Critère de validation croisée pour le choix des modèles des petits domaines au niveau des unités

Ce mémoire s’intéresse à l’étude du critère de validation croisée pour le choix des modèles relatifs aux petits domaines. L’étude est limitée aux modèles de petits domaines au niveau des unités. Le modèle de base des petits domaines est introduit par Battese, Harter et Fuller en 1988. C’est un modèle de régression linéaire mixte avec une ordonnée à l’origine aléatoire. Il se compose d’un certain nombre de paramètres : le paramètre β de la partie fixe, la composante aléatoire et les variances relatives à l’erreur résiduelle. Le modèle de Battese et al. est utilisé pour prédire, lors d’une enquête, la moyenne d’une variable d’intérêt y dans chaque petit domaine en utilisant une variable auxiliaire administrative x connue sur toute la population. La méthode d’estimation consiste à utiliser une distribution normale, pour modéliser la composante résiduelle du modèle. La considération d’une dépendance résiduelle générale, c’est-à-dire autre que la loi normale donne une méthodologie plus flexible. Cette généralisation conduit à une nouvelle classe de modèles échangeables. En effet, la généralisation se situe au niveau de la modélisation de la dépendance résiduelle qui peut être soit normale (c’est le cas du modèle de Battese et al.) ou non-normale. L’objectif est de déterminer les paramètres propres aux petits domaines avec le plus de précision possible. Cet enjeu est lié au choix de la bonne dépendance résiduelle à utiliser dans le modèle. Le critère de validation croisée sera étudié à cet effet.

STATISTICAL METHODS FOR ADVANCED ECONOMETRIC MODELS WITH APPLICATIONS TO VEHICLE HOLDING AND SPEED QUANTILES DISTRIBUTION

This dissertation proposes statistical methods to formulate, estimate and apply complex transportation models. Two main problems are part of the analyses conducted and presented in this dissertation. The first method solves an econometric problem and is concerned with the joint estimation of models that contain both discrete and continuous decision variables. The use of ordered models along with a regression is proposed and their effectiveness is evaluated with respect to unordered models. Procedure to calculate and optimize the log-likelihood functions of both discrete-continuous approaches are derived, and difficulties associated with the estimation of unordered models explained. Numerical approximation methods based on the Genz algortithm are implemented in order to solve the multidimensional integral associated with the unordered modeling structure. The problems deriving from the lack of smoothness of the probit model around the maximum of the log-likelihood function, which makes the optimization and the calculation of standard deviations very difficult, are carefully analyzed. A methodology to perform out-of-sample validation in the context of a joint model is proposed. Comprehensive numerical experiments have been conducted on both simulated and real data. In particular, the discrete-continuous models are estimated and applied to vehicle ownership and use models on data extracted from the 2009 National Household Travel Survey. The second part of this work offers a comprehensive statistical analysis of free-flow speed distribution; the method is applied to data collected on a sample of roads in Italy. A linear mixed model that includes speed quantiles in its predictors is estimated. Results show that there is no road effect in the analysis of free-flow speeds, which is particularly important for model transferability. A very general framework to predict random effects with few observations and incomplete access to model covariates is formulated and applied to predict the distribution of free-flow speed quantiles. The speed distribution of most road sections is successfully predicted; jack-knife estimates are calculated and used to explain why some sections are poorly predicted. Eventually, this work contributes to the literature in transportation modeling by proposing econometric model formulations for discrete-continuous variables, more efficient methods for the calculation of multivariate normal probabilities, and random effects models for free-flow speed estimation that takes into account the survey design. All methods are rigorously validated on both real and simulated data.

Epidemiology and genetic architecture of blood pressure: a family based study of Generation Scotland

Hypertension is a major risk factor for cardiovascular disease and mortality, and a growing global public health concern, with up to one-third of the world’s population affected. Despite the vast amount of evidence for the benefits of blood pressure (BP) lowering accumulated to date, elevated BP is still the leading risk factor for disease and disability worldwide. It is well established that hypertension and BP are common complex traits, where multiple genetic and environmental factors contribute to BP variation. Furthermore, family and twin studies confirmed the genetic component of BP, with a heritability estimate in the range of 30-50%. Contemporary genomic tools enabling the genotyping of millions of genetic variants across the human genome in an efficient, reliable, and cost-effective manner, has transformed hypertension genetics research. This is accompanied by the presence of international consortia that have offered unprecedentedly large sample sizes for genome-wide association studies (GWASs). While GWAS for hypertension and BP have identified more than 60 loci, variants in these loci are associated with modest effects on BP and in aggregate can explain less than 3% of the variance in BP. The aims of this thesis are to study the genetic and environmental factors that influence BP and hypertension traits in the Scottish population, by performing several genetic epidemiological analyses. In the first part of this thesis, it aims to study the burden of hypertension in the Scottish population, along with assessing the familial aggregation and heritialbity of BP and hypertension traits. In the second part, it aims to validate the association of common SNPs reported in the large GWAS and to estimate the variance explained by these variants. In this thesis, comprehensive genetic epidemiology analyses were performed on Generation Scotland: Scottish Family Health Study (GS:SFHS), one of the largest population-based family design studies. The availability of clinical, biological samples, self-reported information, and medical records for study participants has allowed several assessments to be performed to evaluate factors that influence BP variation in the Scottish population. Of the 20,753 subjects genotyped in the study, a total of 18,470 individuals (grouped into 7,025 extended families) passed the stringent quality control (QC) criteria and were available for all subsequent analysis. Based on the BP-lowering treatment exposure sources, subjects were further classified into two groups. First, subjects with both a self-reported medications (SRMs) history and electronic-prescription records (EPRs; n =12,347); second, all the subjects with at least one medication history source (n =18,470). In the first group, the analysis showed a good concordance between SRMs and EPRs (kappa =71%), indicating that SRMs can be used as a surrogate to assess the exposure to BP-lowering medication in GS:SFHS participants. Although both sources suffer from some limitations, SRMs can be considered the best available source to estimate the drug exposure history in those without EPRs. The prevalence of hypertension was 40.8% with higher prevalence in men (46.3%) compared to women (35.8%). The prevalence of awareness, treatment and controlled hypertension as defined by the study definition were 25.3%, 31.2%, and 54.3%, respectively. These findings are lower than similar reported studies in other populations, with the exception of controlled hypertension prevalence, which can be considered better than other populations. Odds of hypertension were higher in men, obese or overweight individuals, people with a parental history of hypertension, and those living in the most deprived area of Scotland. On the other hand, deprivation was associated with higher odds of treatment, awareness and controlled hypertension, suggesting that people living in the most deprived area may have been receiving better quality of care, or have higher comorbidity levels requiring greater engagement with doctors. These findings highlight the need for further work to improve hypertension management in Scotland. The family design of GS:SFHS has allowed family-based analysis to be performed to assess the familial aggregation and heritability of BP and hypertension traits. The familial correlation of BP traits ranged from 0.07 to 0.20, and from 0.18 to 0.34 for parent-offspring pairs and sibling pairs, respectively. A higher correlation of BP traits was observed among first-degree relatives than other types of relative pairs. A variance-component model that was adjusted for sex, body mass index (BMI), age, and age-squared was used to estimate heritability of BP traits, which ranged from 24% to 32% with pulse pressure (PP) having the lowest estimates. The genetic correlation between BP traits showed a high correlation between systolic (SBP), diastolic (DBP) and mean arterial pressure (MAP) (G: 81% to 94%), but lower correlations with PP (G: 22% to 78%). The sibling recurrence risk ratio (λS) for hypertension and treatment were calculated as 1.60 and 2.04 respectively. These findings confirm the genetic components of BP traits in GS:SFHS, and justify further work to investigate genetic determinants of BP. Genetic variants reported in the recent large GWAS of BP traits were selected for genotyping in GS:SFHS using a custom designed TaqMan® OpenArray®. The genotyping plate included 44 single nucleotide polymorphisms (SNPs) that have been previously reported to be associated with BP or hypertension at genome-wide significance level. A linear mixed model that is adjusted for age, age-squared, sex, and BMI was used to test for the association between the genetic variants and BP traits. Of the 43 variants that passed the QC, 11 variants showed statistically significant association with at least one BP trait. The phenotypic variance explained by these variant for the four BP traits were 1.4%, 1.5%, 1.6%, and 0.8% for SBP, DBP, MAP, and PP, respectively. The association of genetic risk score (GRS) that were constructed from selected variants has showed a positive association with BP level and hypertension prevalence, with an average effect of one mmHg increase with each 0.80 unit increases in the GRS across the different BP traits. The impact of BP-lowering medication on the genetic association study for BP traits has been established, with typical practice of adding a fixed value (i.e. 15/10 mmHg) to the measured BP values to adjust for BP treatment. Using the subset of participants with the two treatment exposure sources (i.e. SRMs and EPRs), the influence of using either source to justify the addition of fixed values in SNP association signal was analysed. BP phenotypes derived from EPRs were considered the true phenotypes, and those derived from SRMs were considered less accurate, with some phenotypic noise. Comparing SNPs association signals between the four BP traits in the two model derived from the different adjustments showed that MAP was the least impacted by the phenotypic noise. This was suggested by identifying the same overlapped significant SNPs for the two models in the case of MAP, while other BP traits had some discrepancy between the two sources

Quantification of air quality in space and time and its effects on health

The long-term adverse effects on health associated with air pollution exposure can be estimated using either cohort or spatio-temporal ecological designs. In a cohort study, the health status of a cohort of people are assessed periodically over a number of years, and then related to estimated ambient pollution concentrations in the cities in which they live. However, such cohort studies are expensive and time consuming to implement, due to the long-term follow up required for the cohort. Therefore, spatio-temporal ecological studies are also being used to estimate the long-term health effects of air pollution as they are easy to implement due to the routine availability of the required data. Spatio-temporal ecological studies estimate the health impact of air pollution by utilising geographical and temporal contrasts in air pollution and disease risk across $n$ contiguous small-areas, such as census tracts or electoral wards, for multiple time periods. The disease data are counts of the numbers of disease cases occurring in each areal unit and time period, and thus Poisson log-linear models are typically used for the analysis. The linear predictor includes pollutant concentrations and known confounders such as socio-economic deprivation. However, as the disease data typically contain residual spatial or spatio-temporal autocorrelation after the covariate effects have been accounted for, these known covariates are augmented by a set of random effects. One key problem in these studies is estimating spatially representative pollution concentrations in each areal which are typically estimated by applying Kriging to data from a sparse monitoring network, or by computing averages over modelled concentrations (grid level) from an atmospheric dispersion model. The aim of this thesis is to investigate the health effects of long-term exposure to Nitrogen Dioxide (NO2) and Particular matter (PM10) in mainland Scotland, UK. In order to have an initial impression about the air pollution health effects in mainland Scotland, chapter 3 presents a standard epidemiological study using a benchmark method. The remaining main chapters (4, 5, 6) cover the main methodological focus in this thesis which has been threefold: (i) how to better estimate pollution by developing a multivariate spatio-temporal fusion model that relates monitored and modelled pollution data over space, time and pollutant; (ii) how to simultaneously estimate the joint effects of multiple pollutants; and (iii) how to allow for the uncertainty in the estimated pollution concentrations when estimating their health effects. Specifically, chapters 4 and 5 are developed to achieve (i), while chapter 6 focuses on (ii) and (iii). In chapter 4, I propose an integrated model for estimating the long-term health effects of NO2, that fuses modelled and measured pollution data to provide improved predictions of areal level pollution concentrations and hence health effects. The air pollution fusion model proposed is a Bayesian space-time linear regression model for relating the measured concentrations to the modelled concentrations for a single pollutant, whilst allowing for additional covariate information such as site type (e.g. roadside, rural, etc) and temperature. However, it is known that some pollutants might be correlated because they may be generated by common processes or be driven by similar factors such as meteorology. The correlation between pollutants can help to predict one pollutant by borrowing strength from the others. Therefore, in chapter 5, I propose a multi-pollutant model which is a multivariate spatio-temporal fusion model that extends the single pollutant model in chapter 4, which relates monitored and modelled pollution data over space, time and pollutant to predict pollution across mainland Scotland. Considering that we are exposed to multiple pollutants simultaneously because the air we breathe contains a complex mixture of particle and gas phase pollutants, the health effects of exposure to multiple pollutants have been investigated in chapter 6. Therefore, this is a natural extension to the single pollutant health effects in chapter 4. Given NO2 and PM10 are highly correlated (multicollinearity issue) in my data, I first propose a temporally-varying linear model to regress one pollutant (e.g. NO2) against another (e.g. PM10) and then use the residuals in the disease model as well as PM10, thus investigating the health effects of exposure to both pollutants simultaneously. Another issue considered in chapter 6 is to allow for the uncertainty in the estimated pollution concentrations when estimating their health effects. There are in total four approaches being developed to adjust the exposure uncertainty. Finally, chapter 7 summarises the work contained within this thesis and discusses the implications for future research.

Modelagem univariada e regressão múltipla na análise da oferta e do preço do boi gordo no mercado brasileiro

Dissertação (mestrado)—Universidade de Brasília, Faculdade de Agronomia e Medicina Veterinária, Programa de Pós-Graduação em Agronegócios, 2016.

Determinantes da estrutura de capitais do sector bancário português

Este estudo tem como objectivo analisar quais os factores que determinam a estrutura de capitais do sector bancário Português. Com o intuito de atingir o objectivo e assumindo a existência de uma estrutura óptima de capitais, recorrer-se-á ao modelo de regressão linear múltipla para verificar a aderência do processo de decisão às teorias acerca da estrutura de capitais, bem como quais dos factores analisados a afectarão significativamente. Os resultados obtidos sugerem que a rendibilidade, a dimensão, o risco e a tangibilidade são os principais determinantes da estrutura de capitais do sector bancário português. ABSTRACT: The main aim for this study is to verify which determinants influence the Portuguese bank's capital structure. ln order to achieve the above mentioned aim and assuming an optimal capital structure, we will apply a multiple linear regression model with the purpose of proving the capital structure theories existence and to observe which determinants influence it. The obtained results mention that profitability, size, risk and tangibility are the principal determinants of Portuguese bank's capital structure.

Caractérisation du fonctionnement d'une hydrolienne à membrane ondulante pour la récupération de l'énergie des courants marins

This manuscript presents three approaches : analytical, experimental and numerical, to study the behaviour of a flexible membrane tidal energy converter. This technology, developed by the EEL Energy company, is based on periodic deformations of a pre-stressed flexible structure. Energy converters, located on each side of the device, are set into motion by the wave-like motion. In the analytical model, the membrane is represented by a linear beam model at one dimension and the flow by a 3 dimensions potential fluid. The fluid forces are evaluated by the elongated body theory. Energy is dissipated all over the length of the membrane. A 20th scale experimental prototype has been designed with micro-dampers to simulate the power take-off. Trials have allowed to validate the undulating membrane energy converter concept. A numerical model has been developed. Each element of the device is represented and the energy dissipation is done by dampers element with a damping law linear to damper velocity. Comparison of the three approaches validates their ability to represent the membrane behaviour without damping. The energy dissipation applied with the analytical model is clearly different from the two other models because of the location (where the energy is dissipated) and damping law. The two others show a similar behaviour and the same order of power take off repartition but value of power take off are underestimated by the numerical model. This three approaches have allowed to put forward key-parameters on which depend the behaviour of the membrane and the parametric study highlights the complementarity and the advantage of developing three approaches in parallel to answer industrial optimization problems. To make the link between trials in flume tank and sea trials, a 1/6th prototype has been built. To do so, the change of scale was studied. The behaviour of both prototypes is compared and differences could be explained by differences of boundary conditions and confinement effects. To evaluated membrane long-term behaviour at sea, a method of ageing accelerated by temperature and fatigue tests have been carried out on prototype materials samples submerged in sea water.

Second-order elliptic PDE with discontinuous boundary data

We shall consider the weak formulation of a linear elliptic model problem with discontinuous Dirichlet boundary conditions. Since such problems are typically not well-defined in the standard H^1-H^1 setting, we will introduce a suitable saddle point formulation in terms of weighted Sobolev spaces. Furthermore, we will discuss the numerical solution of such problems. Specifically, we employ an hp-discontinuous Galerkin method and derive an L^2-norm a posteriori error estimate. Numerical experiments demonstrate the effectiveness of the proposed error indicator in both the h- and hp-version setting. Indeed, in the latter case exponential convergence of the error is attained as the mesh is adaptively refined.

Lot production size problem and simulation of urban transport

OBJECTIVES AND STUDY METHOD: There are two subjects in this thesis: “Lot production size for a parallel machine scheduling problem with auxiliary equipment” and “Bus holding for a simulated traffic network”. Although these two themes seem unrelated, the main idea is the optimization of complex systems. The “Lot production size for a parallel machine scheduling problem with auxiliary equipment” deals with a manufacturing setting where sets of pieces form finished products. The aim is to maximize the profit of the finished products. Each piece may be processed in more than one mold. Molds must be mounted on machines with their corresponding installation setup times. The key point of our methodology is to solve the single period lot-sizing decisions for the finished products together with the piece-mold and the mold-machine assignments, relaxing the constraint that a single mold may not be used in two machines at the same time. For the “Bus holding for a simulated traffic network” we deal with One of the most annoying problems in urban bus operations is bus bunching, which happens when two or more buses arrive at a stop nose to tail. Bus bunching reflects an unreliable service that affects transit operations by increasing passenger-waiting times. This work proposes a linear mathematical programming model that establishes bus holding times at certain stops along a transit corridor to avoid bus bunching. Our approach needs real-time input, so we simulate a transit corridor and apply our mathematical model to the data generated. Thus, the inherent variability of a transit system is considered by the simulation, while the optimization model takes into account the key variables and constraints of the bus operation. CONTRIBUTIONS AND CONCLUSIONS: For the “Lot production size for a parallel machine scheduling problem with auxiliary equipment” the relaxation we propose able to find solutions more efficiently, moreover our experimental results show that most of the solutions verify that molds are non-overlapping even if they are installed on several machines. We propose an exact integer linear programming, a Relax&Fix heuristic, and a multistart greedy algorithm to solve this problem. Experimental results on instances based on real-world data show the efficiency of our approaches. The mathematical model and the algorithm for the lot production size problem, showed in this research, can be used for production planners to help in the scheduling of the manufacturing. For the “Bus holding for a simulated traffic network” most of the literature considers quadratic models that minimize passenger-waiting times, but they are harder to solve and therefore difficult to operate by real-time systems. On the other hand, our methodology reduces passenger-waiting times efficiently given our linear programming model, with the characteristic of applying control intervals just every 5 minutes.

Photovoltaic power forecast modeling with artificial neural networks

Dissertação de Mestrado, Engenharia Eletrónica e Telecomunicações, Faculdade de Ciências e Tecnologia, Universidade do Algarve, 2016

Determinantes da fraude financeira : a relação entre os aspectos de racionalidade e a desonestidade

Dissertação (mestrado)—Universidade de Brasília, Universidade Federal da Paraíba, Universidade Federal do Rio Grande do Norte, Programa Multiinstitucional e Inter-regional de Pós-Graduação em Ciências Contábeis, 2016.

Sistema inteligente para estimar a porosidade em sedimentos a partir da análise de sinais GPR

This Thesis presents the elaboration of a methodological propose for the development of an intelligent system, able to automatically achieve the effective porosity, in sedimentary layers, from a data bank built with information from the Ground Penetrating Radar GPR. The intelligent system was built to model the relation between the porosity (response variable) and the electromagnetic attribute from the GPR (explicative variables). Using it, the porosity was estimated using the artificial neural network (Multilayer Perceptron MLP) and the multiple linear regression. The data from the response variable and from the explicative variables were achieved in laboratory and in GPR surveys outlined in controlled sites, on site and in laboratory. The proposed intelligent system has the capacity of estimating the porosity from any available data bank, which has the same variables used in this Thesis. The architecture of the neural network used can be modified according to the existing necessity, adapting to the available data bank. The use of the multiple linear regression model allowed the identification and quantification of the influence (level of effect) from each explicative variable in the estimation of the porosity. The proposed methodology can revolutionize the use of the GPR, not only for the imaging of the sedimentary geometry and faces, but mainly for the automatically achievement of the porosity one of the most important parameters for the characterization of reservoir rocks (from petroleum or water)

Determinantes del precio del derecho de emisión europeo

[ES] Diversos estudios han investigado sobre los posibles determinantes del precio del derecho de emisión europeo. En este trabajo de fin de grado se pretende analizar qué factores influyen en el precio de este producto financiero y de qué manera lo hacen, además de comprobar posibles cambios en el funcionamiento del mercado. La metodología utilizada para llevar a cabo este análisis se basa principalmente en el modelo de regresión lineal general. A diferencia de otros estudios existentes, la muestra utilizada va desde 2008 hasta 2015, por lo que incluye la segunda fase (2008-2012) de este mercado de derechos de emisión y la tercera (2013-2015), lo que permite analizar las posibles diferencias de funcionamiento del mercado entre ambas fases. Los resultados obtenidos sostienen la existencia de este cambio estructural de manera que en la segunda fase los factores más influyentes son el gas natural y el petróleo, mientras que en la tercera fase el comportamiento del mercado cambia drásticamente de forma que el carbón parece ser el factor más influyente.

A Microdata Analysis Approach to Transport Infrastructure Maintenance

Maintenance of transport infrastructure assets is widely advocated as the key in minimizing current and future costs of the transportation network. While effective maintenance decisions are often a result of engineering skills and practical knowledge, efficient decisions must also account for the net result over an asset's life-cycle. One essential aspect in the long term perspective of transport infrastructure maintenance is to proactively estimate maintenance needs. In dealing with immediate maintenance actions, support tools that can prioritize potential maintenance candidates are important to obtain an efficient maintenance strategy. This dissertation consists of five individual research papers presenting a microdata analysis approach to transport infrastructure maintenance. Microdata analysis is a multidisciplinary field in which large quantities of data is collected, analyzed, and interpreted to improve decision-making. Increased access to transport infrastructure data enables a deeper understanding of causal effects and a possibility to make predictions of future outcomes. The microdata analysis approach covers the complete process from data collection to actual decisions and is therefore well suited for the task of improving efficiency in transport infrastructure maintenance. Statistical modeling was the selected analysis method in this dissertation and provided solutions to the different problems presented in each of the five papers. In Paper I, a time-to-event model was used to estimate remaining road pavement lifetimes in Sweden. In Paper II, an extension of the model in Paper I assessed the impact of latent variables on road lifetimes; displaying the sections in a road network that are weaker due to e.g. subsoil conditions or undetected heavy traffic. The study in Paper III incorporated a probabilistic parametric distribution as a representation of road lifetimes into an equation for the marginal cost of road wear. Differentiated road wear marginal costs for heavy and light vehicles are an important information basis for decisions regarding vehicle miles traveled (VMT) taxation policies. In Paper IV, a distribution based clustering method was used to distinguish between road segments that are deteriorating and road segments that have a stationary road condition. Within railway networks, temporary speed restrictions are often imposed because of maintenance and must be addressed in order to keep punctuality. The study in Paper V evaluated the empirical effect on running time of speed restrictions on a Norwegian railway line using a generalized linear mixed model.

The Effect of Climate Variability on Main Components of Cow Milk in Iran

The main purpose of this study is to assess the relationship between six bioclimatic indices for cattle (temperature humidity (THI), environmental stress (ESI), equivalent temperature (ESI), heat load (HLI), modified heat load (HLInew) and respiratory rate predictor(RRP)) and fundamental milk components (fat, protein, and milk yield) considering uncertainty. The climate parameters used to calculate the climate indices were taken from the NASA-Modern Era Retrospective-Analysis for Research and Applications (NASA-MERRA) reanalysis from 2002 to 2010. Cow milk data were considered for the same period from April to September when cows use natural pasture, with possibility for cows to choose to stay in the barn or to graze on the pasture in the pasturing system. The study is based on a linear regression analysis using correlations as a summarizing diagnostic. Bootstrapping is used to represent uncertainty estimation through resampling in the confidence intervals. To find the relationships between climate indices (THI, ETI, HLI, HLInew, ESI and RRP) and main components of cow milk (fat, protein and yield), multiple liner regression is applied. The least absolute shrinkage selection operator (LASSO) and the Akaike information criterion (AIC) techniques are applied to select the best model for milk predictands with the smallest number of climate predictors. Cross validation is used to avoid over-fitting. Based on results of investigation the effect of heat stress indices on milk compounds separately, we suggest the use of ESI and RRP in the summer and ESI in the spring. THI and HLInew are suggested for fat content and HLInew also is suggested for protein content in the spring season. The best linear models are found in spring between milk yield as predictands and THI, ESI,HLI, ETI and RRP as predictors with p-value < 0.001 and R2 0.50, 0.49. In summer, milk yield with independent variables of THI, ETI and ESI show the highest relation (p-value < 0.001) with R2 (0.69). For fat and protein the results are only marginal. It is strongly suggested that new and significant indices are needed to control critical heat stress conditions that consider more predictors of the effect of climate variability on animal products, such as sunshine duration, quality of pasture, the number of days of stress (NDS), the color of skin with attention to large black spots, and categorical predictors such as breed, welfare facility, and management system. This methodology is suggested for studies investigating the impacts of climate variability/change on food quality/security, animal science and agriculture using short term data considering uncertainty or data collection is expensive, difficult, or data with gaps.