results indic...
متن کامل