How are the coefficients in MR-QAP calculated?

Post date: Aug 24, 2016 9:21:7 PM

The same as in OLS. The only difference is in the p-values. For example, suppose we have these two networks (expressed as adjacency matrices):

Now we use MR-QAP to predict the Y matrix from the X matrix. Here are the results:

MODEL FIT

R-Square Adj R-Sqr P-Value Obs Perms

------------ ------------ ------------ ------------ ------------

Model 0.19753 0.15295 0.17299 20.00000 20000.00000

REGRESSION COEFFICIENTS

Un-Stdized Stdized Coef P-value As Large As Small Std Err

------------ ------------ ------------ ------------ ------------ ------------

Xmat 0.44444 0.44444 0.19549 0.19549 1.00000 0.22030

Intercept 0.05556 0.00000 0.00000 0.00000 0.00000 0.00000

Next we run the same regression in Stata. First step is to convert the data matrices into something Stata can understand, which is columns:

We enter these data into Stata, and then run regression:

. regress y x

Source | SS df MS Number of obs = 20

-------------+------------------------------ F( 1, 18) = 4.43

Model | .355555556 1 .355555556 Prob > F = 0.0496

Residual | 1.44444444 18 .080246914 R-squared = 0.1975

-------------+------------------------------ Adj R-squared = 0.1529

Total | 1.8 19 .094736842 Root MSE = .28328

------------------------------------------------------------------------------

y | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

x | .4444444 .2111436 2.10 0.050 .0008482 .8880407

_cons | .0555556 .0667695 0.83 0.416 -.0847219 .195833

------------------------------------------------------------------------------

As you can see, the regression coefficients are the same, but the p-values are different.