For this example we use daily mortality counts in Spain organised by autonomous communities provided by the Spanish government. The dataset records mortality counts from the 18th of April 2018 until the 31th of July 2020. To make the data compositional we divide the autonomous communities counts by the total count for each day.
Compositional data live on a simplex, because the sums add up to a constant. Before analysing such data, it is important to make the data unconstrained. We make the data unconstrained by using a coordinate transformation called the null space coordinate transformation. We use the multivariate outlier detection ensemble discussed above on these unconstrained data. More details are available in our paper.
First let us load this data and plot it.
Next we find the outliers using compositional time series outlier ensemble.
The table above shows the outlying dates and the associated scores. The outlying dates correspond to the COVID-19 outbreak. We can see the decomposed univariate time series in the following plot and the spike around mid March in 2020.
Next we apportion the outlying scores back to the autonomous communities. This is another coordinate transformation from the outlier score space to the original coordinate space.
Next we plot this using the map of Spain.
shapefile_ccaa <- readOGR(dsn="ComunidadesAutonomas_ETRS89_30N/Comunidades_Autonomas_ETRS89_30N.shp")
#> Warning in OGRSpatialRef(dsn, layer, morphFromESRI = morphFromESRI, dumpSRS
#> = dumpSRS, : Discarded datum European_Terrestrial_Reference_System_1989
#> in CRS definition: +proj=utm +zone=30 +ellps=GRS80 +towgs84=0,0,0,0,0,0,0
#> +units=m +no_defs
#> OGR data source with driver: ESRI Shapefile
#> Source: "C:\Users\Sevvandi\AppData\Local\Temp\RtmpaUX1gO\Rbuild2fe0726b4717\composits\vignettes\ComunidadesAutonomas_ETRS89_30N\Comunidades_Autonomas_ETRS89_30N.shp", layer: "Comunidades_Autonomas_ETRS89_30N"
#> with 19 features
#> It has 3 fields
data_ccaa <- tidy(shapefile_ccaa)
#> Warning in bind_rows_(x, .id): Unequal factor levels: coercing to character
#> Warning in bind_rows_(x, .id): binding character and factor vector,
#> coercing into character vector
#> Warning in bind_rows_(x, .id): binding character and factor vector,
#> coercing into character vector
#> Warning in bind_rows_(x, .id): Unequal factor levels: coercing to character
#> Warning in bind_rows_(x, .id): binding character and factor vector,
#> coercing into character vector
#> Warning in bind_rows_(x, .id): binding character and factor vector,
#> coercing into character vector
#> Warning in bind_rows_(x, .id): binding character and factor vector,
#> coercing into character vector
#> Warning in bind_rows_(x, .id): binding character and factor vector,
#> coercing into character vector
#> Warning in bind_rows_(x, .id): binding character and factor vector,
#> coercing into character vector
#> Warning in bind_rows_(x, .id): binding character and factor vector,
#> coercing into character vector
#> Warning in bind_rows_(x, .id): binding character and factor vector,
#> coercing into character vector
#> Warning in bind_rows_(x, .id): binding character and factor vector,
#> coercing into character vector
#> Warning in bind_rows_(x, .id): binding character and factor vector,
#> coercing into character vector
#> Warning in bind_rows_(x, .id): binding character and factor vector,
#> coercing into character vector
#> Warning in bind_rows_(x, .id): binding character and factor vector,
#> coercing into character vector
#> Warning in bind_rows_(x, .id): binding character and factor vector,
#> coercing into character vector
#> Warning in bind_rows_(x, .id): binding character and factor vector,
#> coercing into character vector
#> Warning in bind_rows_(x, .id): binding character and factor vector,
#> coercing into character vector
#> Warning in bind_rows_(x, .id): binding character and factor vector,
#> coercing into character vector
#> Warning in bind_rows_(x, .id): binding character and factor vector,
#> coercing into character vector
#> Warning in bind_rows_(x, .id): binding character and factor vector,
#> coercing into character vector
#> Warning in bind_rows_(x, .id): binding character and factor vector,
#> coercing into character vector
#> Warning in bind_rows_(x, .id): binding character and factor vector,
#> coercing into character vector
#> Warning in bind_rows_(x, .id): binding character and factor vector,
#> coercing into character vector
#> Warning in bind_rows_(x, .id): binding character and factor vector,
#> coercing into character vector
#> Warning in bind_rows_(x, .id): binding character and factor vector,
#> coercing into character vector
#> Warning in bind_rows_(x, .id): binding character and factor vector,
#> coercing into character vector
#> Warning in bind_rows_(x, .id): binding character and factor vector,
#> coercing into character vector
#> Warning in bind_rows_(x, .id): binding character and factor vector,
#> coercing into character vector
#> Warning in bind_rows_(x, .id): binding character and factor vector,
#> coercing into character vector
#> Warning in bind_rows_(x, .id): binding character and factor vector,
#> coercing into character vector
#> Warning in bind_rows_(x, .id): binding character and factor vector,
#> coercing into character vector
#> Warning in bind_rows_(x, .id): binding character and factor vector,
#> coercing into character vector
#> Warning in bind_rows_(x, .id): binding character and factor vector,
#> coercing into character vector
#> Warning in bind_rows_(x, .id): binding character and factor vector,
#> coercing into character vector
#> Warning in bind_rows_(x, .id): binding character and factor vector,
#> coercing into character vector
#> Warning in bind_rows_(x, .id): binding character and factor vector,
#> coercing into character vector
#> Warning in bind_rows_(x, .id): binding character and factor vector,
#> coercing into character vector
#> Warning in bind_rows_(x, .id): binding character and factor vector,
#> coercing into character vector
#> Warning in bind_rows_(x, .id): binding character and factor vector,
#> coercing into character vector
#> Regions defined for each Polygons
nombres_ccaa <- tibble(shapefile_ccaa$Texto) %>%
mutate(id = as.character(seq(0, nrow(.)-1)))
reg <- c("AN", "AR", "AS", "PM", "CN", "CB", "CL", "CM",
"CT", "VC", "EX", "GA", "MD", "MU", "NA", "PV",
"LO", "CE", "CE")
nombres_ccaa <- tibble(reg) %>%
mutate(id = as.character(seq(0, nrow(.)-1)))
data_ccaa_mapa <- data_ccaa %>%
left_join(nombres_ccaa, by = "id")
df3 <- apportioned1 %>%
mutate(reg = str_replace(reg, "RI", "LO")) %>%
mutate(reg = str_replace(reg, "NC", "NA")) %>%
mutate(reg = str_replace(reg, "MC", "MU")) %>%
pivot_longer(-reg, names_to = "date", values_to = "score")
sp_data <- inner_join(data_ccaa_mapa, df3, by="reg") %>%
filter(reg != "CN")
sp_data %>%
ggplot() +
geom_polygon(aes(x= long, y = lat, group=group, fill=score),
color="black", size=0.2) +
theme_bw() +
scale_fill_distiller(palette = "YlOrBr", direction = 1) +
xlab("") +
ylab("") +
coord_fixed() +
facet_wrap(~date, ncol=5) +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
axis.text.x = element_blank(),
axis.text.y = element_blank(),
axis.ticks = element_blank())
