  Fitting regression models for intensity functions of spatial point processes
is of great interest in ecological and epidemiological studies of association
between spatially referenced events and geographical or environmental
covariates. When Cox or cluster process models are used to accommodate
clustering not accounted for by the available covariates, likelihood based
inference becomes computationally cumbersome due to the complicated nature of
the likelihood function and the associated score function. It is therefore of
interest to consider alternative more easily computable estimating functions.
We derive the optimal estimating function in a class of first-order estimating
functions. The optimal estimating function depends on the solution of a certain
Fredholm integral equation which in practice is solved numerically. The
approximate solution is equivalent to a quasi-likelihood for binary spatial
data and we therefore use the term quasi-likelihood for our optimal estimating
function approach. We demonstrate in a simulation study and a data example that
our quasi-likelihood method for spatial point processes is both statistically
and computationally efficient.
