In recent decades, political science literature has experienced significant growth in the popularity of nonlinear models with multiplicative interaction terms. When one or more constitutive variables are not binary, most studies report the marginal effect of the variable of interest at its sample mean while allowing the other constitutive variable/s to vary along its range and holding all other covariates constant at their means, modes, or medians. In this article, we argue that this conventional approach is not always the most suitable since the marginal effect of a variable at its sample mean might not be sufficiently representative of its prevalent effect at a specific value of the conditioning variable and might produce excessively model-dependent predictions. We propose two procedures to help researchers gain a better understanding of how the typical effect of the variable of interest varies as a function of the conditioning variable: (1) computing and plotting the marginal effects at all in-sample combinations of the values of the constitutive variables and (2) computing and plotting what we call the “Distribution-Weighted Average Marginal Effect” over the values of the conditioning variable.

We develop an N-regime Markov-switching model in which the latent state variable driving the regime switching is endogenously determined with the model disturbance term. The models structure captures a wide variety of patterns of endogeneity and yields a simple test of the null hypothesis of exogenous switching. We derive an iterative filter that generates objects of interest, including the model likelihood function and estimated regime probabilities. Using simulation experiments, we demonstrate that the maximum likelihood estimator performs well in finite samples and that a likelihood ratio test of exogenous switching has good size and power properties. We provide results from two applications of the endogenous switching model: a three-state model of US business cycle dynamics and a three-state volatility model of US equity returns. In both cases, we find statistically significant evidence in favor of endogenous switching.

Cover crops are being increasingly recommended as an integrated approach to controlling glyphosate-resistant Palmer amaranth and other troublesome weeds. Thus, a field experiment was conducted in 2010 through 2012 to evaluate the critical period for weed control (CPWC) in cotton as affected by a cereal rye cover crop and tillage. The management systems evaluated included conventional tillage following winter fallow, conservation tillage (CT) following winter fallow, and CT following a cereal rye cover crop managed for maximum biomass. Throughout most of the growing season, weed biomass in cereal rye cover crop plots was less than the CT winter-fallow system in both years and less than both CT winter fallow and conventional tillage in 2012. The CPWC was shortest in 2010 following conventional tillage; however, in 2012, production system influences on CPWC were less. The presence of the rye cover crop delayed the critical timing for weed removal (CTWR) approximately 8 d compared with fallow treatment both years, while conventional tillage delayed CTWR about 2 wk compared with winter fallow. Relative yield losses in both years did not reach the 5% threshold limit until about 2 wk after planting (WAP) for CT following winter fallow, 3 WAP for CT following a cover crop, and 3.5 WAP following conventional tillage. Thus, CT following winter fallow should be avoided to minimize cotton yield loss.

Waterhemp [Amaranthus tuberculatus (Moq.) J. D. Sauer] is a troublesome weed occurring in cropping systems throughout the U.S. Midwest with an ability to rapidly evolve herbicide resistance that could be associated with competitive disadvantages. Little research has investigated the competitiveness of different A. tuberculatus populations under similar environmental conditions. The objectives of this study were to evaluate: (1) the interspecific competitiveness of three herbicide-resistant A. tuberculatus populations (2,4-D and atrazine resistant [2A-R], glyphosate and protoporphyrinogen oxidase [PPO]-inhibitor resistant [GP-R], and 2,4-D, atrazine, glyphosate, and PPO-inhibitor susceptible [2AGP-S]) with soybean [Glycine max (L.) Merr.]; and (2) the density-dependent response of each A. tuberculatus population within a constant soybean population in a greenhouse environment. Amaranthus tuberculatus competitiveness with soybean was evaluated across five target weed densities of 0, 2, 4, 8, and 16 plants pot−1 (equivalent to 0, 20, 40, 80, and 160 plants m−2) with 3 soybean plants pot−1 (equivalent to 300,000 plants ha−1). At the R1 soybean harvest time, no difference in soybean biomass was observed across A. tuberculatus populations. At A. tuberculatus densities <8 plants pot−1, the 2AGP-S population had the greatest biomass and stem diameter per plant. At the R7 harvest time, the 2AGP-S population caused the greatest loss in soybean biomass and number of pods compared with the other populations at densities of <16 plants pot−1. The 2AGP-S population had greater early-season biomass accumulation and stem diameter compared with the other A. tuberculatus populations, which resulted in greater late-season reduction in soybean biomass and number of pods. This research indicates there may be evidence of interspecific competitive fitness cost associated with the evolution of 2,4-D, atrazine, glyphosate, and PPO-inhibitor resistance in A. tuberculatus. Focus should be placed on effectively using cultural weed management practices to enhance crop competitiveness, especially early in the season, to increase suppression of herbicide-resistant A. tuberculatus.

Alfalfa seed yield and Canada thistle densities were measured in 10 fields in southern Alberta to assess the effect of thistles on seed yield. Thistle density and seed yield from each field were fitted to the Weibull, hyperbolic, and linear equations and a random coefficient and linear equation were used to obtain an “average yield loss curve”. Estimated average losses in alfalfa seed yield were >34% and >48% at thistle densities of 10 and 20 shoots m–2, respectively.

Johnsongrass [Sorghum halepense (L.) Pers., ♯3 SORHA] dry weight and johnsongrass culms/ha at harvest were more negatively correlated with soybean yield reductions than the number of johnsongrass plants/ha present at 4 to 6 weeks after planting. However, plant numbers can be determined in sufficient time to implement control measures to prevent yield reduction. Prediction equations for estimating soybean yield at various johnsongrass populations are Ŷ = 1776 + 424e-.023x2 for 0.25-m row spacing and Ŷ = 1668 + 643e-.004x2 for the 1-m row spacing, where Ŷ = estimated yield and x = the number of johnsongrass plants/10 m2. Full-season heavy johnsongrass competition reduced soybean yields from 59 to 88%. Soybeans in the 1-m row spacing were more competitive with low johnsongrass densities than in the 0.25-m row spacing. The johnsongrass-free requirement for soybeans was 4 weeks after planting and soybeans could not tolerate heavy infestations of johnsongrass for more than 5 weeks without loss in yield potential. Application of sethoxydim {2-[1-(ethoxyimino)-butyl]-5-[2-ethylthio)propyl]-3-hydroxy-2-cyclohexen-1-one} at 3 or 4 weeks after planting was effective in controlling heavy infestations of johnsongrass and preventing yield reductions due to competition.

A model, based on a rectangular hyperbola, has been developed to describe the relationship between population density and relative time of seedling emergence of wild oat (Avena fatua L. # AVEFA) and yield of barley (Hordeum vulgare L.) and wheat (Triticum aestivum L.). The equation is where yL is percent yield loss, D is weed density, T is relative time of emergence of weed and crop, and a, b, and c are nonlinear regression coefficients. Significant differences in fitted equations were found between years. From the values of regression coefficients it was concluded that barley is a better competitor than wheat and is less affected by late-emerging wild oat. The model was tested on previously published data. It provided only a slightly better description of the data than a multiple-regression model, but avoided a number of undesirable, implausible properties inherent in the more frequently used approach. In particular, the model does not predict a loss in yield when no weeds are present or a yield increase from late-emerging weeds.

Dose–response analysis is widely used in biological sciences and has application to a variety of risk assessment, bioassay, and calibration problems. In weed science, dose–response methodologies have typically relied on least squares estimation under the assumptions of normal, homoscedastic, and independent errors. Advances in computational abilities and available software, however, have given researchers more flexibility and choices for data analysis when these assumptions are not appropriate. This article will explore these techniques and demonstrate their use to provide researchers with an up-to-date set of tools necessary for analysis of dose–response problems. Demonstrations of the techniques are provided using a variety of data examples from weed science.

We estimate a number of macroeconomic variables as logistic smooth transition autoregressive (LSTAR) processes with uncertainty as the transition variable. The notion is that the effects of increases in uncertainty should not be symmetrical with the effects of decreases in uncertainty. Nonlinear estimation allows us to answer several interesting questions left unanswered by a linear model. For a number of important macroeconomic variables, we show that (i) a positive shock to uncertainty has a greater effect than a negative shock and (ii) the effect of the uncertainty shock is highly dependent on the state of the economy. Hence, the usual linear estimates for the consequences of uncertainty are underestimated in circumstances such as the recent financial crisis.

We develop nonlinear leading-indicator models for GDP growth, with the interest-rate spread and growth in M2 as leading indicators. Since policy makers typically are interested in whether a recession is imminent, we evaluate these models according to their ability to predict the probability of a recession. Using data for the United States, we find that conditional on the spread, the marginal contribution of M2 growth in predicting recessions is negligible.

A survey of nonlinear multivariate macro empirical models is attempted. Although theory may suggest that nonlinearity is to be expected, empirical studies have difficulty in discovering strong consistent effects. Regime switching techniques appear to be the most successful and evidence of nonlinearity is most found for interest rates. Most of the studies emphasize model fitting rather than model evaluation, which limits their usefulness.