cbind vs. ~ in mixed model meta-analysis with the Metafor package

#1
lor.rma.mixed.optimal1 <- rma(EFFECTSIZE1, ESTVAR1, method = "DL", mods = cbind(FERTN, FERTP, FungalGenus, FUNGROUP), data = dfSel)
lor.rma.mixed.optimal2 <- rma(EFFECTSIZE1, ESTVAR1, method = "DL", mods = ~ FERTN + FERTP + FungalGenus + FUNGROUP, data = dfSel)

Both models have slightly different outcomes although they are supposed to be two methods for calculating the same model coefficients. What is the difference between the two outcomes?
 

hlsmith

Less is more. Stay pure. Stay poor.
#2
Hmm, yeah it seems they should function similarly. Is there a verbose output option to see if there is anything there. I am imagining the estimate are very comparable, yes?
 

Dason

Ambassador to the humans
#3
My only two guesses would be that using the formula (~) input versus the cbind input might either add a global intercept or might change things slightly so that the optimization algorithm converges on a slightly different local max/min.
 

hlsmith

Less is more. Stay pure. Stay poor.
#4
I have no basis but could it take a fraction of a second longer and use a different seed somewhere for a starting value? This was my original thought but it seems unfounded and could be examined by setting a seed. I guess I would still be interested on how different estimates were.

Also what happens if you use "=" or "~" in both procedures!!!