Bayes Factor for Complex Model
Message/Author
 Philip Parker posted on Saturday, October 12, 2013 - 1:20 am
Hi,

Two questions.
1. Can I use, is it common, or do people use Bayes Factors for comparing nested BSEM models. For example, longitudinal invariance models. If so I assume I can use the BF > 3 criteria that gets floated around.

2. I am using the BIC approximation of Bayes Factor. Using:

Exp(-.05*BIC_H1)
----------------------
Exp(-.05*BIC_H0)

However, given I have a very complex model and thus large BIC would this work:

Exp(log(H1/2) - log(H0/2))

Cheers,
Phil
 Tihomir Asparouhov posted on Wednesday, October 16, 2013 - 11:35 am
Yes on both.
 Meike Slagt posted on Thursday, February 19, 2015 - 8:53 am
Hi,

I also have large BIC values and have tried comparing the two formula's. They seem to yield different Bayes Factors when you give them the same BIC output, however.

For instance, if BIC_H1 = 1000 and BIC_H0 = 1010, then the BF according to the first formula = 148 (seems credible), and according to the second formula it's .996. This seems strange to me. What's going on?

I'm assuming that with H1 and H0 in the second formula (for complex models), you mean the BIC for H0 and H1?

I have an excel sheet with the formula's programmed into it, if you want.

Best, Meike
 Tihomir Asparouhov posted on Thursday, February 19, 2015 - 5:06 pm
It seems like I created some confusion. I meant to say that it is ok to compute the Bayes factor with either of these two formulas

Exp(-.5*BIC_H1)
----------------------
Exp(-.5*BIC_H0)

or the algebraically equivalent (but avoiding large number exponentiation)

Exp(BIC_H0/2 - BIC_H1/2)

I didn't mean to imply a different computational method. Seems like the original message had some typos or I misunderstood it.
 Meike Slagt posted on Friday, February 20, 2015 - 1:22 am
Thank you, this works perfectly!
 Eric posted on Monday, March 14, 2016 - 2:23 am
Hi,

is there any reference for computing the Bayes factor using this formula?

Regards,
Eric
 Tihomir Asparouhov posted on Tuesday, March 15, 2016 - 2:06 pm
Kass and Raftery (1995) section 4.1.3

https://www.stat.washington.edu/raftery/Research/PDF/kass1995.pdf

is the original reference or see page 26-27 in

http://myweb.uiowa.edu/cavaaugh/ms_lec_5_ho.pdf
 Eric posted on Tuesday, March 15, 2016 - 2:24 pm
Many thanks, Tihomir!