Confounding and Correlation Between Parameters

Correlation between parameters represents the degree to which two separate parameters can be identified independently of each other. Issues with correlation often arise when fitting theoretical models. For example, consider the following relationship 

The correlation between parameters can be determined by an analysis of the ( 4 4) matrix. If the off-diagonal entries of a given parameter are nonzero, then the variable is correlated with this other parameter. For example, for the matrix given as 

The first parameter is correlated with the third parameter, while the second parameter is not correlated with any of the other two. If two or more colunms are a linear combination of each other, then the parameters are said to be crnifounded with each other. In most cases, this will be seen as two columns that are multiples of each other. 

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In order to understand the methods by which optimal experiments may be designed, it is necessary to understand some of the factors that affect the results. The most important topics are sensitivity, confounding and correlation between parameters, blocking and randomisation. In general, the question in the design of experiments reduces to determining whether A A is invertible and well conditioned. A well-conditioned matrix is required when performing computations on a computer, since there will always be inevitable round-off errors. In a well-conditioned matrix, such rotmd-off errors do not have a disproportionate impact on the final result. 

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