2e:null 2f:["$","title",null,{"children":"TTT : Visualiser la \"première loi de la géographie\" de W. Tobler ? - L'autocorrélation spatiale | Laurent Jégou | Observable"}] 34:T11cb,moran_i = function(v, typepoids, seuil) { var va = get_var(v); const n = depts.features.length; const moyv = maths.mean(va); var wi = []; var numerateur = 0; var denominateur = 0; if (typepoids === undefined) {typepoids = vpoids.value;} if (seuil === undefined) {seuil = seuil_poids;} var S0 = 0; var S1 = 0; var S2 = 0; var A = 0; var B = 0; var C = 0; var D = 0; var EI = 0; var EI2 = 0; var VI = 0; var ZI = 0; // Calcul de S0 (somme des poids) for (var i=0; i (d[0])) .y(d => (d[1])); for (var i=0; i 0 && i == 23) { data_lines.push(laproj([turf.centroid(depts.features[i]).geometry.coordinates[0], turf.centroid(depts.features[i]).geometry.coordinates[1]])); data_lines.push(laproj([turf.centroid(depts.features[j]).geometry.coordinates[0], turf.centroid(depts.features[j]).geometry.coordinates[1]])); } } } carteg.append("path") .data([data_lines]) .attr("d", line) .attr("fill", "none") .attr("stroke", "white"); } // Titre var titre =""; var sous_titre = ""; var titre_legende = ""; switch(vrepval) { case "centre": titre = "Test Centre"; sous_titre = ""; titre_legende = "Test"; break; case "sudouest": titre = "Test Sud-Ouest"; sous_titre = ""; titre_legende = "Test"; break; case "damier": titre = "Test Damier"; sous_titre = ""; titre_legende = "Test"; break; case "res2": titre = "Part de résidences secondaires"; sous_titre = "en 2019"; titre_legende = '% des logements'; break; case "resp": titre = "Part de résidences principales"; sous_titre = "en 2019"; titre_legende = '% des logements'; break; case "med_niv_vie": titre = "Médiane du niveau de vie"; sous_titre = "en 2020"; titre_legende = 'Euros'; break; case "part_retraites_rev": titre = "Part des retraites dans le revenu disponible"; sous_titre = "en 2020"; titre_legende = '% du revenu'; break; case "part_mini_soc_rev": titre = "Part des minima sociaux dans le revenu disponible"; sous_titre = "en 2020"; titre_legende = '% du revenn'; break; } if (letyperep == "Moran I local") { sous_titre += " - I de Moran local"; titre_legende = "Indicateur"; } if (letyperep == "M.I.L. Z-Score") { sous_titre += " - Z-Score du I local"; titre_legende = "Indicateur"; } if (letyperep == "Getis&Ord local") { sous_titre += " - Getis & Ord local"; titre_legende = "Indicateur"; } if (letyperep == "Geary C local") { sous_titre += " - C de Geary local"; titre_legende = "Indicateur"; } carteg.append("g") .attr("transform", "translate("+decalage+", -20)") .append("text") .text(titre) .attr("font-size", 20); carteg.append("g") .attr("transform", "translate("+decalage+", 0)") .append("text") .text(sous_titre) .attr("font-size", 16); // Légende carteg.append("g") .attr("transform", "translate("+decalage+", 480)") .append(() => legend({color: colorQtvi, title: titre_legende, width: 420, tickFormat: ".2r"})); // Sources carteg.append("g") .attr("transform", "translate("+decalage+", 540)") .append("text") .text("Sources : INSEE, IGN") .attr("font-size", 10) .attr("font-family", "sans-serif"); }39:T2303,calcul_il = function(v, letypepoids) { var lavar = ''; var d = []; var g; var mi = []; if (v === undefined) { switch (typerep) { case 'Variable': lavar = vrep.value; break; case 'Moran I local': lavar = vrep.value+'_il'; break; case 'M.I.L. Z-Score': lavar = vrep.value+'_iz'; break; case 'Geary C local': lavar = vrep.value+'_cl'; break; case 'G local': lavar = vrep.value+'_gg'; break; case 'Getis&Ord local': lavar = vrep.value + '_go'; break; } } else { lavar = v; } if (letypepoids === undefined) { letypepoids = vpoids.value; } switch (lavar) { case 'centre': d.push(maths.min(centre)); d.push(maths.max(centre)); g = d3.interpolateYlOrRd; break; case 'centre_il': mi = moran_il('centre', letypepoids).il; d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; case 'centre_iz': mi = moran_il('centre', letypepoids).ilz; d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; case 'centre_cl': mi = geary_cl('centre', letypepoids); d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; case 'centre_gg': mi = g_statl('centre', letypepoids); d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; case 'centre_go': mi = go('centre'); d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; case 'sudouest': d.push(maths.min(sudouest)); d.push(maths.max(sudouest)); g = d3.interpolateYlOrRd; break; case 'sudouest_il': mi = moran_il('sudouest', letypepoids).il; d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; case 'sudouest_iz': mi = moran_il('sudouest', letypepoids).ilz; d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; case 'sudouest_cl': mi = geary_cl('sudouest', letypepoids); d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; case 'sudouest_gg': mi = g_statl('sudouest', letypepoids); d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; break; case 'sudouest_go': mi = go('sudouest'); d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; case 'damier': d.push(maths.min(damier)); d.push(maths.max(damier)); g = d3.interpolateYlOrRd; break; case 'damier_il': mi = moran_il('damier', letypepoids).il; d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; case 'damier_iz': mi = moran_il('damier', letypepoids).ilz; d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; case 'damier_cl': mi = geary_cl('damier', letypepoids); d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; case 'damier_gg': mi = g_statl('damier', letypepoids); d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; case 'damier_go': mi = go('damier', letypepoids); d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; case 'resp': d.push(maths.min(resp)); d.push(maths.max(resp)); g = d3.interpolateYlOrRd; break; case 'resp_il': mi = moran_il('resp', letypepoids).il; d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; case 'resp_iz': mi = moran_il('resp', letypepoids).ilz; d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; case 'resp_cl': mi = geary_cl('resp', letypepoids); d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; case 'resp_gg': mi = g_statl('resp', letypepoids); d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; case 'resp_go': mi = go('resp', letypepoids); d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; case 'res2': d.push(maths.min(res2)); d.push(maths.max(res2)); g = d3.interpolateYlOrRd; break; case 'res2_il': mi = moran_il('res2', letypepoids).il; d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; case 'res2_iz': mi = moran_il('res2', letypepoids).ilz; d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; case 'res2_cl': mi = geary_cl('res2', letypepoids); d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; case 'res2_gg': mi = g_statl('res2', letypepoids); d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; case 'res2_go': mi = go('res2', letypepoids); d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; case 'med_niv_vie': d.push(maths.min(med_niv_vie)); d.push(maths.max(med_niv_vie)); g = d3.interpolateYlOrRd; break; case 'med_niv_vie_il': mi = moran_il('med_niv_vie', letypepoids).il; d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; case 'med_niv_vie_iz': mi = moran_il('med_niv_vie', letypepoids).ilz; d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; case 'med_niv_vie_cl': mi = geary_cl('med_niv_vie', letypepoids); d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; case 'med_niv_vie_gg': mi = g_statl('med_niv_vie', letypepoids); d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; case 'med_niv_vie_go': mi = go('med_niv_vie', letypepoids); d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; case 'part_retraites_rev': d.push(maths.min(part_retraites_rev)); d.push(maths.max(part_retraites_rev)); g = d3.interpolateYlOrRd; break; case 'part_retraites_rev_il': mi = moran_il('part_retraites_rev', letypepoids).il; d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; case 'part_retraites_rev_iz': mi = moran_il('part_retraites_rev', letypepoids).ilz; d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; case 'part_retraites_rev_cl': mi = geary_cl('part_retraites_rev', letypepoids); d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; case 'part_retraites_rev_gg': var mi = g_statl('part_retraites_rev', letypepoids); d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; case 'part_retraites_rev_go': var mi = go('part_retraites_rev', letypepoids); d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; case 'part_mini_soc_rev': d.push(maths.min(part_mini_soc_rev)); d.push(maths.max(part_mini_soc_rev)); g = d3.interpolateYlOrRd; break; case 'part_mini_soc_rev_il': var mi = moran_il('part_mini_soc_rev', letypepoids).il; d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; case 'part_mini_soc_rev_iz': var mi = moran_il('part_mini_soc_rev', letypepoids).ilz; d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; case 'part_mini_soc_rev_cl': var mi = geary_cl('part_mini_soc_rev'); d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; case 'part_mini_soc_rev_gg': var mi = g_statl('part_mini_soc_rev', letypepoids); d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; case 'part_mini_soc_rev_go': var mi = go('part_mini_soc_rev', letypepoids); d.push(maths.max(mi)); d.push(maths.min(mi)); g = d3.interpolateRdYlGn; break; } return {domain: d, gradient: g, table_il: mi}; }3a:[{"id":"ca80c518573bf0f33279673a0a552a6a5aa3ca62a31ce00f8153944182a19863f20b182b52c27d1f30ee185ce1a19295c0978bb793e781d4db5efa465e4db8b1","href":"https://static.observableusercontent.com/files/ca80c518573bf0f33279673a0a552a6a5aa3ca62a31ce00f8153944182a19863f20b182b52c27d1f30ee185ce1a19295c0978bb793e781d4db5efa465e4db8b1","name":"fr_deptsresrev@2.json","type":"application/json","lastModified":1677945110098.315,"size":149396}] 32:{"id":"7a3737fc833471e0","slug":"autocorrelation_spatiale","title":"TTT : Visualiser la \"première loi de la géographie\" de W. Tobler ? - L'autocorrélation spatiale","thumbnail":"f042267a27129c2bcfbcf924a366b9e734150ef63a1beeb5082be305cb6d7c4c","access_level":"public","create_time":"$D2023-02-27T07:48:01.067Z","update_time":"$D2023-03-14T17:04:40.885Z","view_time":null,"first_public_time":"$D2023-03-12T13:46:07.794Z","has_unpublished_edits":null,"fork":false,"stars":5,"starred":false,"owner":{"type":"team","id":"1936870012656af6","login":"ljegou","name":"Laurent Jégou","avatar_url":"https://avatars-next.observableusercontent.com/447aa44a872789c3c13d2505fdb5a34daaaa3a44590422f4f782b6ea9a4bd3ac","tier":"starter_2024"},"version":1917,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"dc56e6af58493346","login":"ljegou","name":"Laurent Jégou","avatar_url":"https://avatars-next.observableusercontent.com/447aa44a872789c3c13d2505fdb5a34daaaa3a44590422f4f782b6ea9a4bd3ac","tier":null}],"members":[{"type":"individual","id":"dc56e6af58493346","login":"ljegou","name":"Laurent Jégou","avatar_url":"https://avatars-next.observableusercontent.com/447aa44a872789c3c13d2505fdb5a34daaaa3a44590422f4f782b6ea9a4bd3ac","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":true,"trashed":false,"lapsed":null,"subscribed":null,"forks":4,"collection":{"id":"ecc7c5c7ab16775a","slug":"ttt","title":"TTT","owner":{"id":"1936870012656af6","login":"ljegou","name":"Laurent Jégou"}},"type":"notebook","body":{"title":"TTT : Visualiser la \"première loi de la géographie\" de W. Tobler ? - L'autocorrélation spatiale","cells":[{"id":0,"value":"# TTT : Visualiser la \"première loi de la géographie\" de W. Tobler ? - L'autocorrélation spatiale","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1602,"value":"\n\"I invoke the first law of geography: everything is related to everything else, but near things are more related than distant things.\"\n\n« J'invoque la première loi de la géographie : tout interagit avec tout, mais les objets proches ont plus de relations que les objets éloignés. »\n\nTobler, 1970.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1910,"value":"English version : https://observablehq.com/@ljegou/spatial_autocorrelation","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1913,"value":"Présentation de Tribute To Tobler : https://geoflowiz.hypotheses.org/ttt-tribute-to-tobler","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1615,"value":"W. Tobler a lancé cette idée un peu comme une boutade lors d'une réunion de l'*International Geographical Union* en 1969, lors des premières réflexions sur l'utilisation d'un ordinateur en géographie, puis a creusé cette question dans un article de 1970. Cette hypothèse est devenue une question de recherche fertile, qui a produit de nombreuses autres publications. Elle était déjà apparue chez R.A. Fisher en 1935, mais n'avait pas connu le contexte favorable de la géomatique pour se développer.\n\nCette \"loi\" est à l'origine des concepts de **dépendance spatiale**, de **pondération des distances d'effets** et d'autres analyses du rôle de l'espace et des distances. Nous allons nous intéresser ici à une famille d'indicateurs qui sont directement liés à la notion des relations spatialisées : **l'autocorrélation spatiale**.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1617,"value":"L'autocorrélation spatiale est le degré selon lequel les objets proches sont plus reliés que les objets lointains. Ainsi, *elle mesure la façon dont la valeur d'une variable est semblable dans les objets spatialement proches*.\n\nCela implique donc **une variable spatialisée** et une **métrique de distance**, une façon de tenir compte de la distance spatiale entre les objets.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1619,"value":"Plusieurs recherches ont proposé des indicateurs pour mesurer cette autocorrélation spatiale, nous allons les présenter et les visualiser, en utilisant un jeu de données statistiques sur les logements, les ménages et des jeux de test sur les départements métropolitains français (Source INSEE et IGN). En fin de carnet, vous trouverez une carte interactive qui représente les différents indicateurs et leurs réglages.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1626,"value":"## Un premier exemple d'application : les indicateurs globaux","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1630,"value":"Pour débuter notre analyse, représentons simplement une variable spatialement hétérogène, comme **la proportion de résidences secondaires** dans le total des logements, en 2019 :","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1540,"value":"{\n const svg = d3.create(\"svg\")\n .attr(\"viewBox\", [0, 0, 975, 580]);\n \n carte(svg, \"gauche\", \"res2\", \"Variable\");\n \n return svg.node();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1636,"value":"Assez clairement, les départements qui présentent des valeurs plus élevées sont ceux qui possèdent des aménités géographiques pour le tourisme : littoral, montagne. Les départements se regroupent parfois en zones de valeurs proches, comme le nord-est (faibles %) ou les Alpes et la Corse (fort %).","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1653,"value":"L'autocorrélation spatiale peut être mesurée, évaluée, par le calcul d'**indicateurs globaux**, qui produisent une valeur pour l'ensemble de la variable.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1741,"value":"### L'indice de contiguïté de Geary","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1692,"value":"L'indice de contiguïté de Geary, ou **\"C de Geary\"**, a été développé par Roy C. Geary en 1954. Il mesure l'écart entre les valeurs des entités spatiales (les départements), pondéré par une métrique de distance et rapporté aux écarts des valeurs des entités à la moyenne. S'il est inférieur à 1, il exprime une autocorrélation spatiale positive, les objets proches ont des valeurs plus semblables que les objets éloignés.\n(Cf. l'article Wikipédia : https://fr.wikipedia.org/wiki/Indice_de_Geary).","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1747,"value":"Il est global sur le jeu de données, mais est relativement sensible à la présence d'autocorrélations locales.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1699,"value":"Ci-dessous, on le calcule avec une métrique de distance à l'inverse de la distance des entités voisines (contiguës). Ainsi, **plus un objet est éloigné de celui qui est considéré, moins il va être pris en compte**. De plus, on ne tient compte que des départements voisins. Ce sont les contours des départements qui sont pris en compte pour la mesure des distances, ce qui peut biaiser le calcul pour les petits départements (région parisienne). Pour tenir compte de ce biais, on peut utiliser d'autres métriques de distance, comme le nombre de voisins.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1668,"value":"C_de_Geary_idv = parseFloat(geary_c(\"res2\", \"poids_idv\").toFixed(3));","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1704,"value":"Si on utilise une métrique à l'inverse de la distance au carré (comme la gravité en physique), on obtient un indice C de Geary plus fort (donc une autocorrélation spatiale plus faible) :","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1709,"value":"C_de_Geary_g = parseFloat(geary_c(\"res2\", \"poids_g\").toFixed(3));","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1726,"value":"En utilisant une métrique de l'inverse de la distance des voisins définis par un seuil de distance, on peut observer la variation de l'indicateur C de Geary :","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1721,"value":"viewof seuil_geary = Inputs.range([maths.min(matrice_distances), maths.max(matrice_distances)], {value: parseFloat((etendue_md/2).toPrecision(2)), step: parseFloat((etendue_md/100).toPrecision(2)), label: \"Seuil poids inv/distance km\"});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1717,"value":"C_de_Geary_s = parseFloat(geary_c(\"res2\", \"poids_idseuil\", seuil_geary).toFixed(3));","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1738,"value":"Ci-dessous, on peut visualiser la distance de prise en compte des voisins du département de la Creuse.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1730,"value":"{\n const svg = d3.create(\"svg\")\n .attr(\"viewBox\", [0, 0, 975, 580]);\n\n carte(svg, \"gauche\", \"res2\", \"Variable\", null, seuil_geary, true);\n\n return svg.node();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1785,"value":"### L'indice d'autocorrélation spatiale I de Moran","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1750,"value":"En 1950, **Patrick Moran** met au point un indicateur global d'autocorrélation, le **\"I\"**, qui est moins sensible à la présence de clusters (groupes) locaux de valeurs. Il se base sur la somme des écarts à la moyenne des éléments du jeu de données, pondérée par la métrique de distance (pondération), rapportée à la somme des écarts à la moyenne et à la somme des poids de distance. Cf. l'article Wikipédia : https://fr.wikipedia.org/wiki/Indice_de_Moran","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1758,"value":"Le I de Moran varie de -1 à 1, avec une autocorrélation négative en-dessous de 0 (les éléments proches ont de valeurs très différentes), et positive au-dessus (ils ont des valeurs semblables).\n\nSi on le calcule pour la part de résidences secondaires, avec la métrique des poids de l'inverse de la distance, on obtient une valeur proche de 0,5 :","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1659,"value":"I_de_Moran_idv = parseFloat(moran_i(\"res2\", \"poids_idv\").moran_i.toFixed(3));","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1762,"value":"Avec une métrique de poids gravitaire, la valeur diminue un peu :","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1766,"value":"I_de_Moran_g = parseFloat(moran_i(\"res2\", \"poids_g\").moran_i.toFixed(3));","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1800,"value":"On peut, ici aussi, tester cet indicateur avec un seuil de distance de prise en compte pour l'inverse de la distance :","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1773,"value":"viewof seuil_moran = Inputs.range([maths.min(matrice_distances), maths.max(matrice_distances)], {value: parseFloat((etendue_md/2).toPrecision(2)), step: parseFloat((etendue_md/100).toPrecision(2)), label: \"Seuil poids inv/distance km\"});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1776,"value":"I_de_Moran_g_s = parseFloat(moran_i(\"res2\", \"poids_idseuil\", seuil_moran).moran_i.toFixed(3));","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1787,"value":"Le calcul de cet indice permet aussi le calcul de valeurs attendues et donc d'écart aux valeurs attendues, pour exprimer la significativité de la valeur obtenue.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1791,"value":"I_de_Moran_g_s_vattendue = parseFloat(moran_i(\"res2\", \"poids_idseuil\", seuil_moran).EI.toFixed(3));","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1795,"value":"I_de_Moran_g_s_zscore = parseFloat(moran_i(\"res2\", \"poids_idseuil\", seuil_moran).ZI.toFixed(3));","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1789,"value":"Ces indices globaux sont intéressants mais évidemment très synthétiques. Il est donc intéressant de pouvoir évaluer **localement** la valeur de l'autocorrélation spatiale, c'est à dire pour des portions du jeu de données, autour des éléments évalués chacun leur tour, c'est ce que l'on appelle les indicateurs *locaux *d'autocorrélation spatiale.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1805,"value":"## Les indicateurs locaux d'autocorrélation spatiale","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1807,"value":"Luc Anselin, qui a développé le champ de l'économétrie spatiale, propose en 1995 la description de cette analyse localisée de l'autocorrélation spatiale sous le nom de **LISA** : Local Indicators of Spatial Association (Anselin, 1995).","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1842,"value":"### Le I de Moran local","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1811,"value":"Le plus connu de ces indicateurs est **la version locale du I de Moran** : on va calculer une valeur pour chaque entité spatiale du jeu de données, en choisissant une pondération de la distance pour réduire la portée de la recherche de l'autocorrélation.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1817,"value":"{\n const svg = d3.create(\"svg\")\n .attr(\"viewBox\", [0, 0, 975, 580]);\n \n carte(svg, \"gauche\", \"res2\", \"Variable\");\n carte(svg, \"droite\", \"res2\", \"Moran I local\", \"poids_idv\");\n \n return svg.node();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1821,"value":"Comme pour le I global, le I local va indiquer, par sa valeur entre -1 et 1, des autocorrélations spatiales localisées pouvant être négatives ou positives. Dans notre exemple sur la part des résidences secondaires, comme les valeurs varient assez fortement d'un département à l'autre, on a essentiellement des valeurs faibles ou négatives. Les valeurs plus élevées repèrent des groupes de valeurs semblables, comme dans les Alpes ou autour de Paris.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1824,"value":"Les proximités de valeurs dissemblables sont repérées par des valeurs d'I local négatives : la vallée du Rhône, La Haute-Garonne, la Creuse...","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1826,"value":"Pour évaluer la significativité de ces indicateurs locaux, on peut calculer et représenter l'écart à la valeur attendue, les Z-Scores :","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1594,"value":"{\n const svg = d3.create(\"svg\")\n .attr(\"viewBox\", [0, 0, 975, 580]);\n\n carte(svg, \"gauche\", \"res2\", \"Moran I local\", \"poids_idv\");\n carte(svg, \"droite\", \"res2\", \"M.I.L. Z-Score\", \"poids_idv\");\n \n return svg.node();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1844,"value":"### Les autres indicateurs locaux : C de Geary local et Getis&Ord *","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1847,"value":"La version localisée du ratio **C de Geary** est directement issue de la version globale.\nL'indicateur *** (star) de Getis et Ord (ou GI*)** est plutôt un indicateur de \"points chauds\", c'est à dire de concentrations locales de valeurs extrêmes. Elle fonctionne selon une portée plus longue pour produire des zones plus amples. C'est un Z-Score, donc elle peut s'analyser directement. Cf. Getis and Ord, 1992.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1829,"value":"{\n const svg = d3.create(\"svg\")\n .attr(\"viewBox\", [0, 0, 975, 580]);\n\n carte(svg, \"gauche\", \"res2\", \"Geary C local\", \"poids_idv\");\n carte(svg, \"droite\", \"res2\", \"Getis&Ord local\", \"poids_idv\");\n \n return svg.node();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1832,"value":"# Carte interactive de test : variables, indicateurs, métriques de distances","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1859,"value":"Ci-dessous un \"bac à sable\" de représentation pour différentes variables, *des variables de test*, les différents indicateurs locaux d'autocorrélation spatiale et leur paramétrage (métrique de distance, seuil).\n\nOn peut notamment choisir de travailler avec des matrices de *distances normalisées* en ligne (somme = 1) et d'afficher les lignes de voisinage pour la Creuse pour les métriques comportant un seuil.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1565,"value":"{\n const svg = d3.create(\"svg\")\n .attr(\"viewBox\", [0, 0, 975, 580]);\n\n carte (svg);\n\n return svg.node();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1028,"value":"viewof nb_classes = Inputs.range([1, 24], {value: 10, step: 1, label: \"Nb. de classes\"});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":300,"value":"viewof vrep = Inputs.radio(les_variables, {label: \"Variable :\", value: les_variables[0], format: x => html`${x.label}`});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":911,"value":"viewof typerep = Inputs.radio(['Variable','Moran I local','M.I.L. Z-Score','Getis&Ord local','Geary C local'], {label: \"Type carto. :\", value: 'Variable'});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1062,"value":"viewof type_matrice = Inputs.radio(['Distances km', 'Distances normalisées'], {label: 'Type de matrice :', value: 'Distances km'});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":518,"value":"viewof vpoids = Inputs.radio(les_poids, {label: \"Pondération distance :\", value: les_poids[0], format: x => x.label});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":787,"value":"viewof seuil_poids = Inputs.range([maths.min(matrice_distances), maths.max(matrice_distances)], {value: parseFloat((etendue_md/2).toPrecision(2)), step: parseFloat((etendue_md/100).toPrecision(2)), label: \"Seuil poids inv/distance\"});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1299,"value":"viewof aff_creuse = Inputs.radio([\"Oui\", \"Non\"], {label: 'Distances depuis la Creuse', value: 'Non'});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1891,"value":"# Calculs, algos et formules","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":64,"value":"## Matrices des distances","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":72,"value":"matrice_distances = {\n const n = depts.features.length;\n var d = 0;\n var di = [];\n for (var i=0; i {return o / aj});\n di.push(djp);\n break;\n case 'Distances km':\n di.push(dj);\n break;\n }\n }\n return di;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1081,"value":"etendue_md = maths.max(matrice_distances) - maths.min(matrice_distances)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":245,"value":"matrice_adj = {\n const n = depts.features.length;\n var di = [];\n for (var i=0; i {\n var pt = turf.centroid(d);\n pt.properties = d.properties;\n return pt;\n }\n );\n return centres;\n }","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":614,"value":"get_var = function(nom) {\n var v;\n switch (nom) {\n case 'resp':\n v = resp;\n break;\n case 'res2':\n v = res2;\n break;\n case 'med_niv_vie':\n v = med_niv_vie;\n break;\n case 'part_retraites_rev':\n v = part_retraites_rev;\n break;\n case 'part_mini_soc_rev':\n v = part_mini_soc_rev;\n break;\n case 'centre':\n v = centre;\n break;\n case 'sudouest':\n v = sudouest;\n break;\n case 'damier':\n v = damier;\n break;\n }\n return v;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":213,"value":"poids_g = function (i,j) {\n // Fonction gravitaire\n return 1/Math.pow(matrice_distances[i][j], 2);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":282,"value":"poids_id = function (i,j) {\n // Fonciton inverse de la distance\n return 1/matrice_distances[i][j];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":532,"value":"poids_idv = function (i,j) {\n // Fonciton inverse de la distance des voisins immédiats seulement\n return matrice_adj[i][j] * (1 / matrice_distances[i][j]);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":563,"value":"poids_v = function (i,j) {\n // Fonction qui ne garde que les voisins immédiats\n return matrice_adj[i][j];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":784,"value":"poids_idseuil = function(i,j, s) {\n var v = 0;\n var d = matrice_distances[i][j];\n if (d <= s){\n return 1/d;\n } else {\n return 0;\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1165,"value":"poids_seuil = function(i,j, s) {\n var v = 0;\n var d = matrice_distances[i][j];\n if (d <= s){\n return 1;\n } else {\n return 0;\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":117,"value":"res2 = depts.features.map( d => d.properties.res2);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1106,"value":"res2_cr = {\n var m = maths.mean(res2);\n var sd = maths.std(res2, 'uncorrected');\n return res2.map( d => d/sd - m);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":133,"value":"resp = depts.features.map( d => d.properties.resp);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":572,"value":"med_niv_vie = depts.features.map( d => d.properties.med_niv_vie);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":575,"value":"part_retraites_rev = depts.features.map( d => d.properties.part_retraites_rev);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":578,"value":"part_mini_soc_rev = depts.features.map( d => d.properties.part_mini_soc_rev);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":872,"value":"sudouest = depts.features.map( d => d.properties.sudouest);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1148,"value":"centre = depts.features.map( d => d.properties.centre);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":875,"value":"damier = depts.features.map( d => d.properties.damier);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":502,"value":"les_variables = [\n {value: \"centre\", label: \"Test Centre \"},\n {value: \"sudouest\", label: \"Test Sud-Ouest \"},\n {value: \"damier\", label: \"Test Damier \"},\n {value: \"res2\", label: \"Résidences secondaires\"},\n {value: \"resp\", label: \"Résidences principales \"},\n {value: \"med_niv_vie\", label: \"Médiane du niveau de vie\"},\n {value: \"part_retraites_rev\", label: \"Part des retraites dans le revenu disponible\"},\n {value: \"part_mini_soc_rev\", label: \"Part des minima sociaux dans le revenu disponible\"},\n];","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":524,"value":"les_poids = [\n {value: \"poids_id\", label:\"Inv. distance\"},\n {value:\"poids_g\", label: \"Inv.distance²\"},\n {value: \"poids_idv\", label:\"Inv. distance des contigus\"},\n {value: \"poids_v\", label:\"Contigus\"},\n {value: \"poids_seuil\", label:\"1 si <= seuil en km, sinon 0\"},\n {value: \"poids_idseuil\", label:\"Inv. distance si <= seuil en km\"},];","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1337,"value":"$39","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1344,"value":"cil = calcul_il();","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":168,"value":"colorQt = {\n var d = cil.domain;\n var g = cil.gradient;\n return d3.scaleQuantile()\n .domain(d)\n .range(d3.quantize(g, nb_classes));\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":16,"value":"pathLeft = d3.geoPath(projectionLeft)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1480,"value":"pathRight = d3.geoPath(projectionRight)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":20,"value":"// Projection Albers sur la France, équivalente, carte de gauche\nprojectionLeft = d3.geoAlbers()\n\t.rotate([-2, 0])\n\t.center([2, 46])\n\t.parallels([29.5, 45.5])\n\t.scale(2800)\n\t.translate([975 / 2 - 180, 610 / 2 - 60])\n\t.precision(.1)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1483,"value":"// Projection Albers sur la France, équivalente, carte de droite\nprojectionRight = d3.geoAlbers()\n\t.rotate([-2, 0])\n\t.center([2, 46])\n\t.parallels([29.5, 45.5])\n\t.scale(2800)\n\t.translate([975 / 2 + 280, 610 / 2 - 60])\n\t.precision(.1)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":31,"value":"echelleLeft = d3.geoScaleBar()\n .projection(projectionLeft)\n .size([140, 460])\n .left(10)\n .top(400)\n .distance(200) // The distance of the scale bar\n .label(\"200km\") // The label on top of the scale bar\n .labelAnchor(\"middle\") // The position of the label (you can also pass \"start\" and \"end\")\n .tickSize(null) // The height of the bar\n .tickValues(null); // The tick values below the bar will be removed","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1486,"value":"echelleRight = d3.geoScaleBar()\n .projection(projectionRight)\n .size([660, 460])\n .left(10)\n .top(20)\n .distance(200) // The distance of the scale bar\n .label(\"200km\") // The label on top of the scale bar\n .labelAnchor(\"middle\") // The position of the label (you can also pass \"start\" and \"end\")\n .tickSize(null) // The height of the bar\n .tickValues(null); // The tick values below the bar will be removed","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":770,"value":"## Imports et mise en page","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":9,"value":"topojson = require(\"topojson-client@3\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":24,"value":"d3 = require(\"d3@5\", \"d3-geo-scale-bar@1.0.2\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":27,"value":"import {legend} from \"@d3/color-legend\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":66,"value":"turf = require(\"@turf/turf\");","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":112,"value":"maths = require(\"https://unpkg.com/mathjs@11.5.1\");","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":738,"value":"styles = html`\n `","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":741,"value":"// ToolTip\ndiv = d3.select(\"body\").append(\"div\")\n\t.attr(\"class\", \"tooltip\")\n .style(\"position\", \"absolute\")\n .style(\"visibility\", \"hidden\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1605,"value":"# Bibliographie\n- Tobler, W. R. (1970). A computer movie simulating urban growth in the Detroit region. Economic geography, 46(sup1), 234-240, en ligne : https://www.jstor.org/stable/pdf/143141.pdf\n- Anselin, L. (1995). Local indicators of spatial association—LISA. Geographical analysis, 27(2), 93-115. en ligne : https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1538-4632.1995.tb00338.x\n- Getis, A., & Ord, J. K. (1992). The analysis of spatial association by use of distance statistics. Geographical analysis, 24(3), 189-206., en ligne : https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1538-4632.1992.tb00261.x","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"}],"files":"$W3a","stdlib":"1","titling":"auto"}} 33:"$32:body"