Estimating structural mean models with multiple instrumental variables using the generalised method of moments

Instrumental variables analysis using genetic markers as instruments is now a widely used technique in epidemiology and biostatistics. As single markers tend to explain only a small proportion of phenotypical variation, there is increasing interest in using multiple genetic markers to obtain more precise estimates of causal parameters. Structural mean models (SMMs) are semi-parametric models that use instrumental variables to identify causal parameters, but there has been little work on using these models with multiple instruments, particularly for multiplicative and logistic SMMs. In this paper, we show how additive, multiplicative and logistic SMMs with multiple discrete instrumental variables can be estimated efficiently using the generalised method of moments (GMM) estimator, how the Hansen J-test can be used to test for model mis-specification, and how standard GMM software routines can be used to fit SMMs. We further show that multiplicative SMMs, like the additive SMM, identify a weighted average of local causal effects if selection is monotonic. We use these methods to reanalyse a study of the relationship between adiposity and hypertension using SMMs with two genetic markers as instruments for adiposity. We find strong effects of adiposity on hypertension, but no evidence of unobserved confounding.

Estimating Structural Mean Models with Multiple Instrumental Variables using the Generalised Method of Moments

Instrumental variables analysis using genetic markers as instruments is now a widely used technique in epidemiology and biostatistics. As single markers tend to explain only a small proportion of phenotypical variation, there is increasing interest in using multiple genetic markers to obtain more precise estimates of causal parameters. Structural mean models (SMMs) are semi-parametric models that use instrumental variables to identify causal parameters, but there has been little work on using these models with multiple instruments, particularly for multiplicative and logistic SMMs. In this paper, we show how additive, multiplicative and logistic SMMs with multiple discrete instrumental variables can be estimated efficiently using the generalised method of moments (GMM) estimator, how the Hansen J-test can be used to test for model mis-specification, and how standard GMM software routines can be used to fit SMMs. We further show that multiplicative SMMs, like the additive SMM, identify a weighted average of local causal effects if selection is monotonic. We use these methods to reanalyse a study of the relationship between adiposity and hypertension using SMMs with two genetic markers as instruments for adiposity. We find strong effects of adiposity on hypertension, but no evidence of unobserved confounding.Structural Mean Models, Multiple Instrumental Variables, Generalised Method of Moments, Mendelian Randomisation, Local Average Treatment Effects

Characteristics of magnetoacoustic sausage modes

Aims: We perform an advanced study of the fast magnetoacoustic sausage oscillations of coronal loops in the context of MHD coronal seismology to establish the dependence of the sausage mode period and cut-off wavenumber on the plasma-$\beta$ of the loop-filling plasma. A parametric study of the ratios for different harmonics of the mode is also carried out. Methods: Full magnetohydrodynamic numerical simulations were performed using Lare2d, simulating hot, dense loops in a magnetic slab environment. The symmetric Epstein profile and a simple step-function profile were both used to model the density structure of the simulated loops. Analytical expressions for the cut-off wavenumber and the harmonic ratio between the second longitudinal harmonic and the fundamental were also examined. Results: It was established that the period of the global sausage mode is only very weakly dependent on the value of the plasma-$\beta$ inside a coronal loop, which justifies the application of this model to hot flaring loops. The cut-off wavenumber kc for the global mode was found to be dependent on both internal and external values of the plasma-$\beta$, again only weakly. By far the most important factor in this case was the value of the density contrast ratio between the loop and the surroundings. Finally, the deviation of the harmonic ratio P1/2P2 from the ideal non-dispersive case was shown to be considerable at low k, again strongly dependent on plasma density. Quantifying the behaviour of the cut-off wavenumber and the harmonic ratio has significant applications to the field of coronal seismology

Physical lumping methods for developing linear reduced models for high speed propulsion systems

In gasdynamic systems, information travels in one direction for supersonic flow and in both directions for subsonic flow. A shock occurs at the transition from supersonic to subsonic flow. Thus, to simulate these systems, any simulation method implemented for the quasi-one-dimensional Euler equations must have the ability to capture the shock. In this paper, a technique combining both backward and central differencing is presented. The equations are subsequently linearized about an operating point and formulated into a linear state space model. After proper implementation of the boundary conditions, the model order is reduced from 123 to less than 10 using the Schur method of balancing. Simulations comparing frequency and step response of the reduced order model and the original system models are presented

Moving Beyond Concentrations: The Challenge of Limiting Temperature Change

The UN Framework Convention on Climate Change shifted the attention of the policy community from stabilizing greenhouse gas emissions to stabilizing atmospheric greenhouse gas concentrations. While this represents a step forward, it does not go far enough. We find that, given the uncertainty in the climate system, focusing on atmospheric concentrations is likely to convey a false sense of precision. The causal chain between human activity and impacts is laden with uncertainty. From a benefit-cost perspective, it would be desirable to minimize the sum of mitigation costs and damages. Unfortunately, our ability to quantify and value impacts is limited. For the time being, we must rely on a surrogate. Focusing on temperature rather than on concentrations provides much more information on what constitutes an ample margin of safety. Concentrations mask too many uncertainties that are crucial for policy making.

Sub-arcsecond high sensitivity measurements of the DG~Tau jet with e-MERLIN

We present very high spatial resolution deep radio continuum observations at 5 GHz (6 cm) made with e-MERLIN of the young stars DG Tau A and B. Assuming it is launched very close (~=1 au) from the star, our results suggest that the DG Tau A outflow initially starts as a poorly focused wind and undergoes significant collimation further along the jet (~=50 au). We derive jet parameters for DG Tau A and find an initial jet opening angle of 86 degrees within 2 au of the source, a mass-loss rate of 1.5x10^-8 solar masses/yr for the ionised component of the jet, and the total ejection/accretion ratio to range from 0.06-0.3. These results are in line with predictions from MHD jet-launching theories.Comment: Accepted MNRAS Letter

Hadronic interactions, precocious unification, and cosmic ray showers at Auger energies

At Auger energies only model predictions enable us to extract primary cosmic ray features. The simulation of the shower evolution depends sensitively on the first few interactions, necessarily related to the quality of our understanding of high energy hadronic collisions. Distortions of the standard ``soft semi-hard'' scenario include novel large compact dimensions and a string or quantum gravity scale not far above the electroweak scale. Na\"{\i}vely, the additional degrees of freedom yield unification of all forces in the TeV range. In this article we study the influence of such precocious unification during atmospheric cascade developments by analyzing the most relevant observables in proton induced showers.Comment: 16 pages latex. 4 eps figure

Are neonicotinoid insecticides driving declines of widespread butterflies?

There has been widespread concern that neonicotinoid pesticides may be adversely impacting wild and managed bees for some years, but recently attention has shifted to examining broader effects they may be having on biodiversity. For example in the Netherlands, declines in insectivorous birds are positively associated with levels of neonicotinoid pollution in surface water. In England, the total abundance of widespread butterfly species declined by 58% on farmed land between 2000 and 2009 despite both a doubling in conservation spending in the UK, and predictions that climate change should benefit most species. Here we build models of the UK population indices from 1985 to 2012 for 17 widespread butterfly species that commonly occur at farmland sites. Of the factors we tested, three correlated significantly with butterfly populations. Summer temperature and the index for a species the previous year are both positively associated with butterfly indices. By contrast, the number of hectares of farmland where neonicotinoid pesticides are used is negatively associated with butterfly indices. Indices for 15 of the 17 species show negative associations with neonicotinoid usage. The declines in butterflies have largely occurred in England, where neonicotinoid usage is at its highest. In Scotland, where neonicotinoid usage is comparatively low, butterfly numbers are stable. Further research is needed urgently to show whether there is a causal link between neonicotinoid usage and the decline of widespread butterflies or whether it simply represents a proxy for other environmental factors associated with intensive agriculture

Estimating Linkages between Redfish and Cold Water Coral on the Norwegian Coast

The importance of essential fish habitat in supporting commercial fisheries has received increasing attention in recent years. Bottom trawling is known to cause particularly destructive damage to habitat that is effectively non-renewable, such as cold water corals. This paper applies the production function approach to estimate the link between cold water corals and redfish in Norway. Both the carrying capacity and growth rate of redfish are found to be functions of cold water coral habitat and thus cold water corals can be considered an essential fish habitat. The paper also estimates a facultative relationship between cold water coral and redfish stocks. The essential habitat model shows the best fit to the data. Comparative statics of an essential habitat indicate an approximate annual loss in harvest of between 11 and 29% within the bounds of coral decline estimated by scientists. In terms of policy, our results indicate that essential fish habitat protection should be considered when managing commercially important species.Cold water coral, redfish, production function, habitat-fishery linkages, essential fish habitat, International Development, Research Methods/ Statistical Methods, Q22,