## LOESS analysis of BBS data

James et al. (1996) estimated trends from BBS data using Nonlinear Nonparametric Route Regression (NNRR) and Nonlinear Semiparametric Route Regression (NSRR) analyses. In LOESS-based analyses, locally weighted least squares (LOESS) is used to fit a smooth curve to the data. LOESS is similar to a moving average, in that a datum for a year is smoothed by incorporating information from data in adjacent years, and the smoothed value is then used in the analysis. The amount of smoothing can be controlled by the investigator, although in our (and in James et al.'s) analyses the amount of smoothing is set at an intermediate value. Trend is estimated for a route by finding the difference in the fitted values from the smooth curve at a point near the beginning of the time series and at a point near the end of the time series. These differences are combined in an area-weighted average to get composite trends for a region. NNRR and NSRR differ in that NSRR incorporates observer data as a covariable, as is traditionally done in route regression analyses.

We use the methods outlined in James et al. (1996), with a few exceptions. First, we use the NSRR procedure, because the NNRR procedure appears to produce trends that are significantly more positive than the NSRR trend estimates (Link and Sauer, In Press), a result consistent with other analyses that document the positive bias associated with omitting observer covariables (Sauer et al. 1994). Second, we did not use the square root transformation used by James et al. (1996), because its use often resulted in negative predicted values that could not be transformed back to the original scale. See Peterjohn et. al. (1997) and Link and Sauer (In Press) for more details regarding this analysis.

James, F.C., C.E. McCulloch, and D.A. Wiedenfeld. 1996. New approaches to the analysis of population trends in land birds. Ecology 77:13-27.

Link, W. A., and J. R. Sauer. "New Approaches to the Analysis of Population Trends in Land Birds": A Comment on Statistical Methods. Ecology (In Press).

Peterjohn, B. G., J. R. Sauer, and W. A. Link. 1997. The 1994 and 1995 summary of the North American Breeding Bird Survey. Bird Populations 3:48-66.

Sauer, J.R., B.G. Peterjohn, and W.A. Link. 1994. Observer differences in the North American Breeding Bird Survey. Auk 111: 50-62.