I happen to see a paper which involved a Pearson correlation matrix of variables that the authors then used in their linear regression model. These variables are a mixture of levels of measurement, consisting of interval, ordinal, nominal, and ratio ones. The purpose of doing this was not explicitly presented, but could be implied to descriptively observe the, say, correlation between predictors and outcome variables, as well as among predictors.

Let's say the above purpose was also what authors intended. My question is whether it is a common practice to compose the matrix for that purpose? I'm asking since this looks like an unfamiliar analysis plan and there are a couple of concerns with doing so. For example, whether it's appropriate to use Pearson correlation between a categorical and a continuous variables. Often times, I see people running bivariate analyses between response variable and predictors. So, for example, if the outcome is continuous, then it can be Pearson/Spearman for continuous predictors and t-test for categorical ones. For multicollinearity, VIF/GVIF seem to be common approaches.

Any thoughts are appreciated.

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    $\begingroup$ Provided the meaning is clear -- which would include, at a minimum, an account of how the categorical variables are encoded -- there is no problem at all with computing Pearson correlation coefficients. Indeed, many of the familiar "measures of association" in contingency tables are just Pearson (or Spearman) coefficients in disguise or one-to-one transformations of them. But a full covariance matrix contains a lot of detail, usually much more than most readers are interested in, so you rarely see them published. $\endgroup$
    – whuber
    May 22, 2023 at 13:47

1 Answer 1


I would say it is not necessary but it might provide information assuming that statistics are calculated from the variables which have conforming measurement levels. It might be not be appropriate to calculate product moment correlation coeffient when having nominal and scale measured variables.


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