Aims

By the end of this practical, you should feel comfortable:

The 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.

Load the packages and data

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")

Pre-model fitting

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.

Fitting DSMs

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

Visualising output

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:

  1. The plot is on the scale of the link function, the offset is not taken into account – the contour values do not represent abundance, just the “influence” of the smooth.
  2. We set 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)
  3. plot.type="contour" gives this “flat” plot, set plot.type="persp" for a “perspective” plot, in 3D.
  4. The 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.
  5. asp=1 ensures that the aspect ratio of the plot is 1, making the pixels square.
  6. Read the ?vis.gam manual page for more information on the plotting options.

Checking the model

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)