{"id":1193,"date":"2023-07-27T08:19:55","date_gmt":"2023-07-27T08:19:55","guid":{"rendered":"https:\/\/statorials.org\/pt\/regressao-de-crista-em-r\/"},"modified":"2023-07-27T08:19:55","modified_gmt":"2023-07-27T08:19:55","slug":"regressao-de-crista-em-r","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/regressao-de-crista-em-r\/","title":{"rendered":"Regress\u00e3o ridge em r (passo a passo)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/pt\/regressao-do-cume\/\" target=\"_blank\" rel=\"noopener noreferrer\">A regress\u00e3o Ridge<\/a> \u00e9 um m\u00e9todo que podemos usar para ajustar um modelo de regress\u00e3o quando <a href=\"https:\/\/statorials.org\/pt\/regressao-multicolinearidade\/\" target=\"_blank\" rel=\"noopener noreferrer\">a multicolinearidade<\/a> est\u00e1 presente nos dados.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Resumindo, a regress\u00e3o de m\u00ednimos quadrados tenta encontrar estimativas de coeficientes que minimizem a soma residual dos quadrados (RSS):<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>RSS = \u03a3(y <sub>i<\/sub> \u2013 \u0177 <sub>i<\/sub> )2<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Ouro:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u03a3<\/strong> : Um s\u00edmbolo grego que significa <em>soma<\/em><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>y <sub>i<\/sub><\/strong> : o valor real da resposta para a <sup>i-\u00e9sima<\/sup> observa\u00e7\u00e3o<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u0177 <sub>i<\/sub><\/strong> : O valor da resposta prevista com base no modelo de regress\u00e3o linear m\u00faltipla<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Por outro lado, a regress\u00e3o de crista procura minimizar o seguinte:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>RSS + <sub>\u03bb\u03a3\u03b2j<\/sub> <sup>2<\/sup><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">onde <em>j<\/em> vai de 1 a <em>p<\/em> vari\u00e1veis preditoras e \u03bb \u2265 0.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Este segundo termo da equa\u00e7\u00e3o \u00e9 conhecido como <em>penalidade de retirada<\/em> . Na regress\u00e3o de crista, selecionamos um valor para \u03bb que produz o teste MSE mais baixo poss\u00edvel (erro quadr\u00e1tico m\u00e9dio).<\/span><\/p>\n<p> <span style=\"color: #000000;\">Este tutorial fornece um exemplo passo a passo de como realizar a regress\u00e3o de crista em R.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Etapa 1: carregar dados<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Para este exemplo, usaremos o conjunto de dados integrado do R chamado <strong>mtcars<\/strong> . Usaremos <strong>hp<\/strong> como vari\u00e1vel de resposta e as seguintes vari\u00e1veis como preditores:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">mpg<\/span><\/li>\n<li> <span style=\"color: #000000;\">peso<\/span><\/li>\n<li> <span style=\"color: #000000;\">merda<\/span><\/li>\n<li> <span style=\"color: #000000;\">qsec<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Para realizar a regress\u00e3o de crista, usaremos fun\u00e7\u00f5es do pacote <strong>glmnet<\/strong> . Este pacote requer que a <a href=\"https:\/\/statorials.org\/pt\/respostas-explicativas-das-variaveis\/\" target=\"_blank\" rel=\"noopener noreferrer\">vari\u00e1vel de resposta<\/a> seja um vetor e que o conjunto de vari\u00e1veis preditoras seja da classe <strong>data.matrix<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">O c\u00f3digo a seguir mostra como definir nossos dados:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\">#define response variable<\/span>\ny &lt;- mtcars$hp\n\n<span style=\"color: #008080;\">#define matrix of predictor variables\n<\/span>x &lt;- data.matrix(mtcars[, c('mpg', 'wt', 'drat', 'qsec')])\n<\/strong><\/span><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>Etapa 2: ajustar o modelo de regress\u00e3o Ridge<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A seguir, usaremos a fun\u00e7\u00e3o <strong>glmnet()<\/strong> para ajustar o modelo de regress\u00e3o Ridge e especificar <strong>alpha=0<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Observe que definir alfa igual a 1 equivale a usar a regress\u00e3o Lasso e definir alfa com um valor entre 0 e 1 equivale a usar uma rede el\u00e1stica.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Observe tamb\u00e9m que a regress\u00e3o de crista exige que os dados sejam padronizados de modo que cada vari\u00e1vel preditora tenha uma m\u00e9dia de 0 e um desvio padr\u00e3o de 1.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Felizmente, <strong>glmnet()<\/strong> faz essa padroniza\u00e7\u00e3o automaticamente para voc\u00ea. Se voc\u00ea j\u00e1 padronizou as vari\u00e1veis, poder\u00e1 especificar <strong>standardize=False<\/strong> .<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\"><span style=\"color: #000000;\"><span style=\"color: #993300;\">library<\/span> (glmnet)<\/span>\n\n#fit ridge regression model\n<\/span>model &lt;- glmnet(x, y, alpha = <span style=\"color: #008000;\">0<\/span> )\n\n<span style=\"color: #008080;\">#view summary of model\n<\/span>summary(model)\n\n          Length Class Mode   \na0 100 -none- numeric\nbeta 400 dgCMatrix S4     \ndf 100 -none- numeric\ndim 2 -none- numeric\nlambda 100 -none- numeric\ndev.ratio 100 -none- numeric\nnulldev 1 -none- numeric\nnpasses 1 -none- numeric\njerr 1 -none- numeric\noffset 1 -none- logical\ncall 4 -none- call   \nnobs 1 -none- numeric\n<\/strong><\/span><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>Etapa 3: escolha um valor ideal para Lambda<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A seguir, identificaremos o valor lambda que produz o menor erro quadr\u00e1tico m\u00e9dio de teste (MSE) usando <a href=\"https:\/\/statorials.org\/pt\/validacao-cruzada-k-fold\/\" target=\"_blank\" rel=\"noopener noreferrer\">valida\u00e7\u00e3o cruzada k-fold<\/a> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Felizmente, <strong>glmnet<\/strong> tem a fun\u00e7\u00e3o <strong>cv.glmnet()<\/strong> que executa automaticamente a valida\u00e7\u00e3o cruzada k-fold usando k = 10 vezes.<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\">#perform k-fold cross-validation to find optimal lambda value\n<\/span>cv_model &lt;- cv. <span style=\"color: #3366ff;\">glmnet<\/span> (x, y, alpha = <span style=\"color: #008000;\">0<\/span> )\n\n<span style=\"color: #008080;\">#find optimal lambda value that minimizes test MSE\n<\/span>best_lambda &lt;- cv_model$ <span style=\"color: #3366ff;\">lambda<\/span> . <span style=\"color: #3366ff;\">min<\/span>\nbest_lambda\n\n[1] 10.04567\n\n<span style=\"color: #008080;\">#produce plot of test MSE by lambda value<\/span>\nplot(cv_model) \n<\/strong><\/span><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-11860 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/faiter1.png\" alt=\"valida\u00e7\u00e3o cruzada para regress\u00e3o de crista em R\" width=\"443\" height=\"426\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">O valor lambda que minimiza o teste MSE \u00e9 <strong>10.04567<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Passo 4: Analise o modelo final<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Finalmente, podemos analisar o modelo final produzido pelo valor lambda \u00f3timo.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Podemos usar o seguinte c\u00f3digo para obter as estimativas dos coeficientes para este modelo:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\">#find coefficients of best model\n<\/span>best_model &lt;- glmnet(x, y, alpha = <span style=\"color: #008000;\">0<\/span> , lambda = best_lambda)\ncoef(best_model)\n\n5 x 1 sparse Matrix of class \"dgCMatrix\"\n                    s0\n(Intercept) 475.242646\nmpg -3.299732\nwt 19.431238\ndrat -1.222429\nqsec -17.949721<\/strong><\/span><\/pre>\n<p> <span style=\"color: #000000;\">Tamb\u00e9m podemos produzir um gr\u00e1fico Trace para visualizar como as estimativas dos coeficientes mudaram devido ao aumento no lambda:<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\">#produce Ridge trace plot<\/span>\nplot(model, xvar = \" <span style=\"color: #008000;\">lambda<\/span> \")<\/strong><\/span> <\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-11861 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/creter2.png\" alt=\"Tra\u00e7o de cume em R\" width=\"419\" height=\"411\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Finalmente, podemos calcular o <a href=\"https:\/\/statorials.org\/pt\/bom-valor-de-r-ao-quadrado\/\" target=\"_blank\" rel=\"noopener noreferrer\">R-quadrado do modelo<\/a> nos dados de treinamento:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\">#use fitted best model to make predictions\n<\/span>y_predicted &lt;- <span style=\"color: #3366ff;\">predict<\/span> (model, s = best_lambda, newx = x)\n\n<span style=\"color: #008080;\">#find OHS and SSE<\/span>\nsst &lt;- <span style=\"color: #3366ff;\">sum<\/span> ((y - <span style=\"color: #3366ff;\">mean<\/span> (y))^2)\nsse &lt;- <span style=\"color: #3366ff;\">sum<\/span> ((y_predicted - y)^2)\n\n<span style=\"color: #008080;\">#find R-Squared\n<\/span>rsq &lt;- 1 - sse\/sst\nrsq\n\n[1] 0.7999513\n<\/strong><\/span><\/pre>\n<p> <span style=\"color: #000000;\">O R ao quadrado \u00e9 <strong>0,7999513<\/strong> . Ou seja, o melhor modelo conseguiu explicar <strong>79,99%<\/strong> da varia\u00e7\u00e3o nos valores de resposta dos dados de treinamento.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Voc\u00ea pode encontrar o c\u00f3digo R completo usado neste exemplo <a href=\"https:\/\/github.com\/Statorials\/R-Guides\/blob\/main\/ridge_regression.R\" target=\"_blank\" rel=\"noopener noreferrer\">aqui<\/a> .<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A regress\u00e3o Ridge \u00e9 um m\u00e9todo que podemos usar para ajustar um modelo de regress\u00e3o quando a multicolinearidade est\u00e1 presente nos dados. Resumindo, a regress\u00e3o de m\u00ednimos quadrados tenta encontrar estimativas de coeficientes que minimizem a soma residual dos quadrados (RSS): RSS = \u03a3(y i \u2013 \u0177 i )2 Ouro: \u03a3 : Um s\u00edmbolo grego [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-1193","post","type-post","status-publish","format-standard","hentry","category-guia"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Regress\u00e3o Ridge em R (passo a passo)<\/title>\n<meta name=\"description\" content=\"Este tutorial explica como realizar a regress\u00e3o de crista em R, incluindo um exemplo passo a passo.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/pt\/regressao-de-crista-em-r\/\" \/>\n<meta property=\"og:locale\" content=\"pt_PT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Regress\u00e3o Ridge em R (passo a passo)\" \/>\n<meta property=\"og:description\" content=\"Este tutorial explica como realizar a regress\u00e3o de crista em R, incluindo um exemplo passo a passo.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/regressao-de-crista-em-r\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-27T08:19:55+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/faiter1.png\" \/>\n<meta name=\"author\" content=\"Dr. benjamim anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"Dr. benjamim anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tempo estimado de leitura\" \/>\n\t<meta name=\"twitter:data2\" content=\"4 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pt\/regressao-de-crista-em-r\/\",\"url\":\"https:\/\/statorials.org\/pt\/regressao-de-crista-em-r\/\",\"name\":\"Regress\u00e3o Ridge em R (passo a passo)\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-07-27T08:19:55+00:00\",\"dateModified\":\"2023-07-27T08:19:55+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\"},\"description\":\"Este tutorial explica como realizar a regress\u00e3o de crista em R, incluindo um exemplo passo a passo.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/regressao-de-crista-em-r\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/regressao-de-crista-em-r\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/regressao-de-crista-em-r\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Regress\u00e3o ridge em r (passo a passo)\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/pt\/#website\",\"url\":\"https:\/\/statorials.org\/pt\/\",\"name\":\"Statorials\",\"description\":\"O seu guia para a literacia estat\u00edstica!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/pt\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"pt-PT\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\",\"name\":\"Dr. benjamim anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-PT\",\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/pt\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/pt\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Dr. benjamim anderson\"},\"description\":\"Ol\u00e1, sou Benjamin, um professor aposentado de estat\u00edstica que se tornou professor dedicado na Statorials. 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