{"id":1394,"date":"2023-07-26T13:44:31","date_gmt":"2023-07-26T13:44:31","guid":{"rendered":"https:\/\/statorials.org\/pt\/morans-eu\/"},"modified":"2023-07-26T13:44:31","modified_gmt":"2023-07-26T13:44:31","slug":"morans-eu","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/morans-eu\/","title":{"rendered":"O que \u00e9 o eu de moran? (defini\u00e7\u00e3o e #038; exemplo)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>O I de Moran<\/strong> \u00e9 uma forma de medir a autocorrela\u00e7\u00e3o espacial.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Simplificando, \u00e9 uma forma de quantificar o qu\u00e3o pr\u00f3ximos os valores est\u00e3o agrupados no espa\u00e7o 2D. \u00c9 frequentemente usado em geografia e <a href=\"https:\/\/en.wikipedia.org\/wiki\/Geographic_information_science\" target=\"_blank\" rel=\"noopener\">ci\u00eancia da informa\u00e7\u00e3o geogr\u00e1fica (GIS)<\/a> para medir o qu\u00e3o pr\u00f3ximas as diferentes caracter\u00edsticas est\u00e3o agrupadas em um mapa, como renda familiar, n\u00edvel de educa\u00e7\u00e3o, etc.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Moran I: a f\u00f3rmula<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A f\u00f3rmula para calcular o I de Moran \u00e9:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><em>I<\/em> = (N\/W)*\u03a3\u03a3w <sub>ij<\/sub> (x <sub>i<\/sub> \u2013 <span style=\"border-top: 1px solid black;\">x<\/span> )(x <sub>j<\/sub> \u2013 <span style=\"border-top: 1px solid black;\">x<\/span> )\/\u03a3(x <sub>i<\/sub> \u2013 <span style=\"border-top: 1px solid black;\">x<\/span> ) <sup>2<\/sup><\/span><\/p>\n<p> <span style=\"color: #000000;\">Ouro:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>N:<\/strong> O n\u00famero de unidades espaciais indexadas por <em>i<\/em> e <em>j<\/em><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>W:<\/strong> A soma de todos w <sub>ij<\/sub><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>x:<\/strong> A vari\u00e1vel de interesse (renda familiar, anos de escolaridade, etc.)<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><span style=\"border-top: 1px solid black;\">x<\/span> :<\/strong> A m\u00e9dia de x<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>w <sub>ij<\/sub> :<\/strong> Uma matriz de pesos espaciais<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Voc\u00ea provavelmente nunca ter\u00e1 que calcular essa medida manualmente, j\u00e1 que a maioria dos softwares estat\u00edsticos pode calcul\u00e1-la para voc\u00ea, mas ajuda conhecer a f\u00f3rmula usada nos bastidores.<\/span><\/p>\n<p> <span style=\"color: #000000;\">O valor de Moran pode variar de -1 a 1 onde:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>-1:<\/strong> A vari\u00e1vel de interesse est\u00e1 perfeitamente dispersa<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>0:<\/strong> a vari\u00e1vel de interesse est\u00e1 dispersa aleatoriamente<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>1:<\/strong> A vari\u00e1vel de interesse est\u00e1 perfeitamente agrupada<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Junto com o c\u00e1lculo do I de Moran, a maioria dos softwares estat\u00edsticos calcula um valor p correspondente que pode ser usado para determinar se os dados est\u00e3o dispersos aleatoriamente ou n\u00e3o.<\/span><\/p>\n<p> <span style=\"color: #000000;\">O teste de Moran utiliza as seguintes hip\u00f3teses nulas e alternativas:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Hip\u00f3tese nula (H <sub>0<\/sub> ):<\/strong> os dados est\u00e3o dispersos aleatoriamente.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Hip\u00f3tese alternativa ( <sub>HA<\/sub> ):<\/strong> Os dados <em>n\u00e3o<\/em> est\u00e3o dispersos aleatoriamente, ou seja, est\u00e3o agrupados em padr\u00f5es vis\u00edveis.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Se o valor p que corresponde ao I de Moran estiver abaixo de um certo n\u00edvel de signific\u00e2ncia (ou seja, \u03b1 = 0,05), ent\u00e3o podemos rejeitar a hip\u00f3tese nula e concluir que os dados est\u00e3o agrupados espacialmente de tal forma que \u00e9 improv\u00e1vel que sejam agrupados espacialmente. ocorreu por acaso.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Moran&#8217;s I: alguns exemplos<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Os exemplos a seguir representam cartas falsas com valores diferentes para I de Moran.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Vamos supor que cada quadrado no mapa represente um condado e que os condados com renda familiar m\u00e9dia acima de US$ 50.000 sejam mostrados em azul.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>I de Moran = 0:<\/strong> O rendimento m\u00e9dio do agregado familiar est\u00e1 disperso aleatoriamente (isto \u00e9, agrupamentos aleat\u00f3rios em \u00e1reas aleat\u00f3rias).<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-13852 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/morani1.png\" alt=\"Exemplo de Moran's I\" width=\"336\" height=\"323\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\"><strong>I = -1 de Moran:<\/strong> A renda familiar m\u00e9dia est\u00e1 perfeitamente dispersa.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-13853 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/morani2.png\" alt=\"Moran I em estat\u00edstica espacial\" width=\"337\" height=\"334\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\"><strong>I de Moran = 1:<\/strong> a renda familiar m\u00e9dia est\u00e1 perfeitamente agrupada.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-13854 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/morani3.png\" alt=\"Eu por Moran\" width=\"336\" height=\"331\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Consulte <a href=\"https:\/\/mgimond.github.io\/Spatial\/spatial-autocorrelation-in-r.html#app8_5\" target=\"_blank\" rel=\"noopener\">este exemplo<\/a> para obter um exemplo concreto de c\u00e1lculo do I de Moran no software estat\u00edstico R.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>O I de Moran \u00e9 uma forma de medir a autocorrela\u00e7\u00e3o espacial. Simplificando, \u00e9 uma forma de quantificar o qu\u00e3o pr\u00f3ximos os valores est\u00e3o agrupados no espa\u00e7o 2D. \u00c9 frequentemente usado em geografia e ci\u00eancia da informa\u00e7\u00e3o geogr\u00e1fica (GIS) para medir o qu\u00e3o pr\u00f3ximas as diferentes caracter\u00edsticas est\u00e3o agrupadas em um mapa, como renda familiar, [&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-1394","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>O que \u00e9 o eu de Moran? 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