{"id":3993,"date":"2013-10-22T16:00:42","date_gmt":"2013-10-22T07:00:42","guid":{"rendered":"http:\/\/fujiitoshiki.com\/improvesociety\/?p=3993"},"modified":"2017-04-27T16:01:41","modified_gmt":"2017-04-27T07:01:41","slug":"post-3993","status":"publish","type":"post","link":"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=3993","title":{"rendered":"\u591a\u5909\u91cf\u89e3\u6790\u306b\u304a\u3051\u308b\u5909\u6570\u9593\u306e\u591a\u91cd\u5171\u7dda\u6027\u3092 variance inflation factor (VIF) \u3067\u691c\u8a3c\u3059\u308b"},"content":{"rendered":"<div class=\"theContentWrap-ccc\"><p>\u3000\u591a\u91cd\u5171\u7dda\u6027\u306f\u5909\u6570\u9593\u306b\u76f8\u95a2\u304c\u3042\u308b\u5834\u5408\u3084\u7dda\u5f62\u95a2\u4fc2\u304c\u6210\u7acb\u3057\u3066\u3044\u308b\u6642\u306b\u767a\u751f\u3057\uff0c\u591a\u5909\u91cf\u89e3\u6790\u306b\u304a\u3044\u3066\u56de\u5e30\u5f0f\u304c\u4e0d\u5b89\u5b9a\u306b\u306a\u308b\u306a\u3069\u306e\u69d8\u3005\u306a\u554f\u984c\u3092\u5f15\u304d\u8d77\u3053\u3057\u307e\u3059\uff0e\u305d\u306e\u6307\u6a19\u306e\u4e00\u3064\u3068\u3057\u3066 variance inflation factor (VIF) \u304c\u3042\u308a\uff0c\u305d\u306e\u5024\u304c 10 \u4ee5\u4e0a\u306b\u306a\u308b\u3068\u591a\u91cd\u5171\u7dda\u6027\u306e\u5f71\u97ff\u304c\u5f37\u304f\u306a\u308b\u305f\u3081\uff0c\u305d\u306e\u5909\u6570\u306f\u9664\u53bb\u3057\u3066\u89e3\u6790\u3059\u3079\u304d\u3067\u3059\uff0e<\/p>\n<ul>\n<li>\u5c11\u6570\u306e\u30c7\u30fc\u30bf\u3092\u8ffd\u52a0\u30fb\u524a\u9664\u3057\u305f\u3060\u3051\u3067\u56de\u5e30\u5f0f\u304c\u5927\u304d\u304f\u5909\u5316\u3059\u308b<\/li>\n<li>\u7570\u306a\u308b\u30c7\u30fc\u30bf\u306b\u9069\u7528\u3059\u308b\u3068\u56de\u5e30\u5f0f\u304c\u5927\u304d\u304f\u5909\u5316\u3059\u308b<\/li>\n<li>\u56de\u5e30\u4fc2\u6570\u306e\u7b26\u53f7\u304c\u305d\u306e\u5206\u91ce\u306e\u5e38\u8b58\u3068\u9006\u306b\u306a\u308b<\/li>\n<li>\u56de\u5e30\u5f0f\u306e\u5bc4\u4e0e\u7387\u304c\u9ad8\u304f\u30e2\u30c7\u30eb\u306e\u9069\u5408\u5ea6\u3082\u826f\u597d\u3067\u3042\u308b\u304c\uff0c\u3053\u3053\u306e\u56de\u5e30\u4fc2\u6570\u304c\u6709\u610f\u306b\u306a\u3089\u306a\u3044<\/li>\n<li>\u56de\u5e30\u5f0f\u304c\u6c42\u307e\u3089\u306a\u3044<\/li>\n<\/ul>\n<p>\u3000\u4e0a\u8a18\u306e\u73fe\u8c61\u304c\u8d77\u304d\u305f\u969b\u306b\u306f\u591a\u91cd\u5171\u7dda\u6027\u306e\u5b58\u5728\u3092\u7591\u3044\u307e\u3059\uff0eSPSS \u3067\u306f\u901a\u5e38\u306e\u7dda\u5f62\u56de\u5e30\u5206\u6790\u3067\u7d71\u8a08\u91cf\u30aa\u30d7\u30b7\u30e7\u30f3\u304b\u3089\u5171\u7dda\u6027\u306e\u8a3a\u65ad\u3092\u30c1\u30a7\u30c3\u30af\u3057\u3066 VIF \u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u304c\uff0c\u8868\u8a08\u7b97\u30bd\u30d5\u30c8\u3067\u3082\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff0e\u4e00\u3064\u306e\u5909\u6570\u3092\u76ee\u7684\u5909\u6570\u3068\u3057\uff0c\u4ed6\u306e\u5168\u3066\u306e\u5909\u6570\u3092\u8aac\u660e\u5909\u6570\u3068\u3057\u3066\u56de\u5e30\u5206\u6790\u3092\u5b9f\u884c\u3057\uff0c\u6c42\u307e\u3063\u305f\u91cd\u76f8\u95a2\u4fc2\u6570 R<sup>2<\/sup> \u3092\u7528\u3044\u3066\u4e0b\u5f0f\u3067\u6c42\u3081\u307e\u3059\uff0e<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+VIF+%3D+%5Cfrac%7B1%7D%7B1+-+R%5E2%7D&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle VIF = \\frac{1}{1 - R^2}' title='\\displaystyle VIF = \\frac{1}{1 - R^2}' class='latex' \/><\/p>\n<blockquote>\n<p>\nVIF measures the impact of multicollinearity among the X&#8217;s in a regression model on the precision of estimation. It expresses the degree to which multicollinearity amongst the predictors degrades the precision of an estimate. VIF is a statistic used to measure possible multicollinearity amongst the predictor or explanatory variables. VIF is computed as (1\/(1-R<sup>2<\/sup>)) for each of the k \u2013 1 independent variable equations. For example, given 4 independent predictor variables, the independent regression equations are formed by using each k-1 independent variable as the dependent variable:<br \/>\nX<sub>1<\/sub> = X<sub>2<\/sub> X<sub>3<\/sub> X<sub>4<\/sub><br \/>\nX<sub>2<\/sub> = X<sub>1<\/sub> X<sub>3<\/sub> X<sub>4<\/sub><br \/>\nX<sub>3<\/sub> = X<sub>1<\/sub> X<sub>2<\/sub> X<sub>4<\/sub><br \/>\nEach independent variable model will return an R<sup>2<\/sup> value and VIF value. The term to exclude in the model is then based on the value of VIF. If X<sub>j<\/sub> is highly correlated with the remaining predictors, its variance inflation factor will be very large. A general rule is that the VIF should not exceed 10 (Belsley, Kuh, &#038; Welsch, 1980). When X<sub>j<\/sub> is orthogonal to the remaining predictors, its variance inflation factor will be 1.\n<\/p>\n<\/blockquote>\n<blockquote>\n<p>Clearly the shortcomings just mentioned in regard to the use of R as a diagnostic measure for collinearity would seem also to limit the usefulness of R<sup>-1<\/sup> , and this is the case. The prevalence of this measure, however, justifies its separate treatment. Recalling that we are currently assuming the X data to be centered and scaled for unit length, we are considering R<sup>-1<\/sup> = (X<sup>T<\/sup>X)<sup>-1<\/sup>. The diagonal elements of R<sup>-1<\/sup>, the r<sup>ii<\/sup>, are often called the variance inflation factors, VIF<sub>i<\/sub>, [Chatterjee and Price (1077)], and their diagnostic value follows from the relation<br \/>\n<img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+VIF_i+%3D+%5Cfrac%7B1%7D%7B1-R%5E2_i%7D&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle VIF_i = \\frac{1}{1-R^2_i}' title='\\displaystyle VIF_i = \\frac{1}{1-R^2_i}' class='latex' \/><br \/>\nwhere R<sub>i<\/sub><sup>2<\/sup> is the multiple correlation coefficient of X<sub>i<\/sub> regressed on the remaining explanatory variables. Clearly a high VIF indicates an R<sub>i<\/sub><sup>2<\/sup> near unity, and hence points to collinearity. This measure is therefore of some use as an overall indication of collinearity. Its weakness, like those of R, lie in its inability to distinguish among several coexisting near dependencies and in the lack of a meaningful boundary to distinguish between values of VIF that can be considered high and those that can be considered low. [Belsley]<\/p>\n<\/blockquote>\n<p>\u53c2\u7167\uff1a<br \/>\n<a href=\"\/\/mlrv.ua.edu\/2009\/vol35_1\/robinson_schumacke_rproof.pdf\" title=\"Interaction Effects: Centering, Variance  Inflation Factor, and Interpretation Issues\" target=\"_blank\">Cecil Robinson and Randall E. Schumacker: Interaction Effects: Centering, Variance  Inflation Factor, and Interpretation Issues. Multiple Linear Regression Viewpoints, 2009, Vol. 35(1)<\/a><br \/>\n<a href=\"\/\/amstat.tandfonline.com\/doi\/abs\/10.1080\/00031305.1984.10483169#preview\" title=\"Demeaning Conditioning Diagnostics Through Centering\" target=\"_blank\">Belsley, D. A.: Demeaning conditioning diagnostics through centering: The American Statistics 1984; 38: 73 &#8211; 82<\/a><\/p>\n<p><iframe src=\"\/\/rcm-fe.amazon-adsystem.com\/e\/cm?lt1=_blank&#038;bc1=000000&#038;IS2=1&#038;bg1=FFFFFF&#038;fc1=000000&#038;lc1=0000FF&#038;t=fujiitoshiki-22&#038;o=9&#038;p=8&#038;l=as4&#038;m=amazon&#038;f=ifr&#038;ref=ss_til&#038;asins=0471691178\" style=\"width:120px;height:240px;\" scrolling=\"no\" marginwidth=\"0\" marginheight=\"0\" frameborder=\"0\"><\/iframe><\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>\u3000\u591a\u91cd\u5171\u7dda\u6027\u306f\u5909\u6570\u9593\u306b\u76f8\u95a2\u304c\u3042\u308b\u5834\u5408\u3084\u7dda\u5f62\u95a2\u4fc2\u304c\u6210\u7acb\u3057\u3066\u3044\u308b\u6642\u306b\u767a\u751f\u3057\uff0c\u591a\u5909\u91cf\u89e3\u6790\u306b\u304a\u3044\u3066\u56de\u5e30\u5f0f\u304c\u4e0d\u5b89\u5b9a\u306b\u306a\u308b\u306a\u3069\u306e\u69d8\u3005\u306a\u554f\u984c\u3092\u5f15\u304d\u8d77\u3053\u3057\u307e\u3059\uff0e\u305d\u306e\u6307\u6a19\u306e\u4e00\u3064\u3068\u3057\u3066 variance inflation factor ( &hellip; <a href=\"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=3993\" class=\"more-link\"><span class=\"screen-reader-text\">&#8220;\u591a\u5909\u91cf\u89e3\u6790\u306b\u304a\u3051\u308b\u5909\u6570\u9593\u306e\u591a\u91cd\u5171\u7dda\u6027\u3092 variance inflation factor (VIF) \u3067\u691c\u8a3c\u3059\u308b&#8221; \u306e<\/span>\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[7],"tags":[],"class_list":["post-3993","post","type-post","status-publish","format-standard","hentry","category-statistics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/3993","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3993"}],"version-history":[{"count":10,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/3993\/revisions"}],"predecessor-version":[{"id":7752,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/3993\/revisions\/7752"}],"wp:attachment":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3993"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3993"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3993"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}