Peak performance and cardiometabolic responses of modern US army soldiers during heavy, fatiguing vest-borne load carriage

The coefficient of determination R 2 quantifies the proportion of variance explained by a statistical model and is an important summary statistic of biological interest. However, estimating R 2 for generalized linear mixed models (GLMMs) remains challenging. We have previously introduced a version of R 2 that we called for Poisson and binomial GLMMs, but not for other distributional families. Similarly, we earlier discussed how to estimate intra-class correlation coefficients (ICCs) using Poisson and binomial GLMMs. In this paper, we generalize our methods to all other non-Gaussian distributions, in particular to negative binomial and gamma distributions that are commonly used for modelling biological data. While expanding our approach, we highlight two useful concepts for biologists, Jensen's inequality and the delta method, both of which help us in understanding the properties of GLMMs. Jensen's inequality has important implications for biologically meaningful interpretation of GLMMs, whereas the delta method allows a general derivation of variance associated with non-Gaussian distributions. We also discuss some special considerations for binomial GLMMs with binary or proportion data. We illustrate the implementation of our extension by worked examples from the field of ecology and evolution in the R environment. However, our method can be used across disciplines and regardless of statistical environments.

To facilitate the Food and Agriculture Organization/World Health Organization/United Nations University Joint (FAO/WHO/UNU) Expert Consultation on Energy and Protein Requirements which met in Rome in 1981, Schofield et al. reviewed the literature and produced predictive equations for both sexes for the following ages: 0-3, 3-10, 10-18, 18-30, 30-60 and >60 years. These formed the basis for the equations used in 1985 FAO/WHO/UNU document, Energy and Protein Requirements. While Schofield's analysis has served a significant role in re-establishing the importance of using basal metabolic rate (BMR) to predict human energy requirements, recent workers have subsequently queried the universal validity and application of these equations. A survey of the most recent studies (1980-2000) in BMR suggests that in most cases the current FAO/WHO/UNU predictive equations overestimate BMR in many communities. The FAO/WHO/UNU equations to predict BMR were developed using a database that contained a disproportionate number--3388 out of 7173 (47%)--of Italian subjects. The Schofield database contained relatively few subjects from the tropical region. The objective here is to review the historical development in the measurement and application of BMR and to critically review the Schofield et al. BMR database presenting a series of new equations to predict BMR. This division, while arbitrary, will enable readers who wish to omit the historical review of BMR to concentrate on the evolution of the new BMR equations. BMR data collected from published and measured values. A series of new equations (Oxford equations) have been developed using a data set of 10,552 BMR values that (1) excluded all the Italian subjects and (2) included a much larger number (4018) of people from the tropics. In general, the Oxford equations tend to produce lower BMR values than the current FAO/WHO/UNU equations in 18-30 and 30-60 year old males and in all females over 18 years of age. This is an opportune moment to re-examine the role and place of BMR measurements in estimating total energy requirements today. The Oxford equations' future use and application will surely depend on their ability to predict more accurately the BMR in contemporary populations.