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.

Non-testability of equal weights spatial dependence

We show that any invariant test for spatial autocorrelation in a spatial error or spatial lag model with equal weights matrix has power equal to size. This result holds under the assumption of an elliptical distribution. Under Gaussianity, we also show that any test whose power is larger than its size for at least one point in the parameter space must be biased.

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.

An exploration of the equivalent weights particle filter

Particle filters are fully non-linear data assimilation techniques that aim to represent the probability distribution of the model state given the observations (the posterior) by a number of particles. In high-dimensional geophysical applications the number of particles required by the sequential importance resampling (SIR) particle filter in order to capture the high probability region of the posterior, is too large to make them usable. However particle filters can be formulated using proposal densities, which gives greater freedom in how particles are sampled and allows for a much smaller number of particles. Here a particle filter is presented which uses the proposal density to ensure that all particles end up in the high probability region of the posterior probability density function. This gives rise to the possibility of non-linear data assimilation in large dimensional systems. The particle filter formulation is compared to the optimal proposal density particle filter and the implicit particle filter, both of which also utilise a proposal density. We show that when observations are available every time step, both schemes will be degenerate when the number of independent observations is large, unlike the new scheme. The sensitivity of the new scheme to its parameter values is explored theoretically and demonstrated using the Lorenz (1963) model.

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.

The equivalent-weights particle filter in a high-dimensional system

In general, particle filters need large numbers of model runs in order to avoid filter degeneracy in high-dimensional systems. The recently proposed, fully nonlinear equivalent-weights particle filter overcomes this requirement by replacing the standard model transition density with two different proposal transition densities. The first proposal density is used to relax all particles towards the high-probability regions of state space as defined by the observations. The crucial second proposal density is then used to ensure that the majority of particles have equivalent weights at observation time. Here, the performance of the scheme in a high, 65 500 dimensional, simplified ocean model is explored. The success of the equivalent-weights particle filter in matching the true model state is shown using the mean of just 32 particles in twin experiments. It is of particular significance that this remains true even as the number and spatial variability of the observations are changed. The results from rank histograms are less easy to interpret and can be influenced considerably by the parameter values used. This article also explores the sensitivity of the performance of the scheme to the chosen parameter values and the effect of using different model error parameters in the truth compared with the ensemble model runs.

The effect of the equivalent-weights particle filter on dynamical balance in a primitive equation model

The disadvantage of the majority of data assimilation schemes is the assumption that the conditional probability density function of the state of the system given the observations [posterior probability density function (PDF)] is distributed either locally or globally as a Gaussian. The advantage, however, is that through various different mechanisms they ensure initial conditions that are predominantly in linear balance and therefore spurious gravity wave generation is suppressed. The equivalent-weights particle filter is a data assimilation scheme that allows for a representation of a potentially multimodal posterior PDF. It does this via proposal densities that lead to extra terms being added to the model equations and means the advantage of the traditional data assimilation schemes, in generating predominantly balanced initial conditions, is no longer guaranteed. This paper looks in detail at the impact the equivalent-weights particle filter has on dynamical balance and gravity wave generation in a primitive equation model. The primary conclusions are that (i) provided the model error covariance matrix imposes geostrophic balance, then each additional term required by the equivalent-weights particle filter is also geostrophically balanced; (ii) the relaxation term required to ensure the particles are in the locality of the observations has little effect on gravity waves and actually induces a reduction in gravity wave energy if sufficiently large; and (iii) the equivalent-weights term, which leads to the particles having equivalent significance in the posterior PDF, produces a change in gravity wave energy comparable to the stochastic model error. Thus, the scheme does not produce significant spurious gravity wave energy and so has potential for application in real high-dimensional geophysical applications.

Twin experiments with the equivalent weights particle filter and HadCM3

This paper investigates the use of a particle filter for data assimilation with a full scale coupled ocean–atmosphere general circulation model. Synthetic twin experiments are performed to assess the performance of the equivalent weights filter in such a high-dimensional system. Artificial 2-dimensional sea surface temperature fields are used as observational data every day. Results are presented for different values of the free parameters in the method. Measures of the performance of the filter are root mean square errors, trajectories of individual variables in the model and rank histograms. Filter degeneracy is not observed and the performance of the filter is shown to depend on the ability to keep maximum spread in the ensemble.

Effects of forage source and extruded linseed supplementation on methane emissions from growing dairy cattle of differing body weights

Changes in diet carbohydrate amount and type (i.e., starch vs. fiber) and dietary oil supplements can affect ruminant methane emissions. Our objectives were to measure methane emissions, whole-tract digestibility, and energy and nitrogen utilization from growing dairy cattle at 2 body weight (BW) ranges, fed diets containing either high maize silage (MS) or high grass silage (GS), without or with supplemental oil from extruded linseed (ELS). Four Holstein-Friesian heifers aged 13 mo (BW range from start to finish of 382 to 526 kg) were used in experiment 1, whereas 4 lighter heifers aged 12 mo (BW range from start to finish of 292 to 419 kg) were used in experiment 2. Diets were fed as total mixed rations with forage dry matter (DM) containing high MS or high GS and concentrates in proportions (forage:concentrate, DM basis) of either 75:25 (experiment 1) or 60:40 (experiment 2), respectively. Diets were supplemented without or with ELS (Lintec[AU1: Add manufacturer name and location.]; 260 g of oil/ kg of DM) at 6% of ration DM. Each experiment was a 4 × 4 Latin square design with 33-d periods, with measurements during d 29 to 33 while animals were housed in respiration chambers. Heifers fed MS at a heavier BW (experiment 1) emitted 20% less methane per unit of DM intake (yield) compared with GS (21.4 vs. 26.6, respectively). However, when repeated with heifers of a lower BW (experiment 2), methane yield did not differ between the 2 diets (26.6 g/kg of DM intake). Differences in heifer BW had no overall effect on methane emissions, except when expressed as grams per kilogram of digestible organic matter (OMD) intake (32.4 vs. 36.6, heavy vs. light heifers). Heavier heifers fed MS in experiment 1 had a greater DM intake (9.4 kg/d) and lower OMD (755 g/kg), but no difference in N utilization (31% of N intake) compared with heifers fed GS (7.9 kg/d and 799 g/kg, respectively). Tissue energy retention was nearly double for heifers fed MS compared with GS in experiment 1 (15 vs. 8% of energy intake, respectively). Heifers fed MS in experiment 2 had similar DM intake (7.2 kg/d) and retention of energy (5% of intake energy) and N (28% of N intake), compared with GS-fed heifers, but OMD was lower (741 vs. 765 g/kg, respectively). No effect of ELS was noted on any of the variables measured, irrespective of animal BW, and this was likely due to the relatively low amount of supplemental oil provided. Differences in heifer BW did not markedly influence dietary effects on methane emissions. Differences in methane yield were attributable to differences in dietary starch and fiber composition associated with forage type and source.