  Many ecological studies and conservation policies are based on field
observations of species, which can be affected by systematic variability
introduced by the observation process. A recently introduced causal modeling
technique called 'half-sibling regression' can detect and correct for
systematic errors in measurements of multiple independent random variables.
However, it will remove intrinsic variability if the variables are dependent,
and therefore does not apply to many situations, including modeling of species
counts that are controlled by common causes. We present a technique called
'three-quarter sibling regression' to partially overcome this limitation. It
can filter the effect of systematic noise when the latent variables have
observed common causes. We provide theoretical justification of this approach,
demonstrate its effectiveness on synthetic data, and show that it reduces
systematic detection variability due to moon brightness in moth surveys.
