Northern Prairie Wildlife Research Center
We used a linear model (Appendix B) to estimate nest densities among habitats and study areas; large differences existed in amount of habitat searched and in numbers of nests found in some habitats in some area-years. A key feature of this model, like the model we used to improve our estimates of daily survival rates (DSR's) in the following section, is that habitat effects did not interact with other effects.
We included in the model effects for area-year, half-area-year within area-year, habitat, and number of nest searches. Number of searches was included because not all habitat polygons could be searched 3 times (e.g., stubble fields in Cropland usually could be searched only once before they were tilled). We used a transformed variable, log([N + 0.0001] ÷ A) as the dependent variable, where N is the number of nests found for a species and A is the area searched. The log transformation was invoked because we believed the effects of the explanatory variables were more likely to be proportional than additive. We added 0.0001 to avoid difficulties involved with taking the log of zero. We fitted the linear model by the method of weighted least squares (Snedecor and Cochran 1980) with weights equal to the product of number of breeding pairs and area of each habitat class searched in individual half-area-years. Theoretically, these weights reflected the relative precision of each density estimate. Habitat preference values were calculated by scaling least-squares estimates of habitat effects so that they summed to 1.0.