Regression Models with Heteroscedasticity using Bayesian Approach

In this paper, we compare the performance of two statistical approaches for the analysis of data obtained from the social research area. In the first approach, we use normal models with joint regression modelling for the mean and for the variance heterogeneity. In the second approach, we use hierarchical models. In the first case, individual and social variables are included in the regression modelling for the mean and for the variance, as explanatory variables, while in the second case, the variance at level 1 of the hierarchical model depends on the individuals (age of the individuals), and in the level 2 of the hierarchical model, the variance is assumed to change according to socioeconomic stratum. Applying these methodologies, we analyze a Colombian tallness data set to find differences that can be explained by socioeconomic conditions. We also present some theoretical and empirical results concerning the two models. From this comparative study, we conclude that it is better to jointly modelling the mean and variance heterogeneity in all cases. We also observe that the convergence of the Gibbs sampling chain used in the Markov Chain Monte Carlo method for the jointly modeling the mean and variance heterogeneity is quickly achieved.

Influence diagnostics in nonlinear mixed-effects elliptical models

In this work we propose and analyze nonlinear elliptical models for longitudinal data, which represent an alternative to gaussian models in the cases of heavy tails, for instance. The elliptical distributions may help to control the influence of the observations in the parameter estimates by naturally attributing different weights for each case. We consider random effects to introduce the within-group correlation and work with the marginal model without requiring numerical integration. An iterative algorithm to obtain maximum likelihood estimates for the parameters is presented, as well as diagnostic results based on residual distances and local influence [Cook, D., 1986. Assessment of local influence. journal of the Royal Statistical Society - Series B 48 (2), 133-169; Cook D., 1987. Influence assessment. journal of Applied Statistics 14 (2),117-131; Escobar, L.A., Meeker, W.Q., 1992, Assessing influence in regression analysis with censored data, Biometrics 48, 507-528]. As numerical illustration, we apply the obtained results to a kinetics longitudinal data set presented in [Vonesh, E.F., Carter, R.L., 1992. Mixed-effects nonlinear regression for unbalanced repeated measures. Biometrics 48, 1-17], which was analyzed under the assumption of normality. (C) 2009 Elsevier B.V. All rights reserved.

Deviance residuals in generalised log-gamma regression models with censored observations

In this article, we compare three residuals based on the deviance component in generalised log-gamma regression models with censored observations. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and the empirical distribution of each residual is displayed and compared with the standard normal distribution. For all cases studied, the empirical distributions of the proposed residuals are in general symmetric around zero, but only a martingale-type residual presented negligible kurtosis for the majority of the cases studied. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended for the martingale-type residual in generalised log-gamma regression models with censored data. A lifetime data set is analysed under log-gamma regression models and a model checking based on the martingale-type residual is performed.

Bayesian estimation of regression parameters in elliptical measurement error models

The main object of this paper is to discuss the Bayes estimation of the regression coefficients in the elliptically distributed simple regression model with measurement errors. The posterior distribution for the line parameters is obtained in a closed form, considering the following: the ratio of the error variances is known, informative prior distribution for the error variance, and non-informative prior distributions for the regression coefficients and for the incidental parameters. We proved that the posterior distribution of the regression coefficients has at most two real modes. Situations with a single mode are more likely than those with two modes, especially in large samples. The precision of the modal estimators is studied by deriving the Hessian matrix, which although complicated can be computed numerically. The posterior mean is estimated by using the Gibbs sampling algorithm and approximations by normal distributions. The results are applied to a real data set and connections with results in the literature are reported. (C) 2011 Elsevier B.V. All rights reserved.

A new class of survival regression models with heavy-tailed errors: robustness and diagnostics

Birnbaum-Saunders models have largely been applied in material fatigue studies and reliability analyses to relate the total time until failure with some type of cumulative damage. In many problems related to the medical field, such as chronic cardiac diseases and different types of cancer, a cumulative damage caused by several risk factors might cause some degradation that leads to a fatigue process. In these cases, BS models can be suitable for describing the propagation lifetime. However, since the cumulative damage is assumed to be normally distributed in the BS distribution, the parameter estimates from this model can be sensitive to outlying observations. In order to attenuate this influence, we present in this paper BS models, in which a Student-t distribution is assumed to explain the cumulative damage. In particular, we show that the maximum likelihood estimates of the Student-t log-BS models attribute smaller weights to outlying observations, which produce robust parameter estimates. Also, some inferential results are presented. In addition, based on local influence and deviance component and martingale-type residuals, a diagnostics analysis is derived. Finally, a motivating example from the medical field is analyzed using log-BS regression models. Since the parameter estimates appear to be very sensitive to outlying and influential observations, the Student-t log-BS regression model should attenuate such influences. The model checking methodologies developed in this paper are used to compare the fitted models.

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.

Unsupervised learning to cluster the disease stages in parkinson's disease

Parkinson's disease (PD) is the second most common neurodegenerative disorder (after Alzheimer's disease) and directly affects upto 5 million people worldwide. The stages (Hoehn and Yaar) of disease has been predicted by many methods which will be helpful for the doctors to give the dosage according to it. So these methods were brought up based on the data set which includes about seventy patients at nine clinics in Sweden. The purpose of the work is to analyze unsupervised technique with supervised neural network techniques in order to make sure the collected data sets are reliable to make decisions. The data which is available was preprocessed before calculating the features of it. One of the complex and efficient feature called wavelets has been calculated to present the data set to the network. The dimension of the final feature set has been reduced using principle component analysis. For unsupervised learning k-means gives the closer result around 76% while comparing with supervised techniques. Back propagation and J4 has been used as supervised model to classify the stages of Parkinson's disease where back propagation gives the variance percentage of 76-82%. The results of both these models have been analyzed. This proves that the data which are collected are reliable to predict the disease stages in Parkinson's disease.

Six-Day System Test and Component test and System Simulation for Combitanks with Internal heat Exchangers

An international standard, ISO/DP 9459-4 has been proposed to establish a uniform standard of quality for small, factory-made solar heating systerns. In this proposal, system components are tested separatelyand total system performance is calculated using system simulations based on component model parameter values validated using the results from the component tests. Another approach is to test the whole system in operation under representative conditions, where the results can be used as a measure of the general system performance. The advantage of system testing of this form is that it is not dependent on simulations and the possible inaccuracies of the models. Its disadvantage is that it is restricted to the boundary conditions for the test. Component testing and system simulation is flexible, but requires an accurate and reliable simulation model.The heat store is a key component conceming system performance. Thus, this work focuses on the storage system consisting store, electrical auxiliary heater, heat exchangers and tempering valve. Four different storage system configurations with a volume of 750 litre were tested in an indoor system test using a six -day test sequence. A store component test and system simulation was carried out on one of the four configurations, applying the proposed standard for stores, ISO/DP 9459-4A. Three newly developed test sequences for intemalload side heat exchangers, not in the proposed ISO standard, were also carried out. The MULTIPORT store model was used for this work. This paper discusses the results of the indoor system test, the store component test, the validation of the store model parameter values and the system simulations.

Estimation of Parameters in Random Effect Models with Incidence Matrix Uncertainty

Random effect models have been widely applied in many fields of research. However, models with uncertain design matrices for random effects have been little investigated before. In some applications with such problems, an expectation method has been used for simplicity. This method does not include the extra information of uncertainty in the design matrix is not included. The closed solution for this problem is generally difficult to attain. We therefore propose an two-step algorithm for estimating the parameters, especially the variance components in the model. The implementation is based on Monte Carlo approximation and a Newton-Raphson-based EM algorithm. As an example, a simulated genetics dataset was analyzed. The results showed that the proportion of the total variance explained by the random effects was accurately estimated, which was highly underestimated by the expectation method. By introducing heuristic search and optimization methods, the algorithm can possibly be developed to infer the 'model-based' best design matrix and the corresponding best estimates.

First-principle data-driven models for assessment of motor disorders in Parkinson’s disease

Parkinson’s disease (PD) is an increasing neurological disorder in an aging society. The motor and non-motor symptoms of PD advance with the disease progression and occur in varying frequency and duration. In order to affirm the full extent of a patient’s condition, repeated assessments are necessary to adjust medical prescription. In clinical studies, symptoms are assessed using the unified Parkinson’s disease rating scale (UPDRS). On one hand, the subjective rating using UPDRS relies on clinical expertise. On the other hand, it requires the physical presence of patients in clinics which implies high logistical costs. Another limitation of clinical assessment is that the observation in hospital may not accurately represent a patient’s situation at home. For such reasons, the practical frequency of tracking PD symptoms may under-represent the true time scale of PD fluctuations and may result in an overall inaccurate assessment. Current technologies for at-home PD treatment are based on data-driven approaches for which the interpretation and reproduction of results are problematic.  The overall objective of this thesis is to develop and evaluate unobtrusive computer methods for enabling remote monitoring of patients with PD. It investigates first-principle data-driven model based novel signal and image processing techniques for extraction of clinically useful information from audio recordings of speech (in texts read aloud) and video recordings of gait and finger-tapping motor examinations. The aim is to map between PD symptoms severities estimated using novel computer methods and the clinical ratings based on UPDRS part-III (motor examination). A web-based test battery system consisting of self-assessment of symptoms and motor function tests was previously constructed for a touch screen mobile device. A comprehensive speech framework has been developed for this device to analyze text-dependent running speech by: (1) extracting novel signal features that are able to represent PD deficits in each individual component of the speech system, (2) mapping between clinical ratings and feature estimates of speech symptom severity, and (3) classifying between UPDRS part-III severity levels using speech features and statistical machine learning tools. A novel speech processing method called cepstral separation difference showed stronger ability to classify between speech symptom severities as compared to existing features of PD speech. In the case of finger tapping, the recorded videos of rapid finger tapping examination were processed using a novel computer-vision (CV) algorithm that extracts symptom information from video-based tapping signals using motion analysis of the index-finger which incorporates a face detection module for signal calibration. This algorithm was able to discriminate between UPDRS part III severity levels of finger tapping with high classification rates. Further analysis was performed on novel CV based gait features constructed using a standard human model to discriminate between a healthy gait and a Parkinsonian gait. The findings of this study suggest that the symptom severity levels in PD can be discriminated with high accuracies by involving a combination of first-principle (features) and data-driven (classification) approaches. The processing of audio and video recordings on one hand allows remote monitoring of speech, gait and finger-tapping examinations by the clinical staff. On the other hand, the first-principles approach eases the understanding of symptom estimates for clinicians. We have demonstrated that the selected features of speech, gait and finger tapping were able to discriminate between symptom severity levels, as well as, between healthy controls and PD patients with high classification rates. The findings support suitability of these methods to be used as decision support tools in the context of PD assessment.

Fitting spatial models in the R package: hglm

We present a new version of the hglm package for fittinghierarchical generalized linear models (HGLM) with spatially correlated random effects. A CAR family for conditional autoregressive random effects was implemented. Eigen decomposition of the matrix describing the spatial structure (e.g. the neighborhood matrix) was used to transform the CAR random effectsinto an independent, but heteroscedastic, gaussian random effect. A linear predictor is fitted for the random effect variance to estimate the parameters in the CAR model.This gives a computationally efficient algorithm for moderately sized problems (e.g. n<5000).

Fitting conditional and simultaneous autoregressive spatial models in hglm

We present a new version (> 2.0) of the hglm package for fitting hierarchical generalized linear models (HGLMs) with spatially correlated random effects. CAR() and SAR() families for conditional and simultaneous autoregressive random effects were implemented. Eigen decomposition of the matrix describing the spatial structure (e.g., the neighborhood matrix) was used to transform the CAR/SAR random effects into an independent, but eteroscedastic, Gaussian random effect. A linear predictor is fitted for the random effect variance to estimate the parameters in the CAR and SAR models. This gives a computationally efficient algorithm for moderately sized problems.

Predictability of equity models

In this study, we verify the existence of predictability in the Brazilian equity market. Unlike other studies in the same sense, which evaluate original series for each stock, we evaluate synthetic series created on the basis of linear models of stocks. Following Burgess (1999), we use the “stepwise regression” model for the formation of models of each stock. We then use the variance ratio profile together with a Monte Carlo simulation for the selection of models with potential predictability. Unlike Burgess (1999), we carry out White’s Reality Check (2000) in order to verify the existence of positive returns for the period outside the sample. We use the strategies proposed by Sullivan, Timmermann & White (1999) and Hsu & Kuan (2005) amounting to 26,410 simulated strategies. Finally, using the bootstrap methodology, with 1,000 simulations, we find strong evidence of predictability in the models, including transaction costs.

Estimating and forecasting the volatility of Brazilian finance series using arch models (Preliminary Version)

The goal of this paper is to present a comprehensive emprical analysis of the return and conditional variance of four Brazilian …nancial series using models of the ARCH class. Selected models are then compared regarding forecasting accuracy and goodness-of-…t statistics. To help understanding the empirical results, a self-contained theoretical discussion of ARCH models is also presented in such a way that it is useful for the applied researcher. Empirical results show that although all series share ARCH and are leptokurtic relative to the Normal, the return on the US$ has clearly regime switching and no asymmetry for the variance, the return on COCOA has no asymmetry, while the returns on the CBOND and TELEBRAS have clear signs of asymmetry favoring the leverage e¤ect. Regarding forecasting, the best model overall was the EGARCH(1; 1) in its Gaussian version. Regarding goodness-of-…t statistics, the SWARCH model did well, followed closely by the Student-t GARCH(1; 1)

Product placement in movies: a cross cultural study between Brazil and the USA

The broader objective of this study undertaking can briefly be articulated in particulate aims as follows: to measure the attitudes of consumers regarding the brand displayed by this strategy as well as to highlight recall, recognition and purchase intentions generated by product placement on consumers. In addition, check the differences and similarities between the behavior of Brazilian and American consumers caused by the influence of product placements. The study was undertaken targeting consumer audience in Brazil and the U.S. A rang3 modeling set ups were performed in order to realign study instruments and hypothesis towards the research objectives. This study gave focus on the following hypothesized models. H1: Consumers / Participants who viewed the brands / products in the movie have a higher brand / product recall compared to the consumers / participants who did not view the brands / products in the movie. H2: US Consumers / Participants are able to recognize and recall brands / products which appear in the background of the movie than Brazil. H3: Consumers / participants from USA are more accepting of product placements compared to their counterparts in Brazil. H4: There are discernible similarities in consumer / participant brand attitudes and purchase intentions in consumers / participants from USA and Brazil in spite of the fact that their country of origin is different. Cronbach’s Alpha Coefficient ensured the reliability of survey instruments. The study involved the use of the Structural Equation Modeling (SEM) for the hypothesis testing. This study used the Confirmatory Factor Analysis (CFA) to assess both the convergent and discriminant validities instead of using the Exploratory Factor Analysis (EFA) or the Principal Component Analysis (PCA). This reinforced for the use of the regression Chi Square and T statistical tests in further. Only hypothesis H3 was rejected, the rest were not. T test provided insight findings on specific subgroup significant differences. In the SEM testing, the error variance for product placement attitudes was negative for both the groups. On this The Heywood Case came in handy to fix negative values. The researcher used both quantitative and qualitative approach where closed ended questionnaires and interviews respectively were used to collect primary data. The results were additionally provided with tabulations. It can be concluded that, product placement varies markedly in the U.S. from Brazil based on the influence a range of factors provided in the study. However, there are elements of convergence probably driven by the convergence in technology. In order, product placement to become more competitive in the promotional marketing, there will be the need for researchers to extend focus from the traditional variables and add knowledge on the conventional marketplace factors that is the sell-ability of the product placement technologies and strategies.