# Construct a correlation matrix based on pairwise correlation coefficients

For the purpose of simulation, I would like to construct such a correlation matrix that would respect to some extend the given set of preferable/desirable correlation coefficients for each pair of variables.

I tried filling in a matrix with the given coefficients and then enforcing the sum of absolute values of off-diagonal entries in each row/column to be smaller than one. It works, but it considerable weakens the given correlations, which I would like to avoid (as much as possible).

I would appreciate any suggestions. Thank you!

Regards, Ivan

• A relevant reference here – Glen_b -Reinstate Monica Sep 20 '14 at 10:49
• Is your input matrix certain to be symmetric? – Glen_b -Reinstate Monica Sep 20 '14 at 11:16
• @Glen_b, thank you for the reference. I do not have any input matrix; for N variables, I have N*(N-1)/2 Pearson correlation coefficients. Or maybe I misunderstood your question? – Ivan Sep 20 '14 at 11:30
• I have edited my answer to explain in more detail. – Glen_b -Reinstate Monica Sep 20 '14 at 17:44

Arranging the correlations into a matrix: Let $\rho_{ij}$ be the correlation between variables $i$ and $j$. Place $\rho_{ij}$ into positions $(i,j)$ and $(j,i)$ of the correlation matrix. Note that $\rho_{ii}=1$, so place $1$'s down the diagonal. If the set of correlations is consistent, the matrix you have is a proper correlation matrix.