A first example
Data
siland package requires two data objects:
- data.frame of located observations . Data locations have to be indicated in columns “X” and “Y”. The variable of interest as possible local variables are also included here.
- sf object containing description of landscape variables. It can be created using the
st_readfunction of the packagesf. For instance if your GIS data (in shp format) are in the FILE file, named NAME (i.e.FILE contains NAME.shp, NAME.dbf,…), you can easily import your data in landdata using the command:
landdata=st_read(dsn = "FILE",layer="NAME")Here, we use the objects dataSiland and landSiland, included in siland package. You can load data using the data command.
library(siland)
## Loading required package: sf
## Linking to GEOS 3.8.0, GDAL 3.0.4, PROJ 6.3.1
data(dataSiland)
data(landSiland)Main results for this example have been saved in object VignetteSiland and can be loaded to avoid computing time.
data("likresB1","resB1","resB2","resB3","resF1","resF3","resF4","resF5.1","resF5.2","resY")dataSiland is a data.frame with columns: “obs”, variable of interest and “x1” variable, a continuous local variable. The “Id” column indicates the identification number of the plots where observations were made. landSiland is an object of class sf where landscape is characterised by two features named L1 and L2. Landscape is described by polygons. For each polygon, L1 is equal to 1 if the polygon is of type L1, 0 otherwise (so is it for L2).
str(dataSiland)
## 'data.frame': 100 obs. of 5 variables:
## $ X : num 8508 8508 6578 6578 1904 ...
## $ Y : num 7177 7177 3829 3829 1555 ...
## $ x1 : num 6.23 6.23 -3.91 -3.91 7.55 ...
## $ Id : num 1 1 2 2 3 3 4 4 5 5 ...
## $ obs: num 18.34 18.17 1.95 1.09 6.81 ...
str(landSiland)
## Classes 'sf' and 'data.frame': 4884 obs. of 3 variables:
## $ L1 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ L2 : num 0 1 0 0 0 0 0 0 1 0 ...
## $ geometry:sfc_MULTIPOLYGON of length 4884; first list element: List of 1
## ..$ :List of 1
## .. ..$ : num [1:8, 1:2] 5993 5999 5978 5977 5975 ...
## ..- attr(*, "class")= chr [1:3] "XY" "MULTIPOLYGON" "sfg"
## - attr(*, "sf_column")= chr "geometry"
## - attr(*, "agr")= Factor w/ 3 levels "constant","aggregate",..: NA NA
## ..- attr(*, "names")= chr [1:2] "L1" "L2"You can look at spatial configuration of the loaded data using the following commands :
library(ggplot2)
library(sf)
L1pol=st_geometry(landSiland[landSiland$L1==1,])#extract an sf object with only polygons of type L1
L2pol=st_geometry(landSiland[landSiland$L2==1,])#extract an sf object with only polygons of type L2
ggplot(landSiland)+
geom_sf(colour="grey",fill="white")+
geom_sf(data=L1pol,fill="red")+
geom_sf(data=L2pol,fill="blue")+
geom_point(data=dataSiland, aes(X,Y),col="green")
Buffer approach : Bsiland()
Classical disks buffers (point observations)
Buffer approach modelizes effect of lanscape variable with a constant intensity on a buffer (i.e. an area of constant radius) around the observation location. Estimating effects of the local variable x1 and landscape variables L1 and L2 on the variable of interest obs can be done with the command Bsiland():
resB1=Bsiland(obs~x1+L1+L2,land=landSiland,data=dataSiland)resB1
## Model: obs ~ x1 + L1 + L2
##
## Landscape variables: L1 L2
##
## Coefficients:
## (Intercept) x1 L1 L2 B.L1 B.L2
## 2.040 0.111 -11.068 25.401 121.179 218.946
##
## standard error: 1.437742
## AIC: 366.32 AIC (no landscape): 619.37
## (No landscape effect) p-value: <1e-16Coefficients are the parameter estimates. For a landscape variable, there are two values : for instance for L1, L1 (-11.068) is the intensity of the effect and B.L1 ( 121.179) is the estimated buffer size for L1. AIC is AIC the of the model resB1 (Model: obs ~ x1 + L1 + L2) and AIC(no landscape) is the AIC with only local variable (Model0: obs ~ x1). (No landscape effect) p-value is related to the test of landscape global effect significativity, i.e. H0= ‘Model0: obs ~ x1’ vs H1=‘Model: obs ~ x1 + L1 + L2’ (Likelihood ratio test).
Parameter estimates and tests can be obtained using the command summary:
summary(resB1)
## Buffer sizes:
## B.L1 B.L2
## 121.1786 218.9462
##
## -- Tests are given conditionally to the best estimated buffer sizes --
##
## Call:
## obs ~ x1 + L1 + L2
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.9453 -0.9165 -0.1116 0.9083 4.0983
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.04012 0.20636 9.886 2.61e-16 ***
## x1 0.11068 0.02361 4.688 9.12e-06 ***
## L1 -11.06774 1.09401 -10.117 < 2e-16 ***
## L2 25.40082 0.78080 32.532 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 2.067102)
##
## Null deviance: 2965.92 on 99 degrees of freedom
## Residual deviance: 198.44 on 96 degrees of freedom
## AIC: 362.32
##
## Number of Fisher Scoring iterations: 2Note that p.values are given conditionnaly to estimates of buffer radii.
resB1$parambuffer gives the vector of estimated buffers radii. resB1$buffer gives a data.frame of the percentages of each landscape variable (in columns) in buffers of estimated radii for each observation (in rows).
resB1$parambuffer
## B.L1 B.L2
## 121.1786 218.9462The plotBsiland.land() function gives a graphical representation of the estimation. The color intensity is the effect of the landscape variable i.e. the product of the occupancy percentage of the landscape variable in the buffer by the associated coeffcient.
plotBsiland.land(x=resB1,land=landSiland,data=dataSiland)
## Plot for landscape variable L1
## B.L1
## 121.1786
plotBsiland.land(x=resB1,land=landSiland,data=dataSiland,var=2)
## Plot for landscape variable L2
## B.L2
## 218.9462
“Doughnut” buffers (polygonal observations)
In function Bsiland, the argument border=F (by default) indicates that buffers are computed from the observations locations. Buffers are thus a circle of constant radius centered on observation locations.
The option border=T indicates that buffers are computed from the border of the polygon (observation plot) where observations are made. Then the buffers look much more like “doughnuts”, with an empty area in the center.
resB2=Bsiland(obs~x1+L1+L2,land=landSiland,data=dataSiland,family=gaussian,border=T)resB2$parambuffer
plotBsiland.land(x=resB2,land=landSiland,data=dataSiland)
plotBsiland.land(x=resB2,land=landSiland,data=dataSiland,var=2)Visual check of likelihood maximisation procedure.
As with all numerical maximisation procedures, optimization problems may arise. The function Bsiland.lik() allows to point out possible problems of optimization.
likresB1=Bsiland.lik(resB1,land= landSiland,data=dataSiland,varnames=c("L1","L2"))likresB1
On this graphic, the -Log-likelihood is represented in function of buffer radii. The estimation is made by maximazing the likelihood i.e. by minimizing the -Log-likelihood. The orange line indicates the minimal value obtained during the estimation. The black line represents the -loglikelihood for L1 when the buffer radius for L1 is set to given values in seqd argument (seqd=seq(2,200,length=10)) and the other parameters are fixed to their estimation. The black dotted line indicates the value of L1 buffer size estimated during the global estimation procedure. The red continuous and dotted red lines simirlarly indicates the -loglikelihood and the value of buffer size estimated for L2. When minization correctly occurs, the minimal values of the profiled -loglikelihoods are equal and equal the minimal value of the global -Log-likelihood. This means that the minimums of continuous black and red lines are on the orange line (and that dotted black and red lines intersect the continuous black and red lines at their minimum, respectively). If it is not the case, the minimizing procedure has failed and it is necessary to proceed with a new estimation with different initialisation values. This is possible using the argument init in function Bsiland. For instance, for starting estimation from buffer sizes of 20 and 150 for L1 and L2 landscape variables, respectively, use the command Bsiland(obs~x1+L1+L2,land=landSiland,data=dataSiland,init=c(20,150)).
Spatial Influence Function approach : Fsiland()
In the Spatial Influence Function (SIF) approach, each unit of landscape variable (cell/pixel) has an influence which is maximal at its location and decreases as the distance increases. For modelling a given landscape variable influence, we consider every cell where the landscape variable is distributed, and computed its influence by summing spatial influence of all cells. The spatial influence of a cell is determined by its intensity (negative or positive) and its SIF, which is a density function described by its mean distance (in siland package). As for the buffer approach, the siland package allows to estimate the intensity of effect and the scale of effects i.e. here the mean distance of SIF. Estimating effects of the local variable x1 and landscape variables L1 and L2 on the variable of interest obs can be done with the command Fsiland() in a similar syntax than for Bsiland :
resF1=Fsiland(obs~x1+L1+L2,land=landSiland,data=dataSiland)resF1
## Model: obs ~ x1 + L1 + L2
##
## Landscape variables: L1 L2
##
## Coefficients:
## (Intercept) x1 L1 L2 SIF.L1 SIF.L2
## 1.249 0.085 -11.957 29.458 113.489 190.179
##
## standard error: 1.123119
## AIC: 316.93 AIC (no landscape): 619.37
## (No landscape effect) p-value: <1e-16
summary(resF1)
## SIF parameters:
## SIF.L1 SIF.L2
## 113.4894 190.1787
##
## -- Tests are given conditionally to the best SIF parameters --
##
## Call:
## obs ~ x1 + L1 + L2
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.97160 -0.83136 0.02424 0.66240 2.68791
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.24886 0.17868 6.989 3.65e-10 ***
## x1 0.08501 0.01861 4.568 1.46e-05 ***
## L1 -11.95677 0.97356 -12.281 < 2e-16 ***
## L2 29.45810 0.68872 42.772 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 1.261396)
##
## Null deviance: 2965.92 on 99 degrees of freedom
## Residual deviance: 121.09 on 96 degrees of freedom
## AIC: 312.93
##
## Number of Fisher Scoring iterations: 2Here the parameters related to the landscape variable L1 are intensity L1 (-11.957) and the mean distance of its SIF, SIF.L1 (113.4894). The vector resF1$SIF gives for each landscape variable the mean distance of estimated SIFs. The data.frame resF1$landcontri gives for each landscape variable, the cumulative spatial influence received by each observation (i.e. the sum of spatial influence received by each observation from all cells of the landscape).
The command plotFsiland.sif gives a representation of the estimated SIF for each landscape variable.
plotFsiland.sif(resF1)
The command plotFsiland.land gives map of effects of the landscape. By default, it gives the global contribution of all landscape variables:
plotFsiland.land(x=resF1,land=landSiland,data=dataSiland)One can obtain a map for a specific landscape variable by specifying its number with the argument var:
plotFsiland.land(x=resF1,land=landSiland,data=dataSiland,var=2)Fsiland() arguments
The argument
wdindicates the mesh size used to construct spatial unit (cells/pixels) of landscape variable. In fact, lanscape variable described as polygon are discretized on grid during the procedure estimation (like raster). The choice of wd is a tradeoff between computing precision and computing time (and memory size). The smallestwdis, the better are the precision but the longer the computing time is (and the larger the required memory size is). It is worth to note that estimated parameters can be very sensitive to this mesh size. To obtain a reliable estimation, we recommand to ensure, after the estimation procedure, thatwdsize is at least three times smaller than the smallest estimated SIF. If not, it is recommended to proceed with a new estimation with a smallerwdsize.The argument
borderindicates whether an observation receives the spatial influence of cells belonging to the same plot (i.e. the plot where the observation was made). Ifborder=T, its receives influence only from the border of the plot (so no influence from the cells of the plot). By default,border = F(all cells are considered).The argument
sifdefines the family function of SIF, i.e. the form of decrease for the landscape influence. The family can beexponential,gaussian, oruniform. If influence is uniform, it implies that there is no decrease of inlfuence and influence is uniform around each pixel of the raster. Note that all landscape variables have the same form.
Comparison between Fsiland() and Bsiland()
Buffer approach modelizes landscape effect from the observation location whereas SIF approach modelizes landscape from the lanscape variables locations. These difference of point of view made difficult to compare the estimated results directly. It is possible to compare the landscape effect received by each observation, named hereafter (landscape) contribution, estimated by the both models.
resB1$parambuffer
## B.L1 B.L2
## 121.1786 218.9462
resF1$paramSIF
## SIF.L1 SIF.L2
## 113.4894 190.1787
plot(resB1$buffer[,1],resF1$landcontri[,1],xlab="Buffer contribution",ylab="FIS contribution", main="Variable L1")
abline(0,1)
plot(resB1$buffer[,2],resF1$landcontri[,2],xlab="Buffer contribution",ylab="FIS contribution", main="Variable L2")
abline(0,1)
To compare models adequacy to data, one can compare their AIC (the smaller the better) :
resB1$AIC
## [1] 366.3203
resF1$AIC
## [1] 316.9274