A likelihood ratio appropach to family-based association studies with covariates

We introduce a procedure for association based analysis of nuclear families that allows for dichotomous and more general measurements of phenotype and inclusion of covariate information. Standard generalized linear models are used to relate phenotype and its predictors. Our test procedure, based on the likelihood ratio, unifies the estimation of all parameters through the likelihood itself and yields maximum likelihood estimates of the genetic relative risk and interaction parameters. Our method has advantages in modelling the covariate and gene-covariate interaction terms over recently proposed conditional score tests that include covariate information via a two-stage modelling approach. We apply our method in a study of human systemic lupus erythematosus and the C-reactive protein that includes sex as a covariate.

Diagnosis of variability and trends in a global precipitation dataset using a physically motivated statistical model

A physically motivated statistical model is used to diagnose variability and trends in wintertime ( October - March) Global Precipitation Climatology Project (GPCP) pentad (5-day mean) precipitation. Quasi-geostrophic theory suggests that extratropical precipitation amounts should depend multiplicatively on the pressure gradient, saturation specific humidity, and the meridional temperature gradient. This physical insight has been used to guide the development of a suitable statistical model for precipitation using a mixture of generalized linear models: a logistic model for the binary occurrence of precipitation and a Gamma distribution model for the wet day precipitation amount. The statistical model allows for the investigation of the role of each factor in determining variations and long-term trends. Saturation specific humidity q(s) has a generally negative effect on global precipitation occurrence and with the tropical wet pentad precipitation amount, but has a positive relationship with the pentad precipitation amount at mid- and high latitudes. The North Atlantic Oscillation, a proxy for the meridional temperature gradient, is also found to have a statistically significant positive effect on precipitation over much of the Atlantic region. Residual time trends in wet pentad precipitation are extremely sensitive to the choice of the wet pentad threshold because of increasing trends in low-amplitude precipitation pentads; too low a choice of threshold can lead to a spurious decreasing trend in wet pentad precipitation amounts. However, for not too small thresholds, it is found that the meridional temperature gradient is an important factor for explaining part of the long-term trend in Atlantic precipitation.

Responses of leaf traits to climatic gradients: adaptive variation versus compositional shifts

Dynamic global vegetation models (DGVMs) typically rely on plant functional types (PFTs), which are assigned distinct environmental tolerances and replace one another progressively along environmental gradients. Fixed values of traits are assigned to each PFT; modelled trait variation along gradients is thus driven by PFT replacement. But empirical studies have revealed "universal" scaling relationships (quantitative trait variations with climate that are similar within and between species, PFTs and communities); and continuous, adaptive trait variation has been proposed to replace PFTs as the basis for next-generation DGVMs. Here we analyse quantitative leaf-trait variation on long temperature and moisture gradients in China with a view to understanding the relative importance of PFT replacement vs. continuous adaptive variation within PFTs. Leaf area (LA), specific leaf area (SLA), leaf dry matter content (LDMC) and nitrogen content of dry matter were measured on all species at 80 sites ranging from temperate to tropical climates and from dense forests to deserts. Chlorophyll fluorescence traits and carbon, phosphorus and potassium contents were measured at 47 sites. Generalized linear models were used to relate log-transformed trait values to growing-season temperature and moisture indices, with or without PFT identity as a predictor, and to test for differences in trait responses among PFTs. Continuous trait variation was found to be ubiquitous. Responses to moisture availability were generally similar within and between PFTs, but biophysical traits (LA, SLA and LDMC) of forbs and grasses responded differently from woody plants. SLA and LDMC responses to temperature were dominated by the prevalence of evergreen PFTs with thick, dense leaves at the warm end of the gradient. Nutrient (N, P and K) responses to climate gradients were generally similar within all PFTs. Area-based nutrients generally declined with moisture; Narea and Karea declined with temperature, but Parea increased with temperature. Although the adaptive nature of many of these trait-climate relationships is understood qualitatively, a key challenge for modelling is to predict them quantitatively. Models must take into account that community-level responses to climatic gradients can be influenced by shifts in PFT composition, such as the replacement of deciduous by evergreen trees, which may run either parallel or counter to trait variation within PFTs. The importance of PFT shifts varies among traits, being important for biophysical traits but less so for physiological and chemical traits. Finally, models should take account of the diversity of trait values that is found in all sites and PFTs, representing the "pool" of variation that is locally available for the natural adaptation of ecosystem function to environmental change.

Comparing tube models for predicting the linear rheology of branched polymer melts

The hierarchical and "bob" (or branch-on-branch) models are tube-based computational models recently developed for predicting the linear rheology of general mixtures of polydisperse branched polymers. These two models are based on a similar tube-theory framework but differ in their numerical implementation and details of relaxation mechanisms. We present a detailed overview of the similarities and differences of these models and examine the effects of these differences on the predictions of the linear viscoelastic properties of a set of representative branched polymer samples in order to give a general picture of the performance of these models. Our analysis confirms that the hierarchical and bob models quantitatively predict the linear rheology of a wide range of branched polymer melts but also indicate that there is still no unique solution to cover all types of branched polymers without case-by-case adjustment of parameters such as the dilution exponent alpha and the factor p(2) which defines the hopping distance of a branch point relative to the tube diameter. An updated version of the hierarchical model, which shows improved computational efficiency and refined relaxation mechanisms, is introduced and used in these analyses.

Evaluating forecasts from SETAR models of exchange rates

We consider the forecasting performance of two SETAR exchange rate models proposed by Kräger and Kugler [J. Int. Money Fin. 12 (1993) 195]. Assuming that the models are good approximations to the data generating process, we show that whether the non-linearities inherent in the data can be exploited to forecast better than a random walk depends on both how forecast accuracy is assessed and on the ‘state of nature’. Evaluation based on traditional measures, such as (root) mean squared forecast errors, may mask the superiority of the non-linear models. Generalized impulse response functions are also calculated as a means of portraying the asymmetric response to shocks implied by such models.

Statistical downscaling of river flows

An extensive statistical ‘downscaling’ study is done to relate large-scale climate information from a general circulation model (GCM) to local-scale river flows in SW France for 51 gauging stations ranging from nival (snow-dominated) to pluvial (rainfall-dominated) river-systems. This study helps to select the appropriate statistical method at a given spatial and temporal scale to downscale hydrology for future climate change impact assessment of hydrological resources. The four proposed statistical downscaling models use large-scale predictors (derived from climate model outputs or reanalysis data) that characterize precipitation and evaporation processes in the hydrological cycle to estimate summary flow statistics. The four statistical models used are generalized linear (GLM) and additive (GAM) models, aggregated boosted trees (ABT) and multi-layer perceptron neural networks (ANN). These four models were each applied at two different spatial scales, namely at that of a single flow-gauging station (local downscaling) and that of a group of flow-gauging stations having the same hydrological behaviour (regional downscaling). For each statistical model and each spatial resolution, three temporal resolutions were considered, namely the daily mean flows, the summary statistics of fortnightly flows and a daily ‘integrated approach’. The results show that flow sensitivity to atmospheric factors is significantly different between nival and pluvial hydrological systems which are mainly influenced, respectively, by shortwave solar radiations and atmospheric temperature. The non-linear models (i.e. GAM, ABT and ANN) performed better than the linear GLM when simulating fortnightly flow percentiles. The aggregated boosted trees method showed higher and less variable R2 values to downscale the hydrological variability in both nival and pluvial regimes. Based on GCM cnrm-cm3 and scenarios A2 and A1B, future relative changes of fortnightly median flows were projected based on the regional downscaling approach. The results suggest a global decrease of flow in both pluvial and nival regimes, especially in spring, summer and autumn, whatever the considered scenario. The discussion considers the performance of each statistical method for downscaling flow at different spatial and temporal scales as well as the relationship between atmospheric processes and flow variability.

Alternatives to linear analysis of energy balance data from lactating dairy cows

The current energy requirements system used in the United Kingdom for lactating dairy cows utilizes key parameters such as metabolizable energy intake (MEI) at maintenance (MEm), the efficiency of utilization of MEI for 1) maintenance, 2) milk production (k(l)), 3) growth (k(g)), and the efficiency of utilization of body stores for milk production (k(t)). Traditionally, these have been determined using linear regression methods to analyze energy balance data from calorimetry experiments. Many studies have highlighted a number of concerns over current energy feeding systems particularly in relation to these key parameters, and the linear models used for analyzing. Therefore, a database containing 652 dairy cow observations was assembled from calorimetry studies in the United Kingdom. Five functions for analyzing energy balance data were considered: straight line, two diminishing returns functions, (the Mitscherlich and the rectangular hyperbola), and two sigmoidal functions (the logistic and the Gompertz). Meta-analysis of the data was conducted to estimate k(g) and k(t). Values of 0.83 to 0.86 and 0.66 to 0.69 were obtained for k(g) and k(t) using all the functions (with standard errors of 0.028 and 0.027), respectively, which were considerably different from previous reports of 0.60 to 0.75 for k(g) and 0.82 to 0.84 for k(t). Using the estimated values of k(g) and k(t), the data were corrected to allow for body tissue changes. Based on the definition of k(l) as the derivative of the ratio of milk energy derived from MEI to MEI directed towards milk production, MEm and k(l) were determined. Meta-analysis of the pooled data showed that the average k(l) ranged from 0.50 to 0.58 and MEm ranged between 0.34 and 0.64 MJ/kg of BW0.75 per day. Although the constrained Mitscherlich fitted the data as good as the straight line, more observations at high energy intakes (above 2.4 MJ/kg of BW0.75 per day) are required to determine conclusively whether milk energy is related to MEI linearly or not.

Neural and wavelet network models for financial distress classification

This work analyzes the use of linear discriminant models, multi-layer perceptron neural networks and wavelet networks for corporate financial distress prediction. Although simple and easy to interpret, linear models require statistical assumptions that may be unrealistic. Neural networks are able to discriminate patterns that are not linearly separable, but the large number of parameters involved in a neural model often causes generalization problems. Wavelet networks are classification models that implement nonlinear discriminant surfaces as the superposition of dilated and translated versions of a single "mother wavelet" function. In this paper, an algorithm is proposed to select dilation and translation parameters that yield a wavelet network classifier with good parsimony characteristics. The models are compared in a case study involving failed and continuing British firms in the period 1997-2000. Problems associated with over-parameterized neural networks are illustrated and the Optimal Brain Damage pruning technique is employed to obtain a parsimonious neural model. The results, supported by a re-sampling study, show that both neural and wavelet networks may be a valid alternative to classical linear discriminant models.

Model selection approaches for non-linear system identification: a review

The identification of non-linear systems using only observed finite datasets has become a mature research area over the last two decades. A class of linear-in-the-parameter models with universal approximation capabilities have been intensively studied and widely used due to the availability of many linear-learning algorithms and their inherent convergence conditions. This article presents a systematic overview of basic research on model selection approaches for linear-in-the-parameter models. One of the fundamental problems in non-linear system identification is to find the minimal model with the best model generalisation performance from observational data only. The important concepts in achieving good model generalisation used in various non-linear system-identification algorithms are first reviewed, including Bayesian parameter regularisation and models selective criteria based on the cross validation and experimental design. A significant advance in machine learning has been the development of the support vector machine as a means for identifying kernel models based on the structural risk minimisation principle. The developments on the convex optimisation-based model construction algorithms including the support vector regression algorithms are outlined. Input selection algorithms and on-line system identification algorithms are also included in this review. Finally, some industrial applications of non-linear models are discussed.

A stable one-step-ahead predictive control of non-linear systems

In this paper stability of one-step ahead predictive controllers based on non-linear models is established. It is shown that, under conditions which can be fulfilled by most industrial plants, the closed-loop system is robustly stable in the presence of plant uncertainties and input–output constraints. There is no requirement that the plant should be open-loop stable and the analysis is valid for general forms of non-linear system representation including the case out when the problem is constraint-free. The effectiveness of controllers designed according to the algorithm analyzed in this paper is demonstrated on a recognized benchmark problem and on a simulation of a continuous-stirred tank reactor (CSTR). In both examples a radial basis function neural network is employed as the non-linear system model.

Optimal piecewise locally linear modeling

Associative memory networks such as Radial Basis Functions, Neurofuzzy and Fuzzy Logic used for modelling nonlinear processes suffer from the curse of dimensionality (COD), in that as the input dimension increases the parameterization, computation cost, training data requirements, etc. increase exponentially. Here a new algorithm is introduced for the construction of a Delaunay input space partitioned optimal piecewise locally linear models to overcome the COD as well as generate locally linear models directly amenable to linear control and estimation algorithms. The training of the model is configured as a new mixture of experts network with a new fast decision rule derived using convex set theory. A very fast simulated reannealing (VFSR) algorithm is utilized to search a global optimal solution of the Delaunay input space partition. A benchmark non-linear time series is used to demonstrate the new approach.

Assessing the vulnerability of blanket peat to climate change using an ensemble of statistical bioclimatic envelope models

We assessed the vulnerability of blanket peat to climate change in Great Britain using an ensemble of 8 bioclimatic envelope models. We used 4 published models that ranged from simple threshold models, based on total annual precipitation, to Generalised Linear Models (GLMs, based on mean annual temperature). In addition, 4 new models were developed which included measures of water deficit as threshold, classification tree, GLM and generalised additive models (GAM). Models that included measures of both hydrological conditions and maximum temperature provided a better fit to the mapped peat area than models based on hydrological variables alone. Under UKCIP02 projections for high (A1F1) and low (B1) greenhouse gas emission scenarios, 7 out of the 8 models showed a decline in the bioclimatic space associated with blanket peat. Eastern regions (Northumbria, North York Moors, Orkney) were shown to be more vulnerable than higher-altitude, western areas (Highlands, Western Isles and Argyle, Bute and The Trossachs). These results suggest a long-term decline in the distribution of actively growing blanket peat, especially under the high emissions scenario, although it is emphasised that existing peatlands may well persist for decades under a changing climate. Observational data from long-term monitoring and manipulation experiments in combination with process-based models are required to explore the nature and magnitude of climate change impacts on these vulnerable areas more fully.

Are property prices non-linear? An investigation of the behaviour of US REITs and UK property company shares

Linear models of market performance may be misspecified if the market is subdivided into distinct regimes exhibiting different behaviour. Price movements in the US Real Estate Investment Trusts and UK Property Companies Markets are explored using a Threshold Autoregressive (TAR) model with regimes defined by the real rate of interest. In both US and UK markets, distinctive behaviour emerges, with the TAR model offering better predictive power than a more conventional linear autoregressive model. The research points to the possibility of developing trading rules to exploit the systematically different behaviour across regimes.

Temporal constraints on linear BRDF model parameters

Linear models of bidirectional reflectance distribution are useful tools for understanding the angular variability of surface reflectance as observed by medium-resolution sensors such as the Moderate Resolution Imaging Spectrometer. These models are operationally used to normalize data to common view and illumination geometries and to calculate integral quantities such as albedo. Currently, to compensate for noise in observed reflectance, these models are inverted against data collected during some temporal window for which the model parameters are assumed to be constant. Despite this, the retrieved parameters are often noisy for regions where sufficient observations are not available. This paper demonstrates the use of Lagrangian multipliers to allow arbitrarily large windows and, at the same time, produce individual parameter sets for each day even for regions where only sparse observations are available.

Describing seasonal variability in the distribution of daily effective temperatures for 1985-2009 compared to 1904-1984 for De Bilt, Holland

This paper proposes a method for describing the distribution of observed temperatures on any day of the year such that the distribution and summary statistics of interest derived from the distribution vary smoothly through the year. The method removes the noise inherent in calculating summary statistics directly from the data thus easing comparisons of distributions and summary statistics between different periods. The method is demonstrated using daily effective temperatures (DET) derived from observations of temperature and wind speed at De Bilt, Holland. Distributions and summary statistics are obtained from 1985 to 2009 and compared to the period 1904–1984. A two-stage process first obtains parameters of a theoretical probability distribution, in this case the generalized extreme value (GEV) distribution, which describes the distribution of DET on any day of the year. Second, linear models describe seasonal variation in the parameters. Model predictions provide parameters of the GEV distribution, and therefore summary statistics, that vary smoothly through the year. There is evidence of an increasing mean temperature, a decrease in the variability in temperatures mainly in the winter and more positive skew, more warm days, in the summer. In the winter, the 2% point, the value below which 2% of observations are expected to fall, has risen by 1.2 °C, in the summer the 98% point has risen by 0.8 °C. Medians have risen by 1.1 and 0.9 °C in winter and summer, respectively. The method can be used to describe distributions of future climate projections and other climate variables. Further extensions to the methodology are suggested.