Multiply BF10 factors ?

Michael_Jasper

Bayesian correlation of x and y.

Bayesian correlation of z and m. 

Given that they don't share any variables can I multiply their BF10 factors? 

IF x and z are highly correlated? [this is the complication]

If it has any bearing this is a confirmatory study of a predefined hypothesis which foresaw that x and z would be highly correlated.

EJ

You can multiply the BFs if knowledge of the result for x and y would not alter your knowledge for the correlation between z and m. Now you know that x and z are highly correlated, but I don't think this is relevant for the correlation between z and m. The test-relevant parameter is the correlation coefficient, and knowledge about just one of the variables in a correlation does not provide information on that. So I would be inclined to say that you are allowed to multiply the BFs here. A full modeling effort that takes into account the relation between x and z will only lead to a slightly different result.

What is more relevant is this: suppose you analyze the correlation between x and y, and it turns out to be near 0. Does this knowledge affect your expectations for the correlation between z and m? If it does not, then you can multiply the Bayes factors. If it does, then it would be incorrect to multiply the Bayes factors, because the evidence is not independent.

Cheers,

E.J.

Michael_Jasper

Thank you Eric.

If the hypothesis predicts the correlation between x and z, which is observed, then independence is breached and one then cannot multiply the BF factors?

-----

N.B.The hypothesis predicts correlations

between x and y,

between z and m,

and between x and z.

Which are then all observed in the data.

EJ

More precisely: if the size of the correlation between x and z under H1 affects the knowledge about the size of the correlation between z and m under H1, then independence is breached

EJ