Recently, I've been working with Quadratic Assignment Procedure, and Dekker and colleagues (2007) "Double-Semi Partialling" (DSP) method to generate p-values. Unfortunately, regression with QAP/node permutations doesn't really have a system for developing standard errors or confidence intervals for beta coefficients or predicted outcomes. I'd like to build my own standard errors and confidence intervals for these outcomes, but so far I've not had much luck.

I'm going to lay out what I've done so far and what issues I have hit, and any thoughts would be hugely appreciated.

First, I have been using Snijders and Borgatti's (1997) vertex jackknife. This, and their vertex bootstrap was really designed more for statistics on the overall network, like mean degree, etc. But when I draw 95% confidence intervals using the standard errors from the jackknife (eg. beta + se*1.96 and beta - se*1.96), these confidence intervals often cross zero, even though p-values from DSP are statistically significant. My guess is that if I could extract the confidence interval via percentiles from the jackknife distribution instead of using the standard error, that might work better, but I have no idea how to adapt Snijders and Borgatti's logic to confidence intervals. Here's their paper, below.

https://www.stats.ox.ac.uk/~snijders/Snijders_Borgatti.pdf

Alternatively, Chen and colleagues made an amazing snowboot package in R recently that runs the vertex bootstrap (also from Snijders and Borgatti).

https://www.researchgate.net/publication/331055070_Snowboot_Bootstrap_Methods_for_Network_Inference

This is great for network-level statistics, but once you get down to node level statistics or beta coefficients, it doesn't work so well, because the bootstrapped networks returned by snowboot don't contain vertex names. (This isn't Chen's fault; Snidjers and Borgatti's vertex bootstrap requires some switching around dyads any time that the same vertex appears more than once, so it doesn't really make a ton of sense to attach a specific set of node names afterwards.) But what this means is that I can't really adapt the vertex bootstrap easily to any analysis that involves node traits.

So, for anyone who is interested, any ideas how I can generate my own standard errors/confidence intervals for beta coefficients and predictions from a QAP regression model?

Thanks for your time, and I look forward to your responses