Mixed Logit Model Performance and Distributional Assumptions: Preferences and GM foods

Using mixed logit models to analyse choice data is common but requires ex ante specification of the functional forms of preference distributions. We make the case for greater use of bounded functional forms and propose the use of the Marginal Likelihood, calculated using Bayesian techniques, as a single measure of model performance across non nested mixed logit specifications. Using this measure leads to very different rankings of model specifications compared to alternative rule of thumb measures. The approach is illustrated using data from a choice experiment regarding GM food types which provides insights regarding the recent WTO dispute between the EU and the US, Canada and Argentina and whether labelling and trade regimes should be based on the production process or product composition.

Equivalence of truncated count mixture distributions and mixtures of truncated count distributions

This article is about modeling count data with zero truncation. A parametric count density family is considered. The truncated mixture of densities from this family is different from the mixture of truncated densities from the same family. Whereas the former model is more natural to formulate and to interpret, the latter model is theoretically easier to treat. It is shown that for any mixing distribution leading to a truncated mixture, a (usually different) mixing distribution can be found so. that the associated mixture of truncated densities equals the truncated mixture, and vice versa. This implies that the likelihood surfaces for both situations agree, and in this sense both models are equivalent. Zero-truncated count data models are used frequently in the capture-recapture setting to estimate population size, and it can be shown that the two Horvitz-Thompson estimators, associated with the two models, agree. In particular, it is possible to achieve strong results for mixtures of truncated Poisson densities, including reliable, global construction of the unique NPMLE (nonparametric maximum likelihood estimator) of the mixing distribution, implying a unique estimator for the population size. The benefit of these results lies in the fact that it is valid to work with the mixture of truncated count densities, which is less appealing for the practitioner but theoretically easier. Mixtures of truncated count densities form a convex linear model, for which a developed theory exists, including global maximum likelihood theory as well as algorithmic approaches. Once the problem has been solved in this class, it might readily be transformed back to the original problem by means of an explicitly given mapping. Applications of these ideas are given, particularly in the case of the truncated Poisson family.

On the equivalence between radiance and retrieval assimilation

The need for consistent assimilation of satellite measurements for numerical weather prediction led operational meteorological centers to assimilate satellite radiances directly using variational data assimilation systems. More recently there has been a renewed interest in assimilating satellite retrievals (e.g., to avoid the use of relatively complicated radiative transfer models as observation operators for data assimilation). The aim of this paper is to provide a rigorous and comprehensive discussion of the conditions for the equivalence between radiance and retrieval assimilation. It is shown that two requirements need to be satisfied for the equivalence: (i) the radiance observation operator needs to be approximately linear in a region of the state space centered at the retrieval and with a radius of the order of the retrieval error; and (ii) any prior information used to constrain the retrieval should not underrepresent the variability of the state, so as to retain the information content of the measurements. Both these requirements can be tested in practice. When these requirements are met, retrievals can be transformed so as to represent only the portion of the state that is well constrained by the original radiance measurements and can be assimilated in a consistent and optimal way, by means of an appropriate observation operator and a unit matrix as error covariance. Finally, specific cases when retrieval assimilation can be more advantageous (e.g., when the estimate sought by the operational assimilation system depends on the first guess) are discussed.

Equivalence of weak formulations of the steady water waves equations

We prove the equivalence of three weak formulations of the steady water waves equations, namely: the velocity formulation, the stream function formulation and the Dubreil-Jacotin formulation, under weak Hölder regularity assumptions on their solutions.

Toeplitz operators with distributional symbols on Bergman spaces

We study the boundedness and compactness of Toeplitz operators Ta on Bergman spaces , 1 < p < ∞. The novelty is that we allow distributional symbols. It turns out that the belonging of the symbol to a weighted Sobolev space of negative order is sufficient for the boundedness of Ta. We show the natural relation of the hyperbolic geometry of the disc and the order of the distribution. A corresponding sufficient condition for the compactness is also derived.

Natural disaster accounting bias and its equivalence across genetic resource stocks

Two sources of bias arise in conventional loss predictions in the wake of natural disasters. One source of bias stems from neglect of accounting for animal genetic resource loss. A second source of bias stems from failure to identify, in addition to the direct effects of such loss, the indirect effects arising from implications impacting animal-human interactions. We argue that, in some contexts, the magnitude of bias imputed by neglecting animal genetic resource stocks is substantial. We show, in addition, and contrary to popular belief, that the biases attributable to losses in distinct genetic resource stocks are very likely to be the same. We derive the formal equivalence across the distinct resource stocks by deriving an envelope result in a model that forms the mainstay of enquiry in subsistence farming and we validate the theory, empirically, in a World-Society-for-the-Protection-of-Animals application

The distributional consequences of a fiscal food policy: evidence from the UK

The literature on fiscal food policies focuses on their effectiveness in altering diets and improving health, while this paper focuses on their welfare costs. A formal welfare economics framework is developed to calculate the combined individualistic and distributional impacts of a tax-subsidy. Distributional characteristics of foods targeted by a tax tend to be concentrated in lower-income households. Further, consumption of fruit and vegetables tends to be concentrated in higher-income households; therefore, a subsidy on such foods increases regressivity. Aggregate welfare changes that result from a fiscal food policy are found to range from an increase of 1.41 per cent to a reduction of 2.06 per cent according to whether a subsidy is included, the degree of inequality aversion, and whether substitution among foods is allowed.

Strangely dual orbifold equivalence I

In this brief note we prove orbifold equivalence between two potentials described by strangely dual exceptional unimodular singularities of type K14 and Q10 in two different ways. The matrix factorizations proving the orbifold equivalence give rise to equations whose solutions are permuted by Galois groups which differ for different expressions of the same singularity.

The distributional and nutritional impacts and mitigation potential of emission-based food taxes in the UK

Agriculture and food production are responsible for a substantial proportion of greenhouse gas emissions. An emission based food tax has been proposed as one option to reduce food related emissions. This study introduces a method to measure the impacts of emission based food taxes at a household level which involves the use of data augmentation to account for the fact that the data record purchases and not consumption. The method is applied to determine the distributional and nutritional impacts of an emission based food tax across socio-economic classes in the UK. We find that a tax of £2.841/tCO2e on all foods would reduce food related emissions by 6.3% and a tax on foods with above average levels of emissions would reduce emissions by 4.3%. The tax burden falls disproportionately on households in the lowest socio-economic class because they tend to spend a larger proportion of their food expenditure on emission intensive foods and because they buy cheaper products and therefore experience relatively larger price increases.