Model building with multiple dependent variables and constraints

The most widely used method for finding relationships between several quantities is multiple regression. This however is restricted to a single dependent variable. We present a more general method which allows models to be constructed with multiple variables on both sides of an equation and which can be computed easily using a spreadsheet program. The underlying principle (originating from canonical correlation analysis) is that of maximising the correlation between the two sides of the model equation. This paper presents a fitting procedure which makes it possible to force the estimated--model to satisfy constraint conditions which it is required to possess, these may arise from--theory, prior knowledge or be intuitively obvious. We also show that the least squares approach--to the problem is inadequate as it produces models which are not scale invariant.Peer reviewe

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

Thanks are due to Markus Becker for useful comments on an earlier version of this essay. 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 investments 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. Keywords- investment analysis, financial risk, volatility, systematic risk

Fitting equations to data with the perfect correlation relationship

Copyright and all rights therein are retained by the authors. All persons copying this information are expected to adhere to the terms and conditions invoked by each author's copyright. These works may not be re-posted without the explicit permission of the copyright holdersWe present a simple method for estimating a single relationship between multiple variables, which are all treated symmetrically i.e. there is no distinction between dependent and independent variables. This is of interest when estimating a law from observations in the natural sciences, although workers in the social sciences may also find this of interest when fitting relationships to data. All variables are assumed to have error but no information about the error is assumed. Unlike other symmetric methods, the weights or coefficients can be obtained easily – indeed, these can be expressed in terms of least squares coefficients. The approach has the important properties of providing a functional relationship which is scale invariant and uniqu

Selecting the best statistical distribution using multiple criteria

When selecting a statistical distribution to describe a set of data there are a number of criteria that can be used. Rather than select one of these criteria, we look at how multiple criteria can be combined to make the final selection. Two approaches have previously been presented in Computers and Industrial Engineering. We review these, and present a simpler method based on multiplicative aggregation. This has the advantage of being able to combine measures which are not measured on the same scale without having to use a normalisation procedure. Moreover, this method is scale-invariant, thus re-scaling the criteria values does not affect the final ranking. The method requires strictly positive criteria values measured on a ratio scale.Peer reviewe

A better measure of relative prediction accuracy for model selection and model estimation

Surveys show that the mean absolute percentage error (MAPE) is the most widely used measure of forecast accuracy in businesses and organizations. It is however, biased: When used to select among competing prediction methods it systematically selects those whose predictions are too low. This is not widely discussed and so is not generally known among practitioners. We explain why this happens. We investigate an alternative relative accuracy measure which avoids this bias: the log of the accuracy ratio: log (prediction / actual). Relative accuracy is particularly relevant if the scatter in the data grows as the value of the variable grows (heteroscedasticity). We demonstrate using simulations that for heteroscedastic data (modelled by a multiplicative error factor) the proposed metric is far superior to MAPE for model selection. Another use for accuracy measures is in fitting parameters to prediction models. Minimum MAPE models do not predict a simple statistic and so theoretical analysis is limited. We prove that when the proposed metric is used instead, the resulting least squares regression model predicts the geometric mean. This important property allows its theoretical properties to be understood.Peer reviewe

A decision support system for demand and capacity modelling of an accident and emergency department

© 2019 Operational Research Society.Accident and emergency (A&E) departments in England have been struggling against severe capacity constraints. In addition, A&E demands have been increasing year on year. In this study, our aim was to develop a decision support system combining discrete event simulation and comparative forecasting techniques for the better management of the Princess Alexandra Hospital in England. We used the national hospital episodes statistics data-set including period April, 2009 – January, 2013. Two demand conditions are considered: the expected demand condition is based on A&E demands estimated by comparing forecasting methods, and the unexpected demand is based on the closure of a nearby A&E department due to budgeting constraints. We developed a discrete event simulation model to measure a number of key performance metrics. This paper presents a crucial study which will enable service managers and directors of hospitals to foresee their activities in future and form a strategic plan well in advance.Peer reviewe

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