Objectives:

Demonstrate that the Marginalization Index (IM) calculated by principal component analysis (PCA) can be expressed in cardinal terms. Recover the values of the IM for the states since 1970.

Methodology:

We normalize the IM from the concepts of null marginalization and absolute marginalization and prove that this transformation verifies the homogeneity postulate. We estimate the IM by PCA for the period 1970-2020.

Results:

The normalized IM is cardinal in the observed shortcomings for inter-territorial comparisons. Marginalization tends to decrease over time.

Limitations:

We verified that the IM estimated by PCA or by the Pena distance method (DP2) does not allow strict inter-temporal comparisons. Inter-temporal comparisons are only approximate.

Originality:

Contrary to previous studies, we show that the PCA can generate a cardinal IM.

Conclusions:

The IM calculated by PCA is useful for making inter-territorial and inter-temporal cardinal comparisons, even in the long term.

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