Casual empiricism suggests the following pairwise correlations are positive:

(1) TRI, Citations;

(2) TRI, h-index;

(3) TRI, Reads;

(4) TRI, Recommendations;

(5) Citations, h-index;

(6) Citations, Reads;

(7) Citations, Recommendations;

(8) Reads, Recommendations.

The correlation of the h-index with Reads and Recommendations is not entirely clear, but might be expected to be close to zero.

To Chia-Lin Chang:

I agree with your empirical assessment.

The equation to calculate TRI is:

TRI = (0.5 x Citations) + (0.25 x Recommendations) + (0.15 x Full Text Reads)

+ (0.05 x Other Reads)

Reads are by RG members.

The h-index is not used in calculating TRI, so the sign and size of the correlation coefficient between TRI and the h-index is entirely empirical.

Whatever the connection, as stated on other threads, TRI has an internal inconsistency in that Citations include self cites, whereas it is not possible to record Reads and Recommendations of your own publications.

Just as the h-index is reported with and without self citations, TRI should also be reported with and without self citations.

An associated TRI-index that matrix balances Publications against TRI should be reported with and without self citations.