# Modeling Technique Based on the Ranges of Values: Implementation Using Conventional Regression Method

• Arthur Yosef
• Eli Shnaider
Article

## Abstract

Very often, model-building professionals are facing a very difficult choice of selecting relevant variable/s from a set of several similar variables. All those variables are supposedly representing the same factor but are measured differently. They are based on different methodologies, baselines, conversion/comparability methods, etc., thus leading to substantial differences in numerical values for essentially the same things (or at least, the same things from the perspective of the modeler). In this study we introduce a method for modeling, capable of utilizing ranges (intervals) of values and thus enabling to utilize inclusive approach, which means to include all the relevant variables that represent the same factor. The idea of utilizing intervals is not new and has been contemplated in some studies within the domain of artificial intelligence, such as fuzzy information processing, expert systems, etc. In this study we extend traditional modeling methods towards the utilization of intervals. First we discuss the need for the modeling method that can utilize intervals of values. We point out to numerous advantages from the stand point of reliability, better and more efficient data utilization, as well as substantial improvement in our ability to interpret the results—due to the drastic reduction in the amount of regression runs. One important drawback of utilizing intervals is that the size of some intervals could become excessively wide due to the presence of outliers that do not represent typical magnitudes. Therefore, we introduce an interval (range) reduction algorithm, designed to reduce excessive size of intervals, thus bringing them closer to their central tendency cluster. We present extensive discussion of a theoretical basis for the interval based modeling method. Following the theoretical component, we present a case study. The case study involves building a model of background factors facilitating long term economic performance. We utilize international (cross-national) data provided mostly by the World Bank, including several data-bases as well as data extracted from some earlier hard copy reports.

## Keywords

Range of values Intervals Multiple linear regression Central tendency Modeling methods

## References

1. Buckley, J. P., Pass, C. L., & Prescott, K. (1988). Measures of international competitiveness: A critical survey. Journal of Marketing Management, 4(2), 175–200.
2. Fagerberg, J. (1988). International competitiveness. Economic Journal, 98(391), 355–374.
3. Giloni, A., & Padberg, M. (2002). Alternative methods of linear regression. Mathematical and Computer Modelling, 35(3–4), 361–374.
4. Joaquın, D., Federico, J. O., & Santiago, R. G. (1983). A set of independent sequential residuals for the multivariate regression model. Journal of Statistical Planning and Inference, 8, 21–25.
5. Jones, I., & Romer, P. M. (2010). The new Kaldor facts: Ideas, institutions, population and human capital. American Economic Journal: Macroeconomics, 2(1), 224–245.Google Scholar
6. Lucas, R. E. (1988). On the mechanics of economic development. Journal of Monetary Economics, 22, 3–42.
7. Romer, P. M. (1990). Endogenous technological change. The Journal of Political Economy, 98(5,Part 2), 71–102.
8. Shnaider, E., Haruvy, N., & Yosef, A. (2015). Do macro-economic factors influence financial management decision making: The Israeli economy in perspective. Journal of Financial Management and Analysis, 28(2), 64–74.Google Scholar
9. Shnaider, E., & Yosef, A. (2018a). Utilizing intervals of values in modeling due to diversity of measurements. Fuzzy Economic Review, 23(2), 3–26.
10. Shnaider, E., & Yosef, A. (2018b). Relative importance of explanatory variables: Traditional method vs soft regression. International Journal of Intelligent System, 33(6), 1180–1196.
11. Stevens, S. (1946). On the theory of scales of measurement. Science, 103(2685), 677–680.
12. Wagman, D., Schneider, M., & Shnaider, E. (1994). On the use of interval mathematics in fuzzy expert systems. International Journal of Intelligent Systems, 9(2), 241–259.