This is a first in a series of postings about correlation modelling. Amongst other topics covered we will address the uses of correlation modelling, the measurement and stability of correlation coefficients, some frequent misconceptions and consequences of correlations and some alternative modelling techniques within a risk analysis.
This first posting in the series covers the general context and meaning of correlation modelling. The capturing of dependency relationships using correlated variables can be considered as a proxy model, where causal factors that link variables are outside of the model that has been built. An example could be that a data series containing the number of TVs and number of cameras sold each year in a particular country is likely to show a positive correlation. This would generally be thought of as arising because as the wealth of the nation increases over time, more of both are bought. From a modelling perspective, there could be several approaches to building a model of TV and camera sales. The first would be to correlate these two series in some way (with no explicit forecast of the country’s wealth); the second would be to include within the model an explicit forecast of the country’s wealth (and perhaps any other important factors that are deemed to influence the sales of TVs and cameras), and to build in the dependency from wealth to TVs and wealth to cameras through formulae. In this second approach, the TV and camera series would then generally turn out to have a positive measured correlation once a simulation has been done, as an indirect result of the dependencies in the model.
In this sense, a statistically significant correlation coefficient that is measured from historic data (the stability of such coefficients being itself the topic of a later blog) is generally a sign of causality in a situation, whereas the implementation of correlated sampling in a simulation model is a recognition that the causality is exogenous to the model.
The way a decision evaluation model is constructed has a significant impact on the outcome of the statistical analysis.
Dr. Michael Rees
Director of Training and Consulting