Some restriction tests in a new class of regression models for proportions

The main purpose of this work is to study the behaviour of Skovgaard`s [Skovgaard, I.M., 2001. Likelihood asymptotics. Scandinavian journal of Statistics 28, 3-32] adjusted likelihood ratio statistic in testing simple hypothesis in a new class of regression models proposed here. The proposed class of regression models considers Dirichlet distributed observations, and the parameters that index the Dirichlet distributions are related to covariates and unknown regression coefficients. This class is useful for modelling data consisting of multivariate positive observations summing to one and generalizes the beta regression model described in Vasconcellos and Cribari-Neto [Vasconcellos, K.L.P., Cribari-Neto, F., 2005. Improved maximum likelihood estimation in a new class of beta regression models. Brazilian journal of Probability and Statistics 19,13-31]. We show that, for our model, Skovgaard`s adjusted likelihood ratio statistics have a simple compact form that can be easily implemented in standard statistical software. The adjusted statistic is approximately chi-squared distributed with a high degree of accuracy. Some numerical simulations show that the modified test is more reliable in finite samples than the usual likelihood ratio procedure. An empirical application is also presented and discussed. (C) 2009 Elsevier B.V. All rights reserved.

The beta Laplace distribution

The Laplace distribution is one of the earliest distributions in probability theory. For the first time, based on this distribution, we propose the so-called beta Laplace distribution, which extends the Laplace distribution. Various structural properties of the new distribution are derived, including expansions for its moments, moment generating function, moments of the order statistics, and so forth. We discuss maximum likelihood estimation of the model parameters and derive the observed information matrix. The usefulness of the new model is illustrated by means of a real data set. (C) 2011 Elsevier B.V. All rights reserved.

Birnbaum-Saunders nonlinear regression models

We introduce, for the first time, a new class of Birnbaum-Saunders nonlinear regression models potentially useful in lifetime data analysis. The class generalizes the regression model described by Rieck and Nedelman [Rieck, J.R., Nedelman, J.R., 1991. A log-linear model for the Birnbaum-Saunders distribution. Technometrics 33, 51-60]. We discuss maximum-likelihood estimation for the parameters of the model, and derive closed-form expressions for the second-order biases of these estimates. Our formulae are easily computed as ordinary linear regressions and are then used to define bias corrected maximum-likelihood estimates. Some simulation results show that the bias correction scheme yields nearly unbiased estimates without increasing the mean squared errors. Two empirical applications are analysed and discussed. Crown Copyright (C) 2009 Published by Elsevier B.V. All rights reserved.

Bias correction in a multivariate normal regression model with general parameterization

This paper derives the second-order biases Of maximum likelihood estimates from a multivariate normal model where the mean vector and the covariance matrix have parameters in common. We show that the second order bias can always be obtained by means of ordinary weighted least-squares regressions. We conduct simulation studies which indicate that the bias correction scheme yields nearly unbiased estimators. (C) 2009 Elsevier B.V. All rights reserved.

An Analysis of the Telecommunications Business in China by Linear Regression

In this paper, we study the influence of the National Telecom Business Volume by the data in 2008 that have been published in China Statistical Yearbook of Statistics. We illustrate the procedure of modeling “National Telecom Business Volume” on the following eight variables, GDP, Consumption Levels, Retail Sales of Social Consumer Goods Total Renovation Investment, the Local Telephone Exchange Capacity, Mobile Telephone Exchange Capacity, Mobile Phone End Users, and the Local Telephone End Users. The testing of heteroscedasticity and multicollinearity for model evaluation is included. We also consider AIC and BIC criterion to select independent variables, and conclude the result of the factors which are the optimal regression model for the amount of telecommunications business and the relation between independent variables and dependent variable. Based on the final results, we propose several recommendations about how to improve telecommunication services and promote the economic development.

A Note on Proxy Variables and Instrument Variable Regression

This is a note about proxy variables and instruments for identification of structural parameters in regression models. We have experienced that in the econometric textbooks these two issues are treated separately, although in practice these two concepts are very often combined. Usually, proxy variables are inserted in instrument variable regressions with the motivation they are exogenous. Implicitly meaning they are exogenous in a reduced form model and not in a structural model. Actually if these variables are exogenous they should be redundant in the structural model, e.g. IQ as a proxy for ability. Valid proxies reduce unexplained variation and increases the efficiency of the estimator of the structural parameter of interest. This is especially important in situations when the instrument is weak. With a simple example we demonstrate what is required of a proxy and an instrument when they are combined. It turns out that when a researcher has a valid instrument the requirements on the proxy variable is weaker than if no such instrument exists

Improving the precision of the accumulated oxygen deficit using VO2-power regression points from below and above the lactate threshold

The accumulated oxygen deficit (AOD) method assumes a linear VO₂-power relationship for exercise intensities increasing from below the lactate threshold (BLT) to above the lactate threshold (ALT). Factors that were likely to effect the linearity of the VO₂-power regression and the precision of the estimated total energy demand (ETED) were investigated. These included the slow component of VO₂ kinetics (SC), a forced resting y-intercept and exercise intensities BLT and ALT. Criteria for linearity and precision included the Pearson correlation coefficient (PCC) of the VO₂-power relationship, the length of the 95% confidence interval (95% CI) of the ETED and the standard error of the predicted value (SEP), respectively. Eight trained male and one trained female triathlete completed the required cycling tests to establish the AOD when pedalling at 80 rev/min. The influence of the SC on the linear extrapolation of the ETED was reduced by measuring VO₂ after three min of exercise. Measuring VO₂ at this time provided a new linear extrapolation method consisting of ten regression points spread evenly from BLT and ALT. This method produced an ETED with increased precision compared to using regression equations developed from intensities BLT with no forced y-intercept value; (95%CI (L), 0.70±0.26 versus 1.85±1.10, P<0.01; SEP(L/Watt), 0.07±0.02 versus 0.28±0.17; P<0.01). Including a forced y-intercept value with five regression points either BLT or ALT increased the precision of estimating the total energy demand to the same level as when using 10 regression points, (5 points BLT + y-intercept versus 5 points ALT + y-intercept versus 10 points; 95%CI(l), 0.61±0.32, 0.87±0.40, 0.70±0.26; SEP(L/Watt), 0.07±0.03, 0.08±0.04, 0.07±0.02; p>0.05). The VO₂-power regression can be designed using a reduced number of regression points... ABSTRACT FROM AUTHOR

Solving regression problems using competitive ensemble models

The use of ensemble models in many problem domains has increased significantly in the last fewyears. The ensemble modeling, in particularly boosting, has shown a great promise in improving predictive performance of a model. Combining the ensemble members is normally done in a co-operative fashion where each of the ensemble members performs the same task and their predictions are aggregated to obtain the improved performance. However, it is also possible to combine the ensemble members in a competitive fashion where the best prediction of a relevant ensemble member is selected for a particular input. This option has been previously somewhat overlooked. The aim of this article is to investigate and compare the competitive and co-operative approaches to combining the models in the ensemble. A comparison is made between a competitive ensemble model and that of MARS with bagging, mixture of experts, hierarchical mixture of experts and a neural network ensemble over several public domain regression problems that have a high degree of nonlinearity and noise. The empirical results showa substantial advantage of competitive learning versus the co-operative learning for all the regression problems investigated. The requirements for creating the efficient ensembles and the available guidelines are also discussed.

Improving an inverse model of sheet metal forming by neural network based regression

An inverse model for a sheet meta l forming process aims to determine the initial parameter levels required to form the final formed shape. This is a difficult problem that is usually approached by traditional methods such as finite element analysis. Formulating the problem as a classification problem makes it possible to use well established classification algorithms, such as decision trees. Classification is, however, generally based on a winner-takes-all approach when associating the output value with the corresponding class. On the other hand, when formulating the problem as a regression task, all the output values are combined to produce the corresponding class value. For a multi-class problem, this may result in very different associations compared with classification between the output of the model and the corresponding class. Such formulation makes it possible to use well known regression algorithms, such as neural networks. In this paper, we develop a neural network based inverse model of a sheet forming process, and compare its performance with that of a linear model. Both models are used in two modes, classification mode and a function estimation mode, to investigate the advantage of re-formulating the problem as a function estimation. This results in large improvements in the recognition rate of set-up parameters of a sheet metal forming process for both models, with a neural network model achieving much more accurate parameter recognition than a linear model.

There's SEM and 'SEM' : a critique of the use of PLS regression in information systems research

In disciplines other than IS, the use of covariance-based structural equation modelling (SEM) is the mainstream method for SEM analysis, and for confirmatory factor analysis (CFA). Yet a body of IS literature has developed arguing that PLS regression is a superior tool for these analyses, and for establishing reliability and validity. Despite these claims, the views underlying this PLS literature are not universally shared. In this paper the authors review the PLS and mainstream SEM literatures, and describe the key differences between the two classes of tools. The paper also canvasses why PLS regression is rarely used in management, marketing, organizational behaviour, and that branch of psychology concerned with good measurement – psychometrics. The paper offers some practical options to Australasian researchers seeking greater mastery of SEM, and also acts as a roadmap for readers who want to check for themselves what the mainstream SEM literature has to say.

Publication selection bias in minimum-wage research? A meta-regression analysis

Card and Krueger's meta-analysis of the employment effects of minimum wages challenged existing theory. Unfortunately, their meta-analysis confused publication selection with the absence of a genuine empirical effect. We apply recently developed meta-analysis methods to 64 US minimum-wage studies and corroborate that Card and Krueger's findings were nevertheless correct. The minimum-wage effects literature is contaminated by publication selection bias, which we estimate to be slightly larger than the average reported minimum-wage effect. Once this publication selection is corrected, little or no evidence of a negative association between minimum wages and employment remains.

Unions and profits : a meta-regression analysis

The effect of unions on profits continues to be an unresolved theoretical and empirical issue. In this paper, clustered data analysis and hierarchical linear meta-regression models are applied to the population of forty-five econometric studies that report 532 estimates of the direct effect of unions on profits. Unions have a significant negative effect on profits in the United States, and this effect is larger when market-based measures of profits are used. Separate meta-regression analyses are used to identify the effects of market power and long-lived assets on profits, as well as the sources of union-profit effects. The accumulated evidence rejects market power as a source of union-profit effects. While the case is not yet proven, there is some evidence in support of the appropriation of quasi-rent hypothesis. There is a clear need for further American and non-American primary research in this area.

Estimating the total energy demand for supra-maximal exercise using the VO2-power regression from an incremental exercise test

The VO_2-power regression and estimated total energy demand for a 6-minute supramaximal exercise test was predicted from a continuous incremental exercise test. Sub-maximal VO_2- power co-ordinates were established from the last 40 seconds(s) of 150-second exercise stages. The precision of the estimated total energy demand was determined using the 95% confidence interval (95% CI) of the estimated total energy demand. The linearity of the individual VO_2-power regression equations was determined using Pearson's correlation coefficient. The mean 95% CI of the estimated total energy demand was 5.9±2.5 mL O₂ Eq•^-1kg•min^-1, and the mean correlation coefficient was 0.9942±0.0042. The current study contends that the sub-maximal VO_2-power co-ordinates from a continuous incremental exercise test can be used to estimate supra-maximal energy demand without compromising the precision of the accumulated oxygen deficit (AOD) method.

Meta-regression analysis as the socio-economics of economics research

Meta-regression analysis (MRA) provides an empirical framework through which to integrate disparate economics research results, filter out likely publication selection bias, and explain their wide variation using socio-economic and econometric explanatory variables. In dozens of applications, MRA has found excess variation among reported research findings, some of which is explained by socio-economic variables (e.g., researchers’ gender). MRA can empirically model and test socio-economic theories about economics research. Here, we make two strong claims: socio-economic MRAs, broadly conceived, explain much of the excess variation routinely found in empirical economics research; whereas, any other type of literature review (or summary) is biased.