library(readxl)
habitat <- read_excel("Biol2022MultivariateSpreadsheet (4).xlsx",
sheet = "Habitat Variables")
PCA
library(REdaS)
## Loading required package: grid
Correlation Matrix
cormat <- cor((habitat[1:36, 4:15]))
bart_spher(cormat)
## Bartlett's Test of Sphericity
##
## Call: bart_spher(x = cormat)
##
## X2 = 325.279
## df = 66
## p-value < 2.22e-16
cormat
## carparks escalators elevators levels toilets
## carparks 1.00000000 0.1104018 -0.03651974 0.27488040 0.36134990
## escalators 0.11040178 1.0000000 0.73954196 0.50882483 0.71726211
## elevators -0.03651974 0.7395420 1.00000000 0.44497674 0.47146012
## levels 0.27488040 0.5088248 0.44497674 1.00000000 0.38411470
## toilets 0.36134990 0.7172621 0.47146012 0.38411470 1.00000000
## hours 0.12710142 0.1515900 0.09310969 0.01157244 0.08566331
## eateries 0.40250032 0.4862020 0.31493815 0.49847231 0.67115063
## trainstations 0.18535517 0.3602172 0.22379553 0.27026228 0.34410700
## busstops 0.12063463 0.1247951 0.15460860 -0.08987194 -0.02223400
## cinema 0.44525146 0.3371226 0.22596641 0.68586483 0.50876630
## greenspace -0.05889480 -0.2018897 -0.07751053 -0.22812489 -0.14558848
## foodcourts 0.42506151 0.4548239 0.07409223 0.31467775 0.37917306
## hours eateries trainstations busstops cinema
## carparks 0.12710142 0.4025003 0.1853552 0.12063463 0.44525146
## escalators 0.15159000 0.4862020 0.3602172 0.12479512 0.33712259
## elevators 0.09310969 0.3149381 0.2237955 0.15460860 0.22596641
## levels 0.01157244 0.4984723 0.2702623 -0.08987194 0.68586483
## toilets 0.08566331 0.6711506 0.3441070 -0.02223400 0.50876630
## hours 1.00000000 0.2923818 0.1756103 0.39344563 0.09786211
## eateries 0.29238185 1.0000000 0.2516909 0.11067248 0.69984069
## trainstations 0.17561033 0.2516909 1.0000000 -0.12707898 0.30303450
## busstops 0.39344563 0.1106725 -0.1270790 1.00000000 -0.14285714
## cinema 0.09786211 0.6998407 0.3030345 -0.14285714 1.00000000
## greenspace -0.28375623 -0.3502501 -0.2115139 -0.17131295 -0.14151940
## foodcourts 0.10887017 0.4216912 0.3893209 0.06992765 0.34963827
## greenspace foodcourts
## carparks -0.05889480 0.42506151
## escalators -0.20188969 0.45482390
## elevators -0.07751053 0.07409223
## levels -0.22812489 0.31467775
## toilets -0.14558848 0.37917306
## hours -0.28375623 0.10887017
## eateries -0.35025006 0.42169121
## trainstations -0.21151389 0.38932091
## busstops -0.17131295 0.06992765
## cinema -0.14151940 0.34963827
## greenspace 1.00000000 0.06131806
## foodcourts 0.06131806 1.00000000
pca <- prcomp(habitat[1:36, 4:15], scale = TRUE)
pca
## Standard deviations (1, .., p=12):
## [1] 2.0860132 1.2580940 1.1925535 1.0425076 0.9789424 0.8061893 0.7861824
## [8] 0.7214278 0.6048389 0.4627482 0.3870815 0.2830795
##
## Rotation (n x k) = (12 x 12):
## PC1 PC2 PC3 PC4 PC5
## carparks 0.23205954 0.08006170 -0.53709414 -0.18349764 0.18745860
## escalators 0.37647041 -0.08212495 0.39538653 -0.20704267 -0.05740025
## elevators 0.27300122 -0.12052440 0.58108673 -0.11150645 0.12595162
## levels 0.34420670 0.18233218 0.08734796 0.26895706 0.19998701
## toilets 0.38337477 0.07109288 0.11611467 -0.12179440 0.05270884
## hours 0.12893475 -0.56496165 -0.21701805 0.01693406 -0.18049314
## eateries 0.39329232 -0.06436029 -0.16694286 0.15073965 0.19820064
## trainstations 0.24797068 0.06370575 -0.02077734 0.01398219 -0.78631070
## busstops 0.04031147 -0.62617034 -0.08270978 -0.31617962 0.27664883
## cinema 0.35801789 0.24023125 -0.20646450 0.25712886 0.21796496
## greenspace -0.15287461 0.37652796 0.05133484 -0.63211290 0.17647249
## foodcourts 0.28012375 0.12273659 -0.26253209 -0.48476825 -0.23999172
## PC6 PC7 PC8 PC9 PC10
## carparks -0.10426932 0.21909361 -0.599400718 0.35133891 -0.14540896
## escalators -0.09615255 0.09817732 0.136911448 0.26102042 0.21045333
## elevators 0.16075680 -0.03674456 -0.314890013 0.05035678 -0.54336864
## levels 0.56201880 0.22364097 0.048312960 0.17511954 0.31615851
## toilets -0.58613158 -0.18425336 -0.093010319 -0.03136450 0.46949455
## hours 0.25076034 -0.61340324 0.014282144 0.36304628 0.09180864
## eateries -0.24329523 -0.21431501 0.274917661 -0.30010969 -0.45743688
## trainstations 0.12951695 0.04295899 -0.344922891 -0.38884532 0.01938062
## busstops 0.14588221 0.32461422 -0.063277324 -0.49386455 0.21949563
## cinema 0.22460458 -0.23124601 0.001154652 -0.33011530 0.09672403
## greenspace 0.26463106 -0.46549395 -0.107494333 -0.17522661 0.08298754
## foodcourts 0.11839804 0.23973069 0.549105972 0.13263157 -0.19094785
## PC11 PC12
## carparks 0.004397920 0.14035244
## escalators 0.251269494 0.66018641
## elevators 0.099505607 -0.33309103
## levels -0.473036881 -0.07558336
## toilets -0.140400716 -0.43543450
## hours -0.014913637 -0.06656343
## eateries -0.426795672 0.29854810
## trainstations -0.130751084 0.09631381
## busstops -0.003726279 -0.01364596
## cinema 0.659058200 -0.03532629
## greenspace -0.194181379 0.16716628
## foodcourts 0.109159839 -0.32553445
summary(pca)
## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7
## Standard deviation 2.0860 1.2581 1.1926 1.04251 0.97894 0.80619 0.78618
## Proportion of Variance 0.3626 0.1319 0.1185 0.09057 0.07986 0.05416 0.05151
## Cumulative Proportion 0.3626 0.4945 0.6130 0.70360 0.78347 0.83763 0.88913
## PC8 PC9 PC10 PC11 PC12
## Standard deviation 0.72143 0.60484 0.46275 0.38708 0.28308
## Proportion of Variance 0.04337 0.03049 0.01784 0.01249 0.00668
## Cumulative Proportion 0.93251 0.96299 0.98084 0.99332 1.00000
Scree Plot
screeplot(pca, type = "lines")
Principle Component Scores
pcscores <- cbind(habitat, pca$x)
Factor Analysis
fa <- factanal(habitat[1:36, 4:15], 3, rotation = "varimax")
fa
##
## Call:
## factanal(x = habitat[1:36, 4:15], factors = 3, rotation = "varimax")
##
## Uniquenesses:
## carparks escalators elevators levels toilets
## 0.706 0.005 0.435 0.390 0.348
## hours eateries trainstations busstops cinema
## 0.772 0.198 0.830 0.782 0.064
## greenspace foodcourts
## 0.852 0.716
##
## Loadings:
## Factor1 Factor2 Factor3
## carparks 0.504 0.200
## escalators 0.971 0.112 0.201
## elevators 0.750
## levels 0.497 0.571 -0.191
## toilets 0.629 0.411 0.296
## hours 0.134 0.456
## eateries 0.331 0.717 0.423
## trainstations 0.332 0.238
## busstops -0.117 0.449
## cinema 0.265 0.923 -0.116
## greenspace -0.121 -0.171 -0.323
## foodcourts 0.388 0.300 0.208
##
## Factor1 Factor2 Factor3
## SS loadings 2.608 2.337 0.959
## Proportion Var 0.217 0.195 0.080
## Cumulative Var 0.217 0.412 0.492
##
## Test of the hypothesis that 3 factors are sufficient.
## The chi square statistic is 39.88 on 33 degrees of freedom.
## The p-value is 0.191
mobility <- pcscores$PC1
facilities <- pcscores$PC2
ANOVA
Check Assumptions
shapiro.test(mobility)
##
## Shapiro-Wilk normality test
##
## data: mobility
## W = 0.95022, p-value = 0.1063
shapiro.test(facilities)
##
## Shapiro-Wilk normality test
##
## data: facilities
## W = 0.75329, p-value = 2.179e-06
PC1 ANOVA - Mobility
aov1 <- aov(mobility ~ Income*Population, data = pcscores)
summary(aov1)
## Df Sum Sq Mean Sq F value Pr(>F)
## Income 1 9.03 9.031 2.033 0.164
## Population 1 0.03 0.026 0.006 0.940
## Income:Population 1 1.12 1.115 0.251 0.620
## Residuals 32 142.13 4.442
Boxplot - Mobility
library(ggplot2)
mob.box <- ggplot(pcscores, aes(y = PC1, x = Income, fill = Population)) +
geom_boxplot(position = position_dodge(.9))
mob.box
PC2 ANOVA - Facilities
aov2 <- aov(facilities ~ Income*Population, data = pcscores)
summary(aov2)
## Df Sum Sq Mean Sq F value Pr(>F)
## Income 1 0.32 0.3235 0.189 0.667
## Population 1 0.02 0.0180 0.011 0.919
## Income:Population 1 0.34 0.3438 0.201 0.657
## Residuals 32 54.71 1.7098
Boxplot - Facilities
fac.box <- ggplot(pcscores, aes(y= PC2, x = Income, fill = Population)) +
geom_boxplot(position = position_dodge(.9))
fac.box
