I want to fit a Poisson point-process model with spatstat::ppm and I'm unsure what is the best way to feed covariate data to the function. I understand that spatstat expects planar coordinates, so I have transformed my point location data to a planar crs before creating a ppp point pattern object. The covariate data are in a raster stack with unprojected geographic coordinates and I understand that projecting rasters is generally ill-advised. I extracted covariate values for the point locations from the raster using the points' original geographic coordinates and raster::extract. So far so good. The issue is ...
it is not sufficient to have observed the covariate only at the points
of the data point pattern; the covariate must also have been observed
at other locations in the window. -ppm helpfile
I appear to have two options for providing the covariate data to the data argument.
A pixel image; seems ill-advised because of raster projection issues.
A list of functions (one per covariate) that can be evaluated at any location (x,y) to obtain corresponding covariate values. This seems like the way to go, but my attempt at writing such a function turns out to be ridiculously slow. It calls raster::extract for each coordinate pair after transforming the coordinates to the raster's crs. While raster::extract is reasonably fast when given a large number of points, there appears to be a substantial overhead for each call. According to microbenchmark, the coordinate transformation takes about 4ms and the extraction takes about 582ms for a single covariate, or about 4 seconds for each point to get all 7 covariates. I don't know how many times ppm will want to call this, but if it's even once per point in the pattern, it'll take too long.
Is there some way I can find out what is the complete set of points that ppm will query for covariate data so that I can extract those beforehand with a single call?
It seems like my use case (covariates in a geographic raster) should be pretty common, so I'm guessing there's an established way to do this right. What is it?
Thanks for a well written question clearly identifying you need. It would have been even better with a simple reproducible example using e.g. built-in data from raster and spatstat or artificially generated data. In lack of the reproducible example my answer will not contain any code but outline what you could do.
First step in ppm is to make a quadrature scheme or class quad or logiquad depending on which maximum likelihood approximation is used in ppm. These can be generated directly by the user via quadscheme or quadscheme.logi. The quadrature scheme contains all the points where ppm will evaluate the covariates. You can extract the coordinates of the quadrature scheme using the function coords. If you construct a data.frame with all covariates evaluated at these points you can supply that as the data argument to ppm while the quadrature scheme is the first argument. To understand things better try to read the Details section of help(ppm.quad).
Another approach which may give you the optimal use of your data is to extract the grid points of you current raster stack together with all the covariate values and project this point data. Then convert it to a simple data.frame with columns x, y, covar1, covar2, etc. Then you can use x and y together with your point observations of interest to create a quadrature scheme manually and the remaining columns can be supplied as data to ppm.
It would be interesting to compare the results from both these approaches as well as the results from just projecting the raster stack and converting it to a list of im objects.
Related
I am looking to develop a point process that ranges from homogeneous, i.e. no correlation between points to a point cluster process that does have correlation between points. From experimentation I can see that using the Matérn cluster process I can generate landscapes that are clustered.
library(spatstat)
plot(rMatClust(kappa=3,r=0.1,mu=50))
I want to use the simplest code that increases the level of homogeneity, i.e. decreasing dependence of points on each other. I do not want to use a binary model where either the pattern is homogeneous or not. i.e. Just a poisson process which can be generated such as:
plot(rpoispp(150))
From experimentation I noticed that if I increase the radius of the clusters using the Matérn cluster process, I do seem to create a pseudo homogeneous pattern.
plot(rMatClust(kappa=3,r=0.3,mu=50))
plot(rMatClust(kappa=3,r=0.7,mu=50))
Is this a good way of generating degrees of homogeneity? I understand that I can use statistical tests to measure the degree of clustering compared to a complete poisson process, such as the Ripley K test. For example, if I assign the Matérn cluster process data to variables, such as:
a<-rMatClust(kappa=3,r=0.1,mu=50)
b<-rMatClust(kappa=3,r=0.3,mu=50)
c<-rMatClust(kappa=3,r=0.7,mu=50)
Then use the Ripley K test and plot the results:
plot(Kest(a))
plot(Kest(b))
plot(Kest(c))
I can see that the difference between a homogeneous poisson process and the clustered point process decreases. I still do not fully understand the significance of the various K values according to edge effects and so forth, and how to interpret the Ripley K function, but I think this is the right direction to be heading in? How do I interpret the Ripley K function? Another problem is the number of points in each plot, I do not have a consistent number of points in each plot, as can be seen by:
summary(a)
summary(b)
summary(c)
Any knowledgeable feedback on this is greatly appreciated.
The standard terminology is that you want to generate a clustered point pattern.
The function rMatClust generates a clustered point pattern at random, in a two-stage process. The first stage is to generate "parent" points completely at random. The second stage is to generate, for each "parent", a random number of "offspring" points, and to place the "offspring" points inside a circle of radius R around their "parent". The final result is the collection of all "offspring" points. From this description (and help(rMatClust)) you can figure out what happens for different parameter values.
The K function (not the "K test") is a summary of the spacing between points in a point pattern. At a distance r, the value of K(r) is the normalised average number of points observed to fall within distance r of a typical point in the pattern. It is normalised so that it does not depend on the number of points, making it possible to compare patterns with different numbers of points.
When you plot the K function, one of the curves is the theoretical curve that would be expected if the points are completely random, and the other curves are computed from the data point pattern. This allows you to assess whether the point pattern appears to be clustered.
I strongly suggest you do some reading in Chapter 7 of the spatstat book. You can download this chapter for free.
I'm not really sure how to represent the 1-D data set properly in R, so that I will be able to plot a dendrogram.
Please help.
##data set {1,23,45}
##this is what I have done so far, but the dendrogram doesn't seem correct.
data <-c(1,23,45)
datas <-data.frame(data)
d<- dist(datas,method="euclidean")
H.fit<- hclust(d,method="single")
plot(H.fit)
The plot is correct: every point in your list is being set in the same cluster.
The reason is that you are using single linkage which is the minimum distance between each cluster. In you data, the minimum distance between any pair and the remaining point is the same so everyone gets the same hierarchy.
Try using complete linkage. Your data dimensionality is well represented.
Is there a function in the R raster package that is analogous to sampleRandom but which extracts n random pixel values from within an irregularly shaped polygon feature rather than a rectangular extent object?
I know there are alternative approaches such as generating random points within a polygon and then use the extract() function to get pixel values, but am wondering if there is a more direct path I have missed.
Thanks
No, there is not a single function for this.
I'm working with two rasters that differ in their origin, extent, and resolution. I have a bathymetry raster, with a higher resolution (x=0.0008333333, y=0.0008333333) and a MUCH great spatial extent. I also have a sea surface temperature raster, which has a much coarser resolution (x=0.04166667, y=0.04166667). Both rasters have the same projection (longlat, datum=WGS84).
I would like to manipulate the bathymetry raster to match the extent, origin, and resolution of the sea surface temperature raster. However, I have very little experience and I am uncertain of the 'best practices.'
I have tried two different methods, and I would like to know which is better, and maybe an explanation of how they differ in terms of the underlying processes. I'm also open to other methods that might be better at preserving the data.
Method 1:
1) first, I aggregated the bathymetry raster to make it as similar to the SST raster as possible
library(raster)
bathycoarse<-aggregate(bathymetry, fact=c(48,50), fun=mean)
2) second, I cropped the bathymetry raster by the SST raster
bathycoarsecrop<-crop(bathycoarse,sst)
3) third, I resampled the bathymetry raster using the SST raster, resulting in the same origin and extent.
bathyresample<-resample(bathycoarsecrop, sst, method="bilinear")
Method 2: I used the function projectRaster()
bathy2<-projectRaster(bathymetry, sst, method="bilinear")
Obviously, method 2 is much simpler. But I don't really understand what the function is doing, so I want to make sure I am accomplishing my goal in the correct method.
The "projectRaster" function uses the same resampling as the "resample" function (the resampling method is defined by the "method" argument you set to "bilinear" - indicating bilinear interpolation, which is probably what you want when your dealing with continuous numeric datasets).
So using the function should just work fine for you.
If you want to speed things up, you can easily use paralell processing with the "projectRaster" function by starting a cluster with the "beginCluster" function, which then allows automatic parallel processing with the "projectRaster" function.
beginCluster(4) # use the number of cores you want to use
bathy2 <- projectRaster(bathymetry, sst, method="bilinear")
endCluster()
I have a dataset with minute by minute GPS coordinates recorded by a persons cellphone. I.e. the dataset has 1440 rows with LON/LAT values. Based on the data I would like a point estimate (lon/lat value) of where the participants home is. Let's assume that home is the single location where they spend most of their time in a given 24h interval. Furthermore, the GPS sensor most of the time has quite high accuracy, however sometimes it is completely off resulting in gigantic outliers.
I think the best way to go about this is to treat it as a point process and use 2D density estimation to find the peak. Is there a native way to do this in R? I looked into kde2d (MASS) but this didn't really seem to do the trick. Kde2d creates a 25x25 grid of the data range with density values. However, in my data, the person can easily travel 100 miles or more per day, so these blocks are generally too large of an estimate. I could narrow them down and use a much larger grid but I am sure there must be a better way to get a point estimate.
There are "time spent" functions in the trip package (I'm the author). You can create objects from the track data that understand the underlying track process over time, and simply process the points assuming straight line segments between fixes. If "home" is where the largest value pixel is, i.e. when you break up all the segments based on the time duration and sum them into cells, then it's easy to find it. A "time spent" grid from the tripGrid function is a SpatialGridDataFrame with the standard sp package classes, and a trip object can be composed of one or many tracks.
Using rgdal you can easily transform coordinates to an appropriate map projection if lon/lat is not appropriate for your extent, but it makes no difference to the grid/time-spent calculation of line segments.
There is a simple speedfilter to remove fixes that imply movement that is too fast, but that is very simplistic and can introduce new problems, in general updating or filtering tracks for unlikely movement can be very complicated. (In my experience a basic time spent gridding gets you as good an estimate as many sophisticated models that just open up new complications). The filter works with Cartesian or long/lat coordinates, using tools in sp to calculate distances (long/lat is reliable, whereas a poor map projection choice can introduce problems - over short distances like humans on land it's probably no big deal).
(The function tripGrid calculates the exact components of the straight line segments using pixellate.psp, but that detail is hidden in the implementation).
In terms of data preparation, trip is strict about a sensible sequence of times and will prevent you from creating an object if the data have duplicates, are out of order, etc. There is an example of reading data from a text file in ?trip, and a very simple example with (really) dummy data is:
library(trip)
d <- data.frame(x = 1:10, y = rnorm(10), tms = Sys.time() + 1:10, id = gl(1, 5))
coordinates(d) <- ~x+y
tr <- trip(d, c("tms", "id"))
g <- tripGrid(tr)
pt <- coordinates(g)[which.max(g$z), ]
image(g, col = c("transparent", heat.colors(16)))
lines(tr, col = "black")
points(pt[1], pt[2], pch = "+", cex = 2)
That dummy track has no overlapping regions, but it shows that finding the max point in "time spent" is simple enough.
How about using the location that minimises the sum squared distance to all the events? This might be close to the supremum of any kernel smoothing if my brain is working right.
If your data comprises two clusters (home and work) then I think the location will be in the biggest cluster rather than between them. Its not the same as the simple mean of the x and y coordinates.
For an uncertainty on that, jitter your data by whatever your positional uncertainty is (would be great if you had that value from the GPS, otherwise guess - 50 metres?) and recompute. Do that 100 times, do a kernel smoothing of those locations and find the 95% contour.
Not rigorous, and I need to experiment with this minimum distance/kernel supremum thing...
In response to spacedman - I am pretty sure least squares won't work. Least squares is best known for bowing to the demands of outliers, without much weighting to things that are "nearby". This is the opposite of what is desired.
The bisquare estimator would probably work better, in my opinion - but I have never used it. I think it also requires some tuning.
It's more or less like a least squares estimator for a certain distance from 0, and then the weighting is constant beyond that. So once a point becomes an outlier, it's penalty is constant. We don't want outliers to weigh more and more and more as we move away from them, we would rather weigh them constant, and let the optimization focus on better fitting the things in the vicinity of the cluster.