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

Lexical aspect in English

The six verbs BEGIN/START, CONTINUE/KEEP and STOP/FINISH are among J. R. Firth's (1968 : 122) 'verbs of aspect' and can be described in terms of three aspectual features (Lyons (1977: 707): Inception (begin, start), Progressivity (continue, keep ) and Termination (stop, finish). The difference between begin and start is subtle, but a study of a number of features indicates that begin suggests initiation only, while start suggests initiation with progressivity. Both continue and keep indicate progressivity, but continue suggests progressivity with resumption (of a situation already in progress), while keep suggests progressivity with iteration. Similarly, stop and finish both indicate termination , but stop suggests termination at any point in a situation, while finish relates to termination with completion (of the situation). There is a brief consideration of three more marginal verbs: commence, cease and quit

Cost accounting for fruit and vegetable canners

The cost problem of the canner who is handling only one product is comparatively simple and even when two or more products are handled in the same factory at different seasons of the year, it is possible to establish accurate costs without much difficulty if due diligence is maintained in keeping the records of the different commodities distinctly separate. It is when a considerable number of different products are packed simultaneously in a variety of containers involving several grades that the problem of determining the actual costs becomes exceedingly complex. The National Canners\u27 Association has adopted a very workable system of cost accounting suitable for those Canners who handle only one product. They have also adopted a system for Canners handling more than one product which is applicable in many cases

The power group enumeration theorem

AbstractThe number of orbits of a permutation group was determined in a fundamental result of Burnside. This was extended in a classical paper by Pólya to a solution of the problem of enumerating the equivalence classes of functions with a given weight from a set X into a set Y, subject to the action of the permutation group A acting on X. A generalization by de Bruijn solved the counting problem when two permutation groups are involved, A acting on X and B on Y. Thus the Pólya formula is the special case of the de Bruijn result in which B is the identity group. The Power Group Enumeration Theorem achieves the same result using only one permutation group: the power group, BA, acting on the set YX of functions. de Bruijn's method was used to count self-complementary graphs by R. C. Read and finite automata by M. Harrison. These results as well as the number of self-converse directed graphs and others are easily obtained by the proper use of the Power Group Enumeration Theorem

Skimming impact of a thin heavy body on a shallow liquid layer

This study addresses the question of whether a thin, relatively heavy solid body with a smooth under-surface can skim on a shallow layer of liquid (for example water), i.e. impact on the layer and rebound from it. The body impacts obliquely onto the liquid layer with the trailing edge of the underbody making the initial contact. The wetted region then spreads along the underbody and eventually either retracts, generating a rebound, or continues to the leading edge of the body and possibly leads to the body sinking. The present inviscid study involves numerical investigations for increased mass ( M , in scaled terms) and moment of inertia ( I , proportional to the mass) together with an asymptotic analysis of the influential parameters and dynamics at different stages of the skimming motion. Comparisons between the asymptotic analysis and numerical results show close agreement as the body mass becomes large. A major finding is that, for a given impact angle of the underbody relative to the liquid surface, only a narrow band of initial conditions is found to allow the heavy-body skim to take place. This band includes reduced impact velocities of the body vertically and rotationally, both decreasing like M−2/3 , while the associated total time of the skim from entry to exit is found to increase like M1/3 typically. Increased mass thereby enhances the super-elastic behaviour of the skim

Skimming impacts and rebounds of smoothly shaped bodies on shallow liquid layers

Investigated in this paper is the coupled fluid–body motion of a thin solid body undergoing a skimming impact on a shallow-water layer. The underbody shape (the region that makes contact with the liquid layer) is described by a smooth polynomic curve for which the magnitude of underbody thickness is represented by the scale parameter C. The body undergoes an oblique impact (where the horizontal speed of the body is much greater than its vertical speed) onto a liquid layer with the underbody’s trailing edge making the initial contact. This downstream contact point of the wetted region is modelled as fixed (relative to the body) throughout the skimming motion with the liquid layer assumed to detach smoothly from this sharp trailing edge. There are two geometrical scenarios of interest: the concave case (C < 0 producing a hooked underbody) and the convex case (C < 0producing a rounded underbody). As C is varied the rebound dynamics of the motion are predicted. Analyses of small-time water entry and of water exit are presented and are shown to be broadly in agreement with the computational results of the shallow-water model. Reduced analysis and physical insights are also presented in each case alongside numerical investigations and comparisons as C is varied, indicating qualitative analytical/numerical agreement. Increased body thickness substantially changes the interaction structure and accentuates inertial forces in the fluid flow