No abstract

No abstract

The multivariate linear model is

Predictor effect displays, introduced in this article, visualize the response surface of complex regression models by averaging and conditioning, producing a sequence of 2D line graphs, one graph or set of graphs for each predictor in the regression problem. Partial residual plots visualize lack of fit, traditionally in relatively simple additive regression models. We combine partial residuals with effect displays to visualize both fit and lack of fit simultaneously in complex regression models, plotting residuals from a model around 2D slices of the fitted response surface. Employing fundamental results on partial residual plots along with examples for both real and contrived data, we discuss and illustrate both the strengths and limitations of the resulting graphs. The methods described in this paper are implemented in the effects package for R.

Seed of 41 economically important weed species of the Great Plains region of the United States were buried 20 cm deep in soil in eastern and western Nebraska in 1976. The 41 species consisted of 11 annual grass, 14 annual broadleaf, 4 biennial broadleaf, and 12 perennial broadleaf species. Weed seeds were exhumed annually for germination tests the first 9 yr, then after 12 and 17 yr. Germination percentages at the two burial locations averaged over 0, 1 to 4, 5 to 8, and 9 to 17 yr of burial were 57, 28, 9, and 4% for annual grass; 47, 26, 16, and 11 % for annual broadleaf; 52, 49, 44, and 30 % for biennial broadleaf; 36, 18, 13, and 8% for perennial broadleaf; and 47, 26, 16, and 10% for all 41 weed species, respectively. Biennial broadleaf weeds showed the greatest seed germination over years. Annual grass weeds showed less seed germinability over 17 yr of burial than annual broadleaf weeds and perennial broadleaf weed species were intermediate. Weed seed germinability in soil was greater in the reduced rainfall and more moderate soil temperatures of western Nebraska than in the greater rainfall and more fluctuating soil temperatures of eastern Nebraska. The greatest seed survival among the 41 weed species was shown by common mullein, which had 95% germination after 17 yr of burial in western Nebraska. Decay rates of individual weed species in soil will be of most value to weed scientists, agriculturalists, and modelers evaluating past or designing future weed management systems.