1. The mackerel data
A multi-country survey of mackerel eggs was carried out in the Eastern Atlantic in
1992. The aim was to estimate the total biomass of spawning mackerel. However,
a first step is to construct a model which describes the pattern of egg counts in the
water samples collected. A map of the sampling region can be produced by
sm.script(mackmap)
Data from the survey are available through
provide.data(mackerel)
Produce some initial plots to explore the relationship between the egg density (Density)
and latitude, longitude, depth, temperature and salinity (mack.lat, mack.long,
mack.depth, Temperature, Salinity). Consider whether any of these variables
need to be transformed in order to put them on more suitable scales. (For example,
try Density on a log scale.)
You may also find it helpful to use sm.regression(x, y) to highlight the underlying
pattern in these scatterplots.
Consider also the spatial effect by
position <- cbind(mack.lat , mack.long)
sm.regression(position , log(Density ))
Now fit a gam model and use it to identify what the effects of the different explanatory
variables are. Instead of the s notation used earlier, use lo instead, as this will allow
terms such as position to be entered. For example, you might like to try
model <- gam(log(Density) ~ lo(Temperature) +
lo(log(mack.depth )) +
lo(Salinity) + lo(position ))
par(mfrow = c(2, 2))
plot(model)
par(mfrow = c(1, 1))
Use
anova(model)
to identify whether some of the explanatory variables can be dropped from the model.
What is the preferred depth at which mackerel lay their eggs?
2. The Spanish mackerel data
The data collected by Spanish vessels differs from that of most other countries, in
that it is largely in the form of presence or absence of eggs in each water sample.
These data are available through
provide.data(smacker)
Use names(smacker) to see the variables which are available. Create an indicator of
presence or absence by
Presence <- as.numeric(Density > 0)
Use the family = binomial argument to construct a gam for these data, using
temperature, depth and spatial position as explanatory variables. What do you
conclude about the effects of these covariates?
Is there any difference in the indication of preferred depth at which mackerel lay
their eggs?