関: covariation、covary

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(statistics) correlated variation

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出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2016/08/29 13:39:51」(JST)

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In statistics, a covariate is a variable that is possibly predictive of the outcome under study. A covariate may be of direct interest or it may be a confounding or interacting variable.

The alternative terms explanatory variable, independent variable, or predictor, are used in a regression analysis. In econometrics, the term "control variable" is usually used instead of "covariate".^[1]^[2] In a more specific usage, a covariate is a secondary variable that can affect the relationship between the dependent variable and other independent variables of primary interest.

An example is provided by the analysis of trend in sea level by Woodworth (1987). Here the dependent variable (and variable of most interest) was the annual mean sea level at a given location for which a series of yearly values were available. The primary independent variable was time. Use was made of a covariate consisting of yearly values of annual mean atmospheric pressure at sea level. The results showed that inclusion of the covariate allowed improved estimates of the trend against time to be obtained, compared to analyses which omitted the covariate.

References

^ Gujarati, Damodar N.; Porter, Dawn C. (2009). "Terminology and Notation". Basic Econometrics (Fifth international ed.). New York: McGraw-Hill. p. 21. ISBN 978-007-127625-2.
^ Wooldridge, Jeffrey (2012). Introductory Econometrics: A Modern Approach (Fifth ed.). Mason, OH: South-Western Cengage Learning. pp. 22–23. ISBN 978-1-111-53104-1.

Last, John M., ed. (2001). A Dictionary of Epidemiology (Fourth ed.). Oxford UP. ISBN 0-19-514168-7.
Everitt, B. S. (2002). The Cambridge Dictionary of Statistics (2nd ed.). Cambridge UP. ISBN 0-521-81099-X.
Woodworth, P. L. (1987). "Trends in U.K. mean sea level". Marine Geodesy. 11 (1): 57–87. doi:10.1080/15210608709379549.

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English Journal

Age differences in suprathreshold sensory function.

Heft MW, Robinson ME.Author information Department of Oral & Maxillofacial Surgery, University of Florida, Gainesville, FL, USA, mwheft@ufl.edu.AbstractWhile there is general agreement that vision and audition decline with aging, observations for the somatosensory senses and taste are less clear. The purpose of this study was to assess age differences in multimodal sensory perception in healthy, community-dwelling participants. Participants (100 females and 78 males aged 20-89 years) judged the magnitudes of sensations associated with graded levels of thermal, tactile, and taste stimuli in separate testing sessions using a cross-modality matching (CMM) procedure. During each testing session, participants also rated words that describe magnitudes of percepts associated with differing-level sensory stimuli. The words provided contextual anchors for the sensory ratings, and the word-rating task served as a control for the CMM. The mean sensory ratings were used as dependent variables in a MANOVA for each sensory domain, with age and sex as between-subject variables. These analyses were repeated with the grand means for the word ratings as a covariate to control for the rating task. The results of this study suggest that there are modest age differences for somatosensory and taste domains. While the magnitudes of these differences are mediated somewhat by age differences in the rating task, differences in warm temperature, tactile, and salty taste persist.
Age (Dordrecht, Netherlands).Age (Dordr).2014 Feb;36(1):1-8. doi: 10.1007/s11357-013-9536-9. Epub 2013 Apr 28.
While there is general agreement that vision and audition decline with aging, observations for the somatosensory senses and taste are less clear. The purpose of this study was to assess age differences in multimodal sensory perception in healthy, community-dwelling participants. Participants (100 fe
PMID 23625154

High red blood cell distribution width is closely associated with nonalcoholic fatty liver disease.

Yang W, Huang H, Wang Y, Yu X, Yang Z.Author information Geriatric Digestive System Department, Navy General Hospital, Beijing, China.AbstractBACKGROUND: The red blood cell distribution width (RDW) has been reported to be a risk marker of morbidity and mortality for cardiovascular diseases in various study populations. Nonalcoholic fatty liver disease (NAFLD) is also a risk factor for cardiovascular diseases. However, the relationship between RDW and NAFLD is less certain.
European journal of gastroenterology & hepatology.Eur J Gastroenterol Hepatol.2014 Feb;26(2):174-8. doi: 10.1097/MEG.0b013e328365c403.
BACKGROUND: The red blood cell distribution width (RDW) has been reported to be a risk marker of morbidity and mortality for cardiovascular diseases in various study populations. Nonalcoholic fatty liver disease (NAFLD) is also a risk factor for cardiovascular diseases. However, the relationship bet
PMID 24025980

Covariate Shift Adaptation for Discriminative 3D Pose Estimation.

Yamada M1, Sigal L2, Raptis M2.Author information 1NTT Communication Science Laboratories, Kidugawa.2Disney Research, Pittsburgh.AbstractDiscriminative, or (structured) prediction, methods have proved effective for variety of problems in computer vision; a notable example is 3D monocular pose estimation. All methods to date, however, relied on an assumption that training (source) and test (target) data come from the same underlying joint distribution. In many real cases, including standard data sets, this assumption is flawed. In the presence of training set bias, the learning results in a biased model whose performance degrades on the (target) test set. Under the assumption of covariate shift, we propose an unsupervised domain adaptation approach to address this problem. The approach takes the form of training instance reweighting, where the weights are assigned based on the ratio of training and test marginals evaluated at the samples. Learning with the resulting weighted training samples alleviates the bias in the learned models. We show the efficacy of our approach by proposing weighted variants of kernel regression (KR) and twin Gaussian processes (TGP). We show that our weighted variants outperform their unweighted counterparts and improve on the state-of-the-art performance in the public (HumanEva) data set.
IEEE transactions on pattern analysis and machine intelligence.IEEE Trans Pattern Anal Mach Intell.2014 Feb;36(2):235-47. doi: 10.1109/TPAMI.2013.123.
Discriminative, or (structured) prediction, methods have proved effective for variety of problems in computer vision; a notable example is 3D monocular pose estimation. All methods to date, however, relied on an assumption that training (source) and test (target) data come from the same underlying j
PMID 24356346

Japanese Journal

Domain Adaptation for Word Sense Disambiguation under the Problem of Covariate Shift

Hironori Kikuchi,Hiroyuki Shinnou
情報処理学会研究報告. 自然言語処理研究会報告 2013-NL-212(4), 1-6, 2013-07-11
… This problem of domain adaptation for WSD can be regarded as a problem of covariate shift. … In this paper, we solve the problem by parameter learning method to weight the probability density ratio, which is the solution of covariate shift. … In comparison with technique of Daume, which is a standardized approach for adaptive region, the effect of solving the problem in covariate shift was shown. …
NAID 110009586055

Partial linear single index models with distortion measurement errors

Zhang Jun,Yu Yao,Zhu Li-Xing [他]
Annals of the Institute of Statistical Mathematics 65(2), 237-267, 2013-04-00
NAID 40019552404

Multiple Imputation 法によるネステッドケースコントロール研究，ケースコホート研究の解析

野間久史,田中司朗,田中佐智子,和泉志津恵
計量生物学 33(2), 101-124, 2013
… The nested case-control and case-cohort designs are common means of reducing the cost of covariate measurements in large failure-time studies. … Under these designs, complete covariate data are collected only on the cases (i.e., subjects whose failure times are uncensored) and some matched controls selected using risk-set sampling or a subcohort randomly selected from the whole cohort. …
NAID 130003376413

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[1] Gujarati, Damodar N.; Porter, Dawn C. (2009). "Terminology and Notation". Basic Econometrics (Fifth international ed.). New York: McGraw-Hill. p. 21. ISBN 978-007-127625-2.

[2] Wooldridge, Jeffrey (2012). Introductory Econometrics: A Modern Approach (Fifth ed.). Mason, OH: South-Western Cengage Learning. pp. 22–23. ISBN 978-1-111-53104-1.

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