1

everyone!

I'm digging in meta-regression and doing hand calculations using WLS to get better understanding of the topic. I'm fine with calculations for univariative model (that is, 1 covariate is considered) but faced problems when several predictors are considered. I use following formulas for univariative model:

1. intercept and slope

enter image description here

2. variance for intercept, slope, and corresponding mean squared error

enter image description here

enter image description here

3. F-test for estimation of between-study variance in random-effects model enter image description here

*w - weight; y - outcome; x - predictor

My question is how should I modify and extend these formulas for multivariative case when two, three, and more predictors are accounted for? In particular, formulas for variance and F-test are of interest (I guess, covariance is supposed to be incorporated there).

The available infromation on Internet consideres this topic in matrix form, but I ask for the answer in scalar form (not a mathematician, unfortunately).

Thanks in advance for any help.

dub daze
  • 11
  • 2
  • Several predictors makes this *multiple* regression. "Multivariate" regression involves several *response* variables that might be associated. It is not productive to request the multiple regression formulas in "scalar form," because they rapidly get too complicated: see https://stats.stackexchange.com/questions/196807/ – whuber Aug 28 '19 at 13:56
  • Seem to be confused like many other people, even literature often uses multivariate and multiple in other way. The complexity of formulas is anticipated, so, the answer is still needed. – dub daze Aug 29 '19 at 06:04
  • The problem is that the length of the formula grows exponentially in the number of independent variables, even when you use vector products or summation notation. It is neither practical nor of any analytical interest to write it out for more than two or three variables; two ought to be enough. Indeed, implementing such a formula in software (or by hand) isn't a good idea anyway, because there are algorithms with better numerical stability. – whuber Aug 29 '19 at 12:37
  • I got the point, thanks. Assumed this looking at initial formulas. To end-up with the topic, is it possible to give me the input at least for two predictors case? This will be enough for my purpose, yet formulas still have to be managable. – dub daze Aug 29 '19 at 13:06
  • Follow the link in my first comment for the formulas with two predictors. – whuber Aug 29 '19 at 13:08
  • Did it. Also checked the paper reffered in that topic. They give half an answer. I miss how the weight should be incroporated that formulas correctly. Also calcualtion of variances and F-test aren't covered. I appologize for being annoying. – dub daze Aug 29 '19 at 13:24

0 Answers0