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appariciop committed Aug 13, 2024
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20 changes: 10 additions & 10 deletions 03-MethodesRepartitionPonctuelle.qmd
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Expand Up @@ -956,10 +956,10 @@ library(spatstat)
library(ggplot2)
## Indice du plus proche voisin : R observé (équation 3.20)
# le paramètre k indique le nombre de plus proches voisins
Robs2019 <- mean(nndist(st_coordinates(M2019),k=1))
Robs2020 <- mean(nndist(st_coordinates(M2020),k=1))
Robs2021 <- mean(nndist(st_coordinates(M2021),k=1))
Robs2022 <- mean(nndist(st_coordinates(M2022),k=1))
Robs2019 <- mean(nndist(st_coordinates(M2019), k=1))
Robs2020 <- mean(nndist(st_coordinates(M2020), k=1))
Robs2021 <- mean(nndist(st_coordinates(M2021), k=1))
Robs2022 <- mean(nndist(st_coordinates(M2022), k=1))
## Indice du plus proche voisin : R attendu (distribution aléatoire) (équation 3.21)
# Attention, il faut spéficier S, la superficie de l'espace d'étude
Arrondissements <- st_read(dsn = "data/chap03/Arrondissements.shp", quiet=TRUE)
Expand Down Expand Up @@ -1227,7 +1227,7 @@ S <- as.numeric(st_area(st_union(Arrondissements)))
Sq <- (2*S) / npoints
# Longueur du carré et du côté de l'hexagone régulier (équation 3.25)
lq <- sqrt(Sq)
la <- sqrt( (2*Sq) / (3*sqrt(3)))
la <- sqrt((2*Sq) / (3*sqrt(3)))
# Trouver la longueur du côté du carré dans lequel est compris l'hexagone
cellsizeHex <- 2 * sqrt(Sq/((3*sqrt(3)/2))) * sqrt(3)/2
cat("Nombre de points =", npoints,
Expand Down Expand Up @@ -1284,12 +1284,12 @@ La figure ci-dessus permet de constater que certains carrés et hexagones n'inte
RequeteSpatiale <- st_intersects(Carres.sf,
st_union(Arrondissements), sparse = FALSE)
Carres.sf$Intersect <- RequeteSpatiale[, 1]
Carres.sf <- Carres.sf[Carres.sf$Intersect== TRUE, ]
Carres.sf <- Carres.sf[Carres.sf$Intersect == TRUE, ]
## Suppression des hexagones qui n'intersectent pas les quatre arrondissements
RequeteSpatiale <- st_intersects(Hexagones.sf,
st_union(Arrondissements), sparse = FALSE)
Hexagones.sf$Intersect <- RequeteSpatiale[, 1]
Hexagones.sf <- Hexagones.sf[Hexagones.sf$Intersect== TRUE, ]
Hexagones.sf <- Hexagones.sf[Hexagones.sf$Intersect == TRUE, ]
## Jointure spatiale : compter le nombre de méfaits de 2020 dans les carrés et les hexagones
Carres.sf$Mefaits2020 = lengths(st_intersects(Carres.sf, M2020))
Hexagones.sf$Mefaits2020 = lengths(st_intersects(Hexagones.sf, M2020))
Expand Down Expand Up @@ -1338,7 +1338,7 @@ Nous pouvons maintenant construire le tableau de fréquences et mettre en œuvre
#| warning: false
## Construction du tableau de fréquences
TabFreq <- as.data.frame(table(Carres.sf$Mefaits2020))
names(TabFreq) <- c("Npoints","Fo")
names(TabFreq) <- c("Npoints", "Fo")
TabFreq$Npoints <- as.numeric(as.character(TabFreq$Npoints))
# Calcul pour les fréquences observées (fo)
TabFreq$Fo.pro <- TabFreq$Fo / sum(TabFreq$Fo)
Expand All @@ -1347,8 +1347,8 @@ TabFreq$Fo.proCum <- cumsum(TabFreq$Fo.pro)
npoints <- sum(TabFreq$Npoints*TabFreq$Fo)
nquadrats <- sum(TabFreq$Fo)
Lambda <- npoints / nquadrats
TabFreq$Ft.pro <- dpois(TabFreq$Npoints, lambda= Lambda)
TabFreq$Ft.proCum <- ppois(TabFreq$Npoints, lambda= Lambda, lower.tail = TRUE)
TabFreq$Ft.pro <- dpois(TabFreq$Npoints, lambda = Lambda)
TabFreq$Ft.proCum <- ppois(TabFreq$Npoints, lambda = Lambda, lower.tail = TRUE)
TabFreq$Ft <- TabFreq$Ft.pro * TabFreq$Npoints
# Différences absolues entre les fréquences observées et théoriques cumulées
TabFreq$Difffoft <- abs(TabFreq$Fo.proCum - TabFreq$Ft.proCum)
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1 change: 1 addition & 0 deletions 07-RegressionSpatiales.qmd
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Expand Up @@ -132,6 +132,7 @@ Avec la fonction `lm()`, il est facile de construire un modèle de régression l
#| echo: true
#| message: false
#| eval: true
#| warning: false
# Appel des différents packages utilisés dans le chapitre
library(spdep)
## Construction du modèle
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6 changes: 3 additions & 3 deletions data/chap01/export/Carte1.html
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89 changes: 89 additions & 0 deletions data/chap01/export/PointsGPS.geojson
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34 changes: 17 additions & 17 deletions docs/01-ManipulationDonneesSpatiales.html
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144 changes: 72 additions & 72 deletions docs/02-Autocorrelation.html
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Expand Up @@ -2242,7 +2242,7 @@ <h1 class="title"><span id="sec-chap02" class="quarto-section-identifier"><span
<div class="sourceCode" id="cb56"><pre class="downlit sourceCode r code-with-copy"><code class="sourceCode R"><span><span class="co">## Valeurs permutées</span></span>
<span><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/sample.html">sample</a></span><span class="op">(</span><span class="va">Carres</span><span class="op">$</span><span class="va">CasA</span><span class="op">)</span><span class="op">)</span></span></code><button title="Copier vers le presse-papier" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-stdout">
<pre><code> [1] 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 0</code></pre>
<pre><code> [1] 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0</code></pre>
</div>
</div>
</div>
Expand Down Expand Up @@ -2363,7 +2363,7 @@ <h1 class="title"><span id="sec-chap02" class="quarto-section-identifier"><span
alternative hypothesis: greater
sample estimates:
mean of simulation variance of simulation
162.2823 110.6858
162.5606 103.3648


Monte-Carlo simulation of join-count statistic
Expand All @@ -2377,7 +2377,7 @@ <h1 class="title"><span id="sec-chap02" class="quarto-section-identifier"><span
alternative hypothesis: greater
sample estimates:
mean of simulation variance of simulation
214.4114 132.9979 </code></pre>
214.4314 134.7405 </code></pre>
</div>
</div>
<p>L’approche d’inférence basée sur les permutations signale aussi que les deux distributions sont significativement autocorrélées spatialement (<em>p</em>&nbsp;=&nbsp;0,001).</p>
Expand Down Expand Up @@ -2409,104 +2409,104 @@ <h1 class="title"><span id="sec-chap02" class="quarto-section-identifier"><span
</tr></thead>
<tbody>
<tr class="odd">
<td style="text-align: center;">0,79</td>
<td style="text-align: center;">-0,56</td>
<td style="text-align: center;">0,69</td>
<td style="text-align: center;">3,83</td>
</tr>
<tr class="even">
<td style="text-align: center;">1,48</td>
<td style="text-align: center;">4,90</td>
<td style="text-align: center;">0,30</td>
<td style="text-align: center;">3,25</td>
</tr>
<tr class="odd">
<td style="text-align: center;">-4,16</td>
<td style="text-align: center;">-18,25</td>
<td style="text-align: center;">-0,75</td>
<td style="text-align: center;">-1,85</td>
</tr>
<tr class="even">
<td style="text-align: center;">1,58</td>
<td style="text-align: center;">9,92</td>
<td style="text-align: center;">0,72</td>
<td style="text-align: center;">4,07</td>
</tr>
<tr class="odd">
<td style="text-align: center;">0,03</td>
<td style="text-align: center;">-2,25</td>
<td style="text-align: center;">1,23</td>
<td style="text-align: center;">6,90</td>
</tr>
<tr class="even">
<td style="text-align: center;">2,77</td>
<td style="text-align: center;">2,31</td>
<td style="text-align: center;">-1,36</td>
<td style="text-align: center;">1,00</td>
</tr>
<tr class="odd">
<td style="text-align: center;">2,42</td>
<td style="text-align: center;">6,16</td>
<td style="text-align: center;">0,86</td>
<td style="text-align: center;">3,83</td>
</tr>
<tr class="even">
<td style="text-align: center;">-0,08</td>
<td style="text-align: center;">-5,05</td>
<td style="text-align: center;">0,63</td>
<td style="text-align: center;">3,32</td>
</tr>
<tr class="odd">
<td style="text-align: center;">-2,31</td>
<td style="text-align: center;">-6,05</td>
<td style="text-align: center;">-1,02</td>
<td style="text-align: center;">0,95</td>
</tr>
<tr class="even">
<td style="text-align: center;">0,02</td>
<td style="text-align: center;">2,32</td>
<td style="text-align: center;">1,17</td>
<td style="text-align: center;">3,80</td>
</tr>
<tr class="odd">
<td style="text-align: center;">-1,76</td>
<td style="text-align: center;">-7,36</td>
<td style="text-align: center;">1,39</td>
<td style="text-align: center;">8,01</td>
</tr>
<tr class="even">
<td style="text-align: center;">-0,82</td>
<td style="text-align: center;">-3,04</td>
<td style="text-align: center;">2,04</td>
<td style="text-align: center;">8,17</td>
</tr>
<tr class="odd">
<td style="text-align: center;">0,28</td>
<td style="text-align: center;">3,40</td>
<td style="text-align: center;">0,25</td>
<td style="text-align: center;">2,35</td>
</tr>
<tr class="even">
<td style="text-align: center;">-0,23</td>
<td style="text-align: center;">3,94</td>
<td style="text-align: center;">-0,92</td>
<td style="text-align: center;">-3,82</td>
</tr>
<tr class="odd">
<td style="text-align: center;">1,03</td>
<td style="text-align: center;">4,55</td>
<td style="text-align: center;">1,89</td>
<td style="text-align: center;">8,82</td>
</tr>
<tr class="even">
<td style="text-align: center;">-3,66</td>
<td style="text-align: center;">-12,05</td>
<td style="text-align: center;">-1,78</td>
<td style="text-align: center;">-5,34</td>
</tr>
<tr class="odd">
<td style="text-align: center;">2,14</td>
<td style="text-align: center;">5,28</td>
<td style="text-align: center;">-1,54</td>
<td style="text-align: center;">-5,72</td>
</tr>
<tr class="even">
<td style="text-align: center;">0,25</td>
<td style="text-align: center;">0,48</td>
<td style="text-align: center;">-1,97</td>
<td style="text-align: center;">-11,30</td>
</tr>
<tr class="odd">
<td style="text-align: center;">2,76</td>
<td style="text-align: center;">9,60</td>
<td style="text-align: center;">3,47</td>
<td style="text-align: center;">14,86</td>
</tr>
<tr class="even">
<td style="text-align: center;">-0,08</td>
<td style="text-align: center;">-1,61</td>
<td style="text-align: center;">1,56</td>
<td style="text-align: center;">10,70</td>
</tr>
<tr class="odd">
<td style="text-align: center;">-1,29</td>
<td style="text-align: center;">-7,83</td>
<td style="text-align: center;">2,03</td>
<td style="text-align: center;">6,37</td>
</tr>
<tr class="even">
<td style="text-align: center;">0,30</td>
<td style="text-align: center;">-0,40</td>
<td style="text-align: center;">2,37</td>
<td style="text-align: center;">5,46</td>
</tr>
<tr class="odd">
<td style="text-align: center;">-0,87</td>
<td style="text-align: center;">-3,53</td>
<td style="text-align: center;">1,55</td>
<td style="text-align: center;">10,17</td>
</tr>
<tr class="even">
<td style="text-align: center;">-1,47</td>
<td style="text-align: center;">-1,26</td>
<td style="text-align: center;">5,32</td>
<td style="text-align: center;">22,36</td>
</tr>
<tr class="odd">
<td style="text-align: center;">3,18</td>
<td style="text-align: center;">16,63</td>
<td style="text-align: center;">1,41</td>
<td style="text-align: center;">4,75</td>
</tr>
</tbody>
</table>
Expand Down Expand Up @@ -2974,26 +2974,26 @@ <h1 class="title"><span id="sec-chap02" class="quarto-section-identifier"><span
<div class="sourceCode" id="cb80"><pre class="downlit sourceCode r code-with-copy"><code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span><span class="op">(</span><span class="va">localMoranI.mc</span><span class="op">)</span></span></code><button title="Copier vers le presse-papier" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-stdout">
<pre><code> Ii E.Ii Var.Ii Z.Ii
Min. :-0.90053 Min. :-0.060602 Min. :0.0000002 Min. :-2.0071
1st Qu.: 0.08313 1st Qu.:-0.009582 1st Qu.:0.0384774 1st Qu.: 0.4595
Median : 0.49029 Median :-0.001492 Median :0.1338059 Median : 1.4115
Mean : 0.61678 Mean :-0.003182 Mean :0.2176718 Mean : 1.2387
3rd Qu.: 0.97602 3rd Qu.: 0.003631 3rd Qu.:0.2659243 3rd Qu.: 2.1448
Max. : 3.37625 Max. : 0.076793 Max. :1.8333592 Max. : 3.8502
Pr(z != E(Ii)) Pr(z != E(Ii)) Sim Pr(folded) Sim Skewness
Min. :0.000118 Min. :0.0020 Min. :0.0010 Min. :-0.41115
1st Qu.:0.031970 1st Qu.:0.0240 1st Qu.:0.0120 1st Qu.:-0.23013
Median :0.126484 Median :0.1340 Median :0.0670 Median :-0.09598
Mean :0.249030 Mean :0.2549 Mean :0.1275 Mean :-0.01717
3rd Qu.:0.389883 3rd Qu.:0.4020 3rd Qu.:0.2010 3rd Qu.: 0.21404
Max. :0.991627 Max. :0.9980 Max. :0.4990 Max. : 0.43140
Min. :-0.90053 Min. :-0.066253 Min. :0.0000003 Min. :-1.9937
1st Qu.: 0.08313 1st Qu.:-0.010162 1st Qu.:0.0376542 1st Qu.: 0.4443
Median : 0.49029 Median :-0.001633 Median :0.1326308 Median : 1.4322
Mean : 0.61678 Mean :-0.004317 Mean :0.2163282 Mean : 1.2424
3rd Qu.: 0.97602 3rd Qu.: 0.003903 3rd Qu.:0.2600487 3rd Qu.: 2.1688
Max. : 3.37625 Max. : 0.037456 Max. :1.8514704 Max. : 3.8646
Pr(z != E(Ii)) Pr(z != E(Ii)) Sim Pr(folded) Sim Skewness
Min. :0.0001113 Min. :0.0020 Min. :0.0010 Min. :-0.392043
1st Qu.:0.0300950 1st Qu.:0.0220 1st Qu.:0.0110 1st Qu.:-0.216534
Median :0.1324638 Median :0.1340 Median :0.0670 Median :-0.094277
Mean :0.2491768 Mean :0.2538 Mean :0.1269 Mean :-0.006866
3rd Qu.:0.4064456 3rd Qu.:0.4120 3rd Qu.:0.2060 3rd Qu.: 0.222448
Max. :0.9896398 Max. :0.9720 Max. :0.4860 Max. : 0.427961
Kurtosis
Min. :-0.49934
1st Qu.:-0.27116
Median :-0.17963
Mean :-0.16986
3rd Qu.:-0.08581
Max. : 0.43309 </code></pre>
Min. :-0.60083
1st Qu.:-0.28631
Median :-0.18068
Mean :-0.17267
3rd Qu.:-0.07309
Max. : 0.31386 </code></pre>
</div>
</div>
<p>Avec la cartographie du <em>I</em> de Moran local, nous repérons localement l’autocorrélation spatiale positive (valeurs similaires, fortes ou faibles localement) et l’autocorrélation spatiale négative (valeurs dissemblables localement) (<a href="#fig-Chap02CartoIMoranLocal">figure&nbsp;<span>2.28</span></a>).</p>
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