Which formula for national happiness?

© 2019 Elsevier Ltd. All rights reserved.The World Happiness Report is published by the United Nations Sustainable Development Solutions Network and contains an international ranking of national average happiness, as measured by surveys of personal life evaluations. It also contains an analysis which tries to explain the happiness figures from more than 150 countries using data on six key variables. That analysis assumes the factors combine in an additive manner and therefore operate independently of each other. By contrast, we explore a multiplicative model, which allows for interactivity or synergy between factors, as well as the possibility of diminishing marginal benefit at higher levels of achievement. We find that this model provides a better fit to the data and is therefore superior in its explanatory power. The implication for policy-makers is that they should focus on improving those factors which are the lowest for their nation as this will provide greater relative benefits to subjective well-being. At an individual level this means focusing on improving conditions for those who are experiencing the lowest levels of well-being.Peer reviewe

Fitting an Equation to Data Impartially

© 2023 by the author. Licensee MDPI, Basel, Switzerland. This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY), https://creativecommons.org/licenses/by/4.0/We consider the problem of fitting a relationship (e.g., a potential scientific law) to data involving multiple variables. Ordinary (least squares) regression is not suitable for this because the estimated relationship will differ according to which variable is chosen as being dependent, and the dependent variable is unrealistically assumed to be the only variable which has any measurement error (noise). We present a very general method for estimating a linear functional relationship between multiple noisy variables, which are treated impartially, i.e., no distinction between dependent and independent variables. The data are not assumed to follow any distribution, but all variables are treated as being equally reliable. Our approach extends the geometric mean functional relationship to multiple dimensions. This is especially useful with variables measured in different units, as it is naturally scale invariant, whereas orthogonal regression is not. This is because our approach is not based on minimizing distances, but on the symmetric concept of correlation. The estimated coefficients are easily obtained from the covariances or correlations, and correspond to geometric means of associated least squares coefficients. The ease of calculation will hopefully allow widespread application of impartial fitting to estimate relationships in a neutral way.Peer reviewe

On constructing a composite indicator with multiplicative aggregation and the avoidance of zero weights in DEA

Peer reviewe

A novel healthcare resource allocation decision support tool: A forecasting-simulation-optimization approach

© 2020 Informa UK Limited, trading as Taylor & Francis Group. This is an accepted manuscript of an article published by Taylor & Francis in Journal of the Operational Research Society on 03 Feb 2020, available online: https://doi.org/10.1080/01605682.2019.1700186.The increasing pressures on the healthcare system in the UK are well documented. The solution lies in making best use of existing resources (e.g. beds), as additional funding is not available. Increasing demand and capacity shortages are experienced across all specialties and services in hospitals. Modelling at this level of detail is a necessity, as all the services are interconnected, and cannot be assumed to be independent of each other. Our review of the literature revealed two facts; First an entire hospital model is rare, and second, use of multiple OR techniques are applied more frequently in recent years. Hybrid models which combine forecasting, simulation and optimization are becoming more popular. We developed a model that linked each and every service and specialty including A&E, and outpatient and inpatient services, with the aim of, (1) forecasting demand for all the specialties, (2) capturing all the uncertainties of patient pathway within a hospital setting using discrete event simulation, and (3) developing a linear optimization model to estimate the required bed capacity and staff needs of a mid-size hospital in England (using essential outputs from simulation). These results will bring a different perspective to key decision makers with a decision support tool for short and long term strategic planning to make rational and realistic plans, and highlight the benefits of hybrid models.Peer reviewe

Objective weights for scoring: the automatic democratic method

When comparing performance (of products, services, entities, etc.), multiple attributes are involved. This paper deals with a way of weighting these attributes when one is seeking an overall score. It presents an objective approach to generating the weights in a scoring formula which avoids personal judgement. The first step is to find the maximum possible score for each assessed entity. These upper bound scores are found using Data Envelopment Analysis. In the second step the weights in the scoring formula are found by regressing the unique DEA scores on the attribute data. Reasons for using least squares and avoiding other distance measures are given. The method is tested on data where the true scores and weights are known. The method enables the construction of an objective scoring formula which has been generated from the data arising from all assessed entities and is, in that sense, democratic

Investment Volatility: A Critique of Standard Beta Estimation and a Simple Way Forward

Beta is a widely used quantity in investment analysis. We review the common interpretations that are applied to beta in finance and show that the standard method of estimation - least squares regression - is inconsistent with these interpretations. We present the case for an alternative beta estimator which is more appropriate, as well as being easier to understand and to calculate. Unlike regression, the line fit we propose treats both variables in the same way. Remarkably, it provides a slope that is precisely the ratio of the volatility of the investment's rate of return to the volatility of the market index rate of return (or the equivalent excess rates of returns). Hence, this line fitting method gives an alternative beta, which corresponds exactly to the relative volatility of an investment - which is one of the usual interpretations attached to beta.