Additive Response Models Research Articles

Semiparametric additive indices for binary response and generalized additive models

Models are studied where the response Y andcovariates X,T are assumed to fulfill E(Y | X;T) =G{XTbeta + alpha + m1(T1 ) + ...+ md(Td) }. Here G is a known (link) function,beta is an unknown parameter, and m1, ..., md areunknown functions. In particular, we consider additive binary response models where the response Y is binary. In these models, given X and T, the response Y has a Bernoulli distribution with parameter G{ XTbeta + alpha + m1(T1 ) + ... + md(Td) }. The paper discusses estimation of beta and m1, ... , md. Procedures are proposed for testing linearity of the additive components m1, ... , md. Furthermore, bootstrap uniform confidence intervals for the additive components are introduced. The practical performance of the proposed methods is discussed in simulations and in two economic applications.

Interference Between Johnsongrass (Sorghum halepense), Smooth Pigweed (Amaranthus hybridus), and Soybean (Glycine max)

Competitive relationships between johnsongrass, smooth pigweed, and soybean were examined in 1986 and 1987, and the adequacy of an additive response model (ARM) and product response model (PRM) in predicting yield reductions due to multispecies weed populations was assessed. A severe drought reduced soybean yields statewide in 1986, whereas ideal conditions for soybean production were experienced in 1987. Averaged over monospecific weed densities of 1, 2, 4, and 8 plants 4.6 m−1of row, smooth pigweed intercepted 2.5 and 1.8 times more light than johnsongrass in 1986 and 1987, respectively. In multispecies populations having either 4 or 8 smooth pigweed plants 4.6 m−1of row, light interception by johnsongrass was negligible. Averaged over monospecific weed densities, smooth pigweed produced 5160 and 1760 kg ha−1, while johnsongrass produced 1530 and 450 kg ha−1dry weight in 1986 and 1987, respectively. In multispecies populations, smooth pigweed contributed more than 80% of the total weed biomass. As monospecific johnsongrass density increased, reductions in soybean seed yield were linear, whereas exponential response patterns adequately characterized reductions in soybean seed yield due to smooth pigweed interference. Based on calibrated monospecific responses, the ARM and PRM generally projected higher soybean seed yield reductions for multispecies weed populations than were observed. When crop production conditions were favorable and competitive effects of weeds were low, both models adequately predicted soybean seed yield reductions. When dry conditions unfavorable for crop production existed, the PRM best accommodated the interactive effects between johnsongrass, smooth pigweed, and soybean.

Genetics of histocompatibility in mice. II. Survey for interactions between minor (non-H-2) antigens by skin grafting.

Twenty-five congenic mouse strains differing at distinguishable minor (non-H-2) histocompatibility loci were paired in 71 different combinations. F1 offspring were used as skin-graft donors for more than 4000 recipients to test whether immune responses to parental strain antigens were statistically independent. Thirty-four (48 percent) of the 71 combinations were predicted adequately by an independent response hypothesis. A simple additive model was consistent with 39 (55 percent) of the observed responses, although 18 of these were among those in agreement with the independent hypothesis. A synergistic response faster than that predicted by either the independent or additive response model was seen in 12 (17 percent) of the combinations. The remaining 5 percent were not well described by any of these models. No strain was represented with unusual frequency among those involved in synergistic interactions.