Multicollinearity and financial constraint in investment decisions: a Bayesian generalized ridge regression

This paper addresses the investment decisions considering the presence of financial constraints of 373 large Brazilian firms from 1997 to 2004, using panel data. A Bayesian econometric model was used considering ridge regression for multicollinearity problems among the variables in the model. Prior distributions are assumed for the parameters, classifying the model into random or fixed effects. We used a Bayesian approach to estimate the parameters, considering normal and Student t distributions for the error and assumed that the initial values for the lagged dependent variable are not fixed, but generated by a random process. The recursive predictive density criterion was used for model comparisons. Twenty models were tested and the results indicated that multicollinearity does influence the value of the estimated parameters. Controlling for capital intensity, financial constraints are found to be more important for capital-intensive firms, probably due to their lower profitability indexes, higher fixed costs and higher degree of property diversification.

Use of ridge regression for the prediction of early growth performance in crossbred calves

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Multicollinearity and financial constraint in investment decisions: a bayesian generalized ridge regression

This paper addresses the investment decisions considering the presence of financial constraints of 373 large Brazilian firms from 1997 to 2004, using panel data. A Bayesian econometric model was used considering ridge regression for multicollinearity problems among the variables in the model. Prior distributions are assumed for the parameters, classifying the model into random or fixed effects. We used a Bayesian approach to estimate the parameters, considering normal and Student t distributions for the error and assumed that the initial values for the lagged dependent variable are not fixed, but generated by a random process. The recursive predictive density criterion was used for model comparisons. Twenty models were tested and the results indicated that multicollinearity does influence the value of the estimated parameters. Controlling for capital intensity, financial constraints are found to be more important for capital-intensive firms, probably due to their lower profitability indexes, higher fixed costs and higher degree of property diversification.

DISTRIBUTION FUNCTIONS, MEAN SQUARED ERRORS, AND CONFIDENCE LIMITS FOR RIDGE REGRESSION ESTIMATORS

A large number of ridge regression estimators have been proposed and used with little knowledge of their true distributions. Because of this lack of knowledge, these estimators cannot be used to test hypotheses or to form confidence intervals.^ This paper presents a basic technique for deriving the exact distribution functions for a class of generalized ridge estimators. The technique is applied to five prominent generalized ridge estimators. Graphs of the resulting distribution functions are presented. The actual behavior of these estimators is found to be considerably different than the behavior which is generally assumed for ridge estimators.^ This paper also uses the derived distributions to examine the mean squared error properties of the estimators. A technique for developing confidence intervals based on the generalized ridge estimators is also presented. ^

THE IMPROVEMENT REGION IN RIDGE REGRESSION

One of the difficulties in the practical application of ridge regression is that, for a given data set, it is unknown whether a selected ridge estimator has smaller squared error than the least squares estimator. The concept of the improvement region is defined, and a technique is developed which obtains approximate confidence intervals for the value of ridge k which produces the maximum reduction in mean squared error. Two simulation experiments were conducted to investigate how accurate these approximate confidence intervals might be. ^

Prevendo inflação usando ridge regressions

Este estudo tem como objetivo analisar o desempenho de vários modelos econométricos ao prever Inflação . Iniciamos o trabalho utilizando como base de comparação para todos os modelos a tradicional curva de Phillips que usa a taxa de desemprego como variável explicativa para diferenças de preço. Dentre os modelos analisados temos univariados e bivariados, sendo estes últimos uma curva de Phillips alternativa já que apenas sustitui a variável desemprego por outra variável macroeconômica. Além destes modelos também comparamos o desempenho de previsão de modelos que usam como covariadas uma combinação das previsões dos modelos anteriores (univariados e bivariados). O resultado deste estudo aponta a combinação de modelos por "ridge regression" como uma técnica - dentre as analisadas para combinação de previsões - de menor erro de previsão sempre; sendo alcançado pela combinação da média em apenas um dos casos analisados. No entanto, a combinação de previsões não apresentou melhor resultado que algumas das covariadas testadas em modelos bivariados

Comparison of Some Improved Estimators for Linear Regression Model under Different Conditions

Multiple linear regression model plays a key role in statistical inference and it has extensive applications in business, environmental, physical and social sciences. Multicollinearity has been a considerable problem in multiple regression analysis. When the regressor variables are multicollinear, it becomes difficult to make precise statistical inferences about the regression coefficients. There are some statistical methods that can be used, which are discussed in this thesis are ridge regression, Liu, two parameter biased and LASSO estimators. Firstly, an analytical comparison on the basis of risk was made among ridge, Liu and LASSO estimators under orthonormal regression model. I found that LASSO dominates least squares, ridge and Liu estimators over a significant portion of the parameter space for large dimension. Secondly, a simulation study was conducted to compare performance of ridge, Liu and two parameter biased estimator by their mean squared error criterion. I found that two parameter biased estimator performs better than its corresponding ridge regression estimator. Overall, Liu estimator performs better than both ridge and two parameter biased estimator.

Generalized linear and generalized additive models in studies of species distributions: setting the scene

An important statistical development of the last 30 years has been the advance in regression analysis provided by generalized linear models (GLMs) and generalized additive models (GAMs). Here we introduce a series of papers prepared within the framework of an international workshop entitled: Advances in GLMs/GAMs modeling: from species distribution to environmental management, held in Riederalp, Switzerland, 6-11 August 2001.We first discuss some general uses of statistical models in ecology, as well as provide a short review of several key examples of the use of GLMs and GAMs in ecological modeling efforts. We next present an overview of GLMs and GAMs, and discuss some of their related statistics used for predictor selection, model diagnostics, and evaluation. Included is a discussion of several new approaches applicable to GLMs and GAMs, such as ridge regression, an alternative to stepwise selection of predictors, and methods for the identification of interactions by a combined use of regression trees and several other approaches. We close with an overview of the papers and how we feel they advance our understanding of their application to ecological modeling.

Association between Inflammatory and Obesity Markers in a Swiss Population-Based Sample (CoLaus Study).

Objective: To assess the associations between obesity markers (BMI, waist circumference and %body fat) and inflammatory markers (interleukin-1β (IL-1β); interleukin-6 (IL-6); tumor necrosis factor-α (TNF-α) and high-sensitivity C-reactive protein (hs-CRP)). Methods: Population sample of 2,884 men and 3,201 women aged 35-75 years. Associations were assessed using ridge regression adjusting for age, leisure-time physical activity, and smoking. Results: No differences were found in IL-1β levels between participants with increased obesity markers and healthy counterparts; multivariate regression showed %body fat to be negatively associated with IL-1β. Participants with high %body fat or abdominal obesity had higher IL-6 levels, but no independent association between IL-6 levels and obesity markers was found on multivariate regression. Participants with abdominal obesity had higher TNF-α levels, and positive associations were found between TNF-α levels and waist circumference in men and between TNF-α levels and BMI in women. Obese participants had higher hs-CRP levels, and these differences persisted after multivariate adjustment; similarly, positive associations were found between hs-CRP levels and all obesity markers studied. Conclusion: Obesity markers are differentially associated with cytokine levels. %Body fat is negatively associated with IL-1β; BMI (in women) and waist circumference (in men) are associated with TNF-α; all obesity markers are positively associated with hs-CRP. Copyright © 2012 S. Karger GmbH, Freiburg.

Implisiittisen kalibroinnin soveltamismahdollisuudet kemiantekniikassa

Työn taustalla oli tavoite parantaa erään teollisuusprosessin toimintaa ja sen tuottoa mallintamalla reaktiovaiheen alussa tapahtuvan välituotteen muodostumisen reaktiokinetiikka sekä perinteisellä tavalla että implisiittisellä kalibroinnilla. Toisena tavoitteena oli selvittää, kuinka implisiittistä kalibrointia voidaan yleisemmin hyödyntää kemiantekniikassa. Implisiittinen kalibrointi on menetelmä, jolla voidaan ratkaista jonkin teoreettisen mallin parametrit suoraan epäsuorasta mittausdatasta (esimerkiksi spektreistä) lähes kokonaan ilman off-line analyysejä. Tämän työn kirjallisuusosassa on esitetty implisiittisen kalibroinnin toimintaperiaate sekä lyhyesti FTIR-spektrometrian perusteita. Työn kokeellisessa osassa on estimoitu tutkitun välituotteen muodostumisen kineettiset parametrit sekä tavanomaisella parametriestimoinnilla että implisiittisellä kalibroinnilla. Lisäksi kokeellisessa osassa on selvitetty lyhyesti tutkitun prosessin FTIR-spektrien lämpötilariippuvuuksia ja esitetty neljä mahdollista uutta sovelluskohdetta implisiittiselle kalibroinnille. Tavanomaisella parametriestimoinnilla saatiin estimoitua varsin yksiselitteiset arvot kineettisille parametreille. Myös mallin sovitus koedataan on hyvä kolmessa kokeessa viidestä. Parametriestimointi implisiittisellä kalibroinnilla onnistui lupaavasti vaikka tulokset eivät ole aivan niin hyviä kuin tavanomaisessa parametriestimoinnissa. Parhaat tulokset implisiittisessä kalibroinnissa saavutettiin suoralla kalibrointitavalla GRR (Generalized Ridge Regression)-kalibrointimenetelmää käyttämällä.

Hire me: Computational inference of hirability in employment interviews based on nonverbal behavior

Understanding the basis on which recruiters form hirability impressions for a job applicant is a key issue in organizational psychology and can be addressed as a social computing problem. We approach the problem from a face-to-face, nonverbal perspective where behavioral feature extraction and inference are automated. This paper presents a computational framework for the automatic prediction of hirability. To this end, we collected an audio-visual dataset of real job interviews where candidates were applying for a marketing job. We automatically extracted audio and visual behavioral cues related to both the applicant and the interviewer. We then evaluated several regression methods for the prediction of hirability scores and showed the feasibility of conducting such a task, with ridge regression explaining 36.2% of the variance. Feature groups were analyzed, and two main groups of behavioral cues were predictive of hirability: applicant audio features and interviewer visual cues, showing the predictive validity of cues related not only to the applicant, but also to the interviewer. As a last step, we analyzed the predictive validity of psychometric questionnaires often used in the personnel selection process, and found that these questionnaires were unable to predict hirability, suggesting that hirability impressions were formed based on the interaction during the interview rather than on questionnaire data.

Sélection de modèle d'imputation à partir de modèles bayésiens hiérarchiques linéaires multivariés

Les logiciels utilisés sont Splus et R.

A comparative review of dimension reduction methods in approximate Bayesian computation

Approximate Bayesian computation (ABC) methods make use of comparisons between simulated and observed summary statistics to overcome the problem of computationally intractable likelihood functions. As the practical implementation of ABC requires computations based on vectors of summary statistics, rather than full data sets, a central question is how to derive low-dimensional summary statistics from the observed data with minimal loss of information. In this article we provide a comprehensive review and comparison of the performance of the principal methods of dimension reduction proposed in the ABC literature. The methods are split into three nonmutually exclusive classes consisting of best subset selection methods, projection techniques and regularization. In addition, we introduce two new methods of dimension reduction. The first is a best subset selection method based on Akaike and Bayesian information criteria, and the second uses ridge regression as a regularization procedure. We illustrate the performance of these dimension reduction techniques through the analysis of three challenging models and data sets.

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).

A comparison of statistical methods for genomic selection in a mice population

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)