Post-Stratification as a Bias Reduction Technique

Abstract

Opportunistic, non-random surveys often provide information for management of wildlife re- sources, yet managers may be seriously misled due to biases in the data. We show how post-stratification may be used to reduce bias. For a given factor of interest, a variable is identified that correlates well with it. Observations on the variable are ordered, and strata are defined by determining appropriate cutpoints. The variable might be an estimator of the factor itself, or estimated from the same data as are used to estimate the factor, and evaluated for each of a number of small geographic units, (e.g., grid squares). In this circumstance, post-stratification is itself biased, especially with respect to variances, which are under- estimated. We avoid this by smoothing the individual unit estimates so that the strata tend to comprise blocks of adjacent units rather than many disconnected units. Where several possible variables for defining strata are available, principal components analysis and projection pursuit may be used to combine information from the variables. Often, the estimator of a factor of interest can be separated into components, for which different stratifications may be appropriate. Post-stratification can be applied to obtain an estimate of each component for a random point in the area occupied by the resource, and bootstrapping may be used to yield a robust variance of the composite estimate that does not require the assumption that the component estimates are uncorrelated. Our techniques can be applied to reduce bias in estimates of abundance (or any other factor of interest) in a wide range of situations where available resources or field conditions preclude a random sampling design.