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CADDIS Volume 4: Data Analysis

Predicting Environmental Conditions from Biological Observations (PECBO) Appendix

Survey Weighting

Sample data collected using probabilistic survey designs are particularly useful for estimating taxon-environment relationships because each collected sample represents a known proportion of the total length of stream in a region. Therefore, taxon-environment relationships can be developed that are truly representative of all the streams in the region. To take advantage of survey design information, it is necessary to introduce sample weights to the regressions.

Sample weighting map
Figure 12. Map showing sample locations for EMAP-West. Size of the symbol is roughly proportional to sample weight.

The length of stream each sample represents varies in EMAP-West because the sample design was stratified by state, so certain states with fewer streams were over-represented in the sample.

taxon-env with weights
Figure 13. Taxon-environment relationships estimated using sample weights. Blue line is weighted estimate; black line is the original estimate.  Horizontal axis in units of degrees C.

Taking into account sample weights can have substantial effects for certain taxon-environment relationships. All previous examples shown for Heterlimnius and Malenka have been unweighted. After weighting observations in the regression model, Heterlimnius exhibited a much higher probability of capture at its optimal temperature when the regression was computed with sample weights, compared to the unweighted version. Changes to the taxon-environment relationship for Malenka were small.

comparison with weighted results
Figure 14. Comparison of weighted and unweighted inferences of stream temperature (°C). EMAP-West data used to estimate taxon-environment relationships, and inferences computed for Wyoming. Dashed line shows the 1:1 relationship.

Taxon-environment relationships computed using weighted regressions can change the values of biological inferences. On the whole, inferences of stream temperature in Wyoming based on weighted regressions were very similar to inferences based on unweighted models. However, at certain sites the differences between weighted and unweighted models were quite large.

Incorporating survey weights into regression models provides a strong statistical basis for using data to make inferences about stream characteristics in the region. As such, if survey weights are available, they generally should be used.

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