Optimal linearization trajectories for tangent linear models

We examine differential equations where nonlinearity is a result of the advection part of the total derivative or the use of quadratic algebraic constraints between state variables (such as the ideal gas law). We show that these types of nonlinearity can be accounted for in the tangent linear model by a suitable choice of the linearization trajectory. Using this optimal linearization trajectory, we show that the tangent linear model can be used to reproduce the exact nonlinear error growth of perturbations for more than 200 days in a quasi-geostrophic model and more than (the equivalent of) 150 days in the Lorenz 96 model. We introduce an iterative method, purely based on tangent linear integrations, that converges to this optimal linearization trajectory. The main conclusion from this article is that this iterative method can be used to account for nonlinearity in estimation problems without using the nonlinear model. We demonstrate this by performing forecast sensitivity experiments in the Lorenz 96 model and show that we are able to estimate analysis increments that improve the two-day forecast using only four backward integrations with the tangent linear model. Copyright © 2011 Royal Meteorological Society

The socioeconomics of food crop production and climate change vulnerability: a global scale quantitative analysis of how grain crops are sensitive to drought

Many studies warn that climate change may undermine global food security. Much work on this topic focuses on modelling crop-weather interactions but these models do not generally account for the ways in which socio-economic factors influence how harvests are affected by weather. To address this gap, this paper uses a quantitative harvest vulnerability index based on annual soil moisture and grain production data as the dependent variables in a Linear Mixed Effects model with national scale socio-economic data as independent variables for the period 1990-2005. Results show that rice, wheat and maize production in middle income countries were especially vulnerable to droughts. By contrast, harvests in countries with higher investments in agriculture (e.g higher amounts of fertilizer use) were less vulnerable to drought. In terms of differences between the world's major grain crops, factors that made rice and wheat crops vulnerable to drought were quite consistent, whilst those of maize crops varied considerably depending on the type of region. This is likely due to the fact that maize is produced under very different conditions worldwide. One recommendation for reducing drought vulnerability risks is coordinated development and adaptation policies, including institutional support that enables farmers to take proactive action.

On the approximation of local and linear radiative damping in the middle atmosphere

The validity of approximating radiative heating rates in the middle atmosphere by a local linear relaxation to a reference temperature state (i.e., ‘‘Newtonian cooling’’) is investigated. Using radiative heating rate and temperature output from a chemistry–climate model with realistic spatiotemporal variability and realistic chemical and radiative parameterizations, it is found that a linear regressionmodel can capture more than 80% of the variance in longwave heating rates throughout most of the stratosphere and mesosphere, provided that the damping rate is allowed to vary with height, latitude, and season. The linear model describes departures from the climatological mean, not from radiative equilibrium. Photochemical damping rates in the upper stratosphere are similarly diagnosed. Threeimportant exceptions, however, are found.The approximation of linearity breaks down near the edges of the polar vortices in both hemispheres. This nonlinearity can be well captured by including a quadratic term. The use of a scale-independentdamping rate is not well justified in the lower tropical stratosphere because of the presence of a broad spectrum of vertical scales. The local assumption fails entirely during the breakup of the Antarctic vortex, where large fluctuations in temperature near the top of the vortex influence longwave heating rates within the quiescent region below. These results are relevant for mechanistic modeling studies of the middle atmosphere, particularly those investigating the final Antarctic warming.

Forecasting US output growth with non-linear models in the presence of data uncertainty

We consider the impact of data revisions on the forecast performance of a SETAR regime-switching model of U.S. output growth. The impact of data uncertainty in real-time forecasting will affect a model's forecast performance via the effect on the model parameter estimates as well as via the forecast being conditioned on data measured with error. We find that benchmark revisions do affect the performance of the non-linear model of the growth rate, and that the performance relative to a linear comparator deteriorates in real-time compared to a pseudo out-of-sample forecasting exercise.

Nonlinearity of ocean heat uptake during warming and cooling in the FAMOUS climate model

Atmospheric CO2 concentration is expected to continue rising in the coming decades, but natural or artificial processes may eventually reduce it. We show that, in the FAMOUS atmosphere-ocean general circulation model, the reduction of ocean heat content as radiative forcing decreases is greater than would be expected from a linear model simulation of the response to the applied forcings. We relate this effect to the behavior of the Atlantic meridional overturning circulation (AMOC): the ocean cools more efficiently with a strong AMOC. The AMOC weakens as CO2 rises, then strengthens as CO2 declines, but temporarily overshoots its original strength. This nonlinearity comes mainly from the accumulated advection of salt into the North Atlantic, which gives the system a longer memory. This implies that changes observed in response to different CO2 scenarios or from different initial states, such as from past changes, may not be a reliable basis for making projections.

COMPARISON BETWEEN LINEAR AND DAILY UNDULATING PERIODIZED RESISTANCE TRAINING TO INCREASE STRENGTH

Prestes, J, Frollini, AB, De Lima, C, Donatto, FF, Foschini, D, de Marqueti, RC, Figueira Jr, A, and Fleck, SJ. Comparison between linear and daily undulating periodized resistance training to increase strength. J Strength Cond Res 23(9): 2437-2442, 2009-To determine the most effective periodization model for strength and hypertrophy is an important step for strength and conditioning professionals. The aim of this study was to compare the effects of linear (LP) and daily undulating periodized (DUP) resistance training on body composition and maximal strength levels. Forty men aged 21.5 +/- 8.3 and with a minimum 1-year strength training experience were assigned to an LP (n = 20) or DUP group (n = 20). Subjects were tested for maximal strength in bench press, leg press 45 degrees, and arm curl (1 repetition maximum [RM]) at baseline (T1), after 8 weeks (T2), and after 12 weeks of training (T3). Increases of 18.2 and 25.08% in bench press 1 RM were observed for LP and DUP groups in T3 compared with T1, respectively (p <= 0.05). In leg press 45 degrees, LP group exhibited an increase of 24.71% and DUP of 40.61% at T3 compared with T1. Additionally, DUP showed an increase of 12.23% at T2 compared with T1 and 25.48% at T3 compared with T2. For the arm curl exercise, LP group increased 14.15% and DUP 23.53% at T3 when compared with T1. An increase of 20% was also found at T2 when compared with T1, for DUP. Although the DUP group increased strength the most in all exercises, no statistical differences were found between groups. In conclusion, undulating periodized strength training induced higher increases in maximal strength than the linear model in strength-trained men. For maximizing strength increases, daily intensity and volume variations were more effective than weekly variations.

Transformed generalized linear models

The estimation of data transformation is very useful to yield response variables satisfying closely a normal linear model, Generalized linear models enable the fitting of models to a wide range of data types. These models are based on exponential dispersion models. We propose a new class of transformed generalized linear models to extend the Box and Cox models and the generalized linear models. We use the generalized linear model framework to fit these models and discuss maximum likelihood estimation and inference. We give a simple formula to estimate the parameter that index the transformation of the response variable for a subclass of models. We also give a simple formula to estimate the rth moment of the original dependent variable. We explore the possibility of using these models to time series data to extend the generalized autoregressive moving average models discussed by Benjamin er al. [Generalized autoregressive moving average models. J. Amer. Statist. Assoc. 98, 214-223]. The usefulness of these models is illustrated in a Simulation study and in applications to three real data sets. (C) 2009 Elsevier B.V. All rights reserved.

Job rotation in assembly lines employing disabled workers

In this paper we consider the programming of job rotation in the assembly line worker assignment and balancing problem. The motivation for this study comes from the designing of assembly lines in sheltered work centers for the disabled, where workers have different task execution times. In this context, the well-known training aspects associated with job rotation are particularly desired. We propose a metric along with a mixed integer linear model and a heuristic decomposition method to solve this new job rotation problem. Computational results show the efficacy of the proposed heuristics. (C) 2009 Elsevier B.V. All rights reserved.

Performance of balanced two-stage empirical predictors of realized cluster latent values from finite populations: A simulation study

Predictors of random effects are usually based on the popular mixed effects (ME) model developed under the assumption that the sample is obtained from a conceptual infinite population; such predictors are employed even when the actual population is finite. Two alternatives that incorporate the finite nature of the population are obtained from the superpopulation model proposed by Scott and Smith (1969. Estimation in multi-stage surveys. J. Amer. Statist. Assoc. 64, 830-840) or from the finite population mixed model recently proposed by Stanek and Singer (2004. Predicting random effects from finite population clustered samples with response error. J. Amer. Statist. Assoc. 99, 1119-1130). Predictors derived under the latter model with the additional assumptions that all variance components are known and that within-cluster variances are equal have smaller mean squared error (MSE) than the competitors based on either the ME or Scott and Smith`s models. As population variances are rarely known, we propose method of moment estimators to obtain empirical predictors and conduct a simulation study to evaluate their performance. The results suggest that the finite population mixed model empirical predictor is more stable than its competitors since, in terms of MSE, it is either the best or the second best and when second best, its performance lies within acceptable limits. When both cluster and unit intra-class correlation coefficients are very high (e.g., 0.95 or more), the performance of the empirical predictors derived under the three models is similar. (c) 2007 Elsevier B.V. All rights reserved.

Detecting Major Genes Controlling Robustness of Chicken Body Weight Using Double Generalized Linear Models

Detecting both the majors genes that control the phenotypic mean and those controlling phenotypic variance has been raised in quantitative trait loci analysis. In order to mapping both kinds of genes, we applied the idea of the classic Haley-Knott regression to double generalized linear models. We performed both kinds of quantitative trait loci detection for a Red Jungle Fowl x White Leghorn F2 intercross using double generalized linear models. It is shown that double generalized linear model is a proper and efficient approach for localizing variance-controlling genes. We compared two models with or without fixed sex effect and prefer including the sex effect in order to reduce the residual variances. We found that different genes might take effect on the body weight at different time as the chicken grows.

Novel Statistical Methods in Quantitative Genetics : Modeling Genetic Variance for Quantitative Trait Loci Mapping and Genomic Evaluation

This thesis develops and evaluates statistical methods for different types of genetic analyses, including quantitative trait loci (QTL) analysis, genome-wide association study (GWAS), and genomic evaluation. The main contribution of the thesis is to provide novel insights in modeling genetic variance, especially via random effects models. In variance component QTL analysis, a full likelihood model accounting for uncertainty in the identity-by-descent (IBD) matrix was developed. It was found to be able to correctly adjust the bias in genetic variance component estimation and gain power in QTL mapping in terms of precision.  Double hierarchical generalized linear models, and a non-iterative simplified version, were implemented and applied to fit data of an entire genome. These whole genome models were shown to have good performance in both QTL mapping and genomic prediction. A re-analysis of a publicly available GWAS data set identified significant loci in Arabidopsis that control phenotypic variance instead of mean, which validated the idea of variance-controlling genes.  The works in the thesis are accompanied by R packages available online, including a general statistical tool for fitting random effects models (hglm), an efficient generalized ridge regression for high-dimensional data (bigRR), a double-layer mixed model for genomic data analysis (iQTL), a stochastic IBD matrix calculator (MCIBD), a computational interface for QTL mapping (qtl.outbred), and a GWAS analysis tool for mapping variance-controlling loci (vGWAS).

Estimation of genetic variance for macro- and micro-environmental sensitivity using double hierarchical generalized linear models

Background: Genetic variation for environmental sensitivity indicates that animals are genetically different in their response to environmental factors. Environmental factors are either identifiable (e.g. temperature) and called macro-environmental or unknown and called micro-environmental. The objectives of this study were to develop a statistical method to estimate genetic parameters for macro- and micro-environmental sensitivities simultaneously, to investigate bias and precision of resulting estimates of genetic parameters and to develop and evaluate use of Akaike’s information criterion using h-likelihood to select the best fitting model. Methods: We assumed that genetic variation in macro- and micro-environmental sensitivities is expressed as genetic variance in the slope of a linear reaction norm and environmental variance, respectively. A reaction norm model to estimate genetic variance for macro-environmental sensitivity was combined with a structural model for residual variance to estimate genetic variance for micro-environmental sensitivity using a double hierarchical generalized linear model in ASReml. Akaike’s information criterion was constructed as model selection criterion using approximated h-likelihood. Populations of sires with large half-sib offspring groups were simulated to investigate bias and precision of estimated genetic parameters. Results: Designs with 100 sires, each with at least 100 offspring, are required to have standard deviations of estimated variances lower than 50% of the true value. When the number of offspring increased, standard deviations of estimates across replicates decreased substantially, especially for genetic variances of macro- and micro-environmental sensitivities. Standard deviations of estimated genetic correlations across replicates were quite large (between 0.1 and 0.4), especially when sires had few offspring. Practically, no bias was observed for estimates of any of the parameters. Using Akaike’s information criterion the true genetic model was selected as the best statistical model in at least 90% of 100 replicates when the number of offspring per sire was 100. Application of the model to lactation milk yield in dairy cattle showed that genetic variance for micro- and macro-environmental sensitivities existed. Conclusion: The algorithm and model selection criterion presented here can contribute to better understand genetic control of macro- and micro-environmental sensitivities. Designs or datasets should have at least 100 sires each with 100 offspring.

Comparison of treatment of incomplete abortion with misoprostol by physicians and midwives at district level in Uganda : a randomised controlled equivalence trial

BACKGROUND: Misoprostol is established for the treatment of incomplete abortion but has not been systematically assessed when provided by midwives at district level in a low-resource setting. We investigated the effectiveness and safety of midwives diagnosing and treating incomplete abortion with misoprostol, compared with physicians. METHODS: We did a multicentre randomised controlled equivalence trial at district level at six facilities in Uganda. Eligibility criteria were women with signs of incomplete abortion. We randomly allocated women with first-trimester incomplete abortion to clinical assessment and treatment with misoprostol either by a physician or a midwife. The randomisation (1:1) was done in blocks of 12 and was stratified for study site. Primary outcome was complete abortion not needing surgical intervention within 14-28 days after initial treatment. The study was not masked. Analysis of the primary outcome was done on the per-protocol population with a generalised linear-mixed effects model. The predefined equivalence range was -4% to 4%. The trial was registered at ClinicalTrials.gov, number NCT01844024. FINDINGS: From April 30, 2013, to July 21, 2014, 1108 women were assessed for eligibility. 1010 women were randomly assigned to each group (506 to midwife group and 504 to physician group). 955 women (472 in the midwife group and 483 in the physician group) were included in the per-protocol analysis. 452 (95·8%) of women in the midwife group had complete abortion and 467 (96·7%) in the physician group. The model-based risk difference for midwife versus physician group was -0·8% (95% CI -2·9 to 1·4), falling within the predefined equivalence range (-4% to 4%). The overall proportion of women with incomplete abortion was 3·8% (36/955), similarly distributed between the two groups (4·2% [20/472] in the midwife group, 3·3% [16/483] in the physician group). No serious adverse events were recorded. INTERPRETATION: Diagnosis and treatment of incomplete abortion with misoprostol by midwives is equally safe and effective as when provided by physicians, in a low-resource setting. Scaling up midwives' involvement in treatment of incomplete abortion with misoprostol at district level would increase access to safe post-abortion care. FUNDING: The Swedish Research Council, Karolinska Institutet, and Dalarna University.

Women's acceptability of misoprostol treatment for incomplete abortion by midwives and physicians : secondary outcome analysis from a randomized controlled equivalence trial at district level in Uganda

OBJECTIVE: This study aimed to assess women´s acceptability of diagnosis and treatment of incomplete abortion with misoprostol by midwives, compared with physicians. METHODS: This was an analysis of secondary outcomes from a multi-centre randomized controlled equivalence trial at district level in Uganda. Women with first trimester incomplete abortion were randomly allocated to clinical assessment and treatment with misoprostol by a physician or a midwife. The randomisation (1:1) was done in blocks of 12 and stratified for health care facility. Acceptability was measured in expectations and satisfaction at a follow up visit 14-28 days following treatment. Analysis of women's overall acceptability was done using a generalized linear mixed-effects model with an equivalence range of -4% to 4%. The study was not masked. The trial is registered at ClinicalTrials.org, NCT 01844024. RESULTS: From April 2013 to June 2014, 1108 women were assessed for eligibility of which 1010 were randomized (506 to midwife and 504 to physician). 953 women were successfully followed up and included in the acceptability analysis. 95% (904) of the participants found the treatment satisfactory and overall acceptability was found to be equivalent between the two study groups. Treatment failure, not feeling calm and safe following treatment, experiencing severe abdominal pain or heavy bleeding following treatment, were significantly associated with non-satisfaction. No serious adverse events were recorded. CONCLUSIONS: Treatment of incomplete abortion with misoprostol by midwives and physician was highly, and equally, acceptable to women. TRIAL REGISTRATION: ClinicalTrials.gov NCT01844024.

Forecasting Multivariate Time Series under Present-Value-Model Short- and Long-run Co-movement Restrictions

This paper has two original contributions. First, we show that the present value model (PVM hereafter), which has a wide application in macroeconomics and fi nance, entails common cyclical feature restrictions in the dynamics of the vector error-correction representation (Vahid and Engle, 1993); something that has been already investigated in that VECM context by Johansen and Swensen (1999, 2011) but has not been discussed before with this new emphasis. We also provide the present value reduced rank constraints to be tested within the log-linear model. Our second contribution relates to forecasting time series that are subject to those long and short-run reduced rank restrictions. The reason why appropriate common cyclical feature restrictions might improve forecasting is because it finds natural exclusion restrictions preventing the estimation of useless parameters, which would otherwise contribute to the increase of forecast variance with no expected reduction in bias. We applied the techniques discussed in this paper to data known to be subject to present value restrictions, i.e. the online series maintained and up-dated by Shiller. We focus on three different data sets. The fi rst includes the levels of interest rates with long and short maturities, the second includes the level of real price and dividend for the S&P composite index, and the third includes the logarithmic transformation of prices and dividends. Our exhaustive investigation of several different multivariate models reveals that better forecasts can be achieved when restrictions are applied to them. Moreover, imposing short-run restrictions produce forecast winners 70% of the time for target variables of PVMs and 63.33% of the time when all variables in the system are considered.