EVALUATION OF THE POWER-LAW AND PATCHINESS REGRESSIONS WITH REGRESSION DIAGNOSTICS

We used regression diagnostics to evaluate the robustness of the least -squares regression method for estimating the power law and patchiness regression parameters for 3 data sets of insect counts, specifically for the Bemisia argentifolii Bellows & Perring, and the squash bug, An asa tristis (De Geer). Extreme values in the independent variable, x, and dependent variable, y were detected with the leverage term, h(i), and standardized residuals, e(s), respectively. The assumption of homo geneity of variances was evaluated with plots of e(s) against s for al l regressions, and significant autocorrelations were tested with the D urbin-Watson statistic. For both techniques, we compared least-squares regression results for all data with regressions obtained after outli er data points were removed. We also calculated power law regressions excluding means (m) <2 and variances (s(2)) <4 to reduce possible bias resulting from small mean densities. Outlier data points did not have a significant effect on the power law regressions, but they had a str ong influence on some patchiness regressions. The distribution of stan dardized residuals of some power law regressions were biased toward po sitive values for low mean densities, indicating underestimation of va riances. Additionally, least-squares regression estimates for m greate r than or equal to 2, s(2) greater than or equal to 4 indicated a gene ral increase in slopes for the power law. The distribution of standard ized residuals for patchiness regressions indicated strong heterosceda sticity; therefore, the assumption of constant variance for y was not fulfilled. Our results show that suitability of least-squares regressi on assumptions should be considered whenever pest management decisions are based on the power law or patchiness regressions.