By the end of this practical, you should feel comfortable:
dsm()
dsm()
callformula=
argumentsummary()
when called on a dsm
objectk
parameter of smooth terms to increase their flexibilitygam.check
and rqgam.check
plots and diagnostic outputThe example code below uses the df_hn
detection function in the density surface models. You can substitute this for your own best model as you go, or copy and paste the code at the end and see what results you get using your model for the detection function.
library(Distance)
## Loading required package: mrds
## This is mrds 2.1.14
## Built: R 3.2.0; ; 2015-07-30 10:07:19 UTC; unix
library(dsm)
## Loading required package: mgcv
## Loading required package: nlme
## This is mgcv 1.8-7. For overview type 'help("mgcv-package")'.
## This is dsm 2.2.11
## Built: R 3.2.2; ; 2015-10-23 20:20:41 UTC; unix
library(ggplot2)
library(knitr)
Loading the RData
files where we saved our results:
load("sperm-data.RData")
load("df-models.RData")
Before we fit a model using dsm()
we must first remove the observations from the spatial data that we excluded when we fitted the detection function – those observations at distances greater than the truncation.
obs <- obs[obs$distance <= df_hn$ddf$meta.data$width,]
Here we’ve used the value of the truncation stored in the detection function object, but we could also use the numeric value (which we can also find by checking the model’s summary()
).
Also note that if you want to fit DSMs using detection functions with different truncation distances, then you’ll need to reload the sperm-data.RData
and do the truncation again for that detection function.
Using the data that we’ve saved so far, we can build a call to the dsm()
function and fit out first density surface model. Here we’re only going to look at models that include spatial smooths.
Let’s start with a very simple model – a bivariate smooth of x
and y
:
dsm_nb_xy <- dsm(count~s(x,y),
ddf.obj=df_hn, segment.data = segs, observation.data=obs,
family=nb(), method="REML")
Note again that we try to have informative model object names so that we can work out what the main features of the model were from its name alone.
We can look at a summary()
of this model. Look through the summary output and try to pick out the important information based on what we’ve talked about in the lectures so far.
summary(dsm_nb_xy)
##
## Family: Negative Binomial(0.105)
## Link function: log
##
## Formula:
## count ~ s(x, y) + offset(off.set)
##
## Parametric coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -20.7009 0.2538 -81.56 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df Chi.sq p-value
## s(x,y) 17.95 22.23 75.89 6.27e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.0879 Deviance explained = 40.5%
## -REML = 392.65 Scale est. = 1 n = 949
As discussed in the lectures, the plot
output is not terribly useful for bivariate smooths like these. We’ll use vis.gam()
to visualise the smooth instead:
vis.gam(dsm_nb_xy, view=c("x","y"), plot.type="contour", too.far=0.1, main="s(x,y) (link scale)", asp=1)
Notes:
view=c("x","y")
to display the smooths for x
and y
(we can choose any two variables in our model to display like this)plot.type="contour"
gives this “flat” plot, set plot.type="persp"
for a “perspective” plot, in 3D.too.far=0.1
argument displays the values of the smooth not “too far” from the data (try changing this value to see what happens.asp=1
ensures that the aspect ratio of the plot is 1, making the pixels square.?vis.gam
manual page for more information on the plotting options.We can use the gam.check()
and rqgam.check
functions to check the model.
gam.check(dsm_nb_xy)
##
## Method: REML Optimizer: outer newton
## full convergence after 7 iterations.
## Gradient range [-1.910812e-06,2.784947e-06]
## (score 392.646 & scale 1).
## Hessian positive definite, eigenvalue range [2.157928,29.21001].
## Model rank = 30 / 30
##
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
##
## k' edf k-index p-value
## s(x,y) 29.000 17.953 0.532 0
rqgam.check(dsm_nb_xy)
Remember that the left side of the gam.check()
plot and the right side of the rqgam.check()
plot are most useful.
Looking back through the lecture notes, do you see any problems in these plots or in the text output from gam.check()
.
We can set the basis complexity via the k
argument to the s()
term in the formula. For example the following re-fits the above model with a much smaller basis complexity than before:
dsm_nb_xy_smallk <- dsm(count~s(x, y, k=10),
ddf.obj=df_hn, segment.data = segs, observation.data=obs,
family=nb(), method="REML")
Compare the output of vis.gam()
and gam.check()
for this model to the model with a larger basis complexity.
So far we’ve just used count
as the response. That is, we adjusted the offset of the model to make it take into account the “effective area” of the segments (see lecture notes for a refresher).
Instead of using count
we could use abundance.est
, which will leave the segment areas as they are and calculate the Horvitz-Thompson estimates of the abundance per segment and use that as the response in the model. This is most useful when we have covariates in the detection function (though we can use it any time).
Try copying the code that fits the model dsm_nb_xy
and make a model dsm_nb_xy_ae
that replaces count
for abundance.est
in the model formula and uses the df_hr_ss_size
detection function. Compare the results of summaries, plots and checks between this and the count model.
Instead of fitting a bivariate smooth of x
and y
using s(x, y)
, we could instead use the additive nature and fit the following model:
dsm_nb_x_y <- dsm(count~s(x)+ s(y),
ddf.obj=df_hn, segment.data = segs, observation.data=obs,
family=nb(), method="REML")
Compare this model with dsm_nb_xy
using vis.gam()
(Note you can display two plots side-by-side using par(mfrow=c(1,2))
). Investigate the output from summary()
and the check functions too, comparing with the other models, adjust k
if necessary.
So far, we’ve used nb()
as the response – the negative binomial distribution. We can also try out the Tweedie distribution as a response by replacing nb()
with tw()
.
Try this out and compare the resulting check plots.
It’ll be interesting to see how these models compare to the more complex models we’ll see later on. Let’s save the fitted models at this stage.
# add your models here
save(dsm_nb_x_y, dsm_nb_xy,
file="dsms-xy.RData")
If you have time, try the following:
family=quasipoisson()
? Compare results of gam.check
and rqgam.check
for this and the other models.k
value very big (~100 or so), what do you notice?