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I am having troubles interpreting results from a BMA of a multinomial logit.

THE SETUP

My goal is to analyze how companies choose a payment method in M&A based on the acquirer's financial characteristics and some dummy variables such as whether both acquirer and target are from the same industry, country, etc. Anyways, I do not have any alternative specific variables, all are individual specific.

My dependent variable is a factor with three levels - cash, stock, mix, where cash is the base dependent, i.e. the multinomial logit results in two sets of coefficients - one for comparing cash vs. stock cases, and the other for cash vs. mix cases.

THE PROBLEM

Now, since I have in total 13 IVs, I am using a bayesian model averaging of my multinomial logit. There is an R package mlogitBMA with function bic.mlogit. The formula argument of the function can take on two forms - please see below.

The formula f is of the form response ~ x1 + x2 | y1 + y2. Coefficients for variables in the first part of the formula (i.e. before ’|’), here x1 and x2, are forced to be the same for all alternatives. Variables in the second part of the formula (i.e. after ’|’), here y1 and y2, have different coefficients for different alternatives. Either part of the formula can be omitted. Alternative specific constants (asc) are included automatically. To exclude asc, use -1 in the first part. The equation of the base alternative is always set to 0.

THE QUESTION

My question is simple. Should I use the first part of the formula, i.e.

response ~ x1 + x2

and have one set of coefficients regardless of the dependent alternative or use the second part, i.e.

response ~ y1 + y2

meaning I will get two sets of coefficients (26 in total). In this case do I proceed to interpret the results in a way as with a classic multinomial logit, i.e. in terms of log-odds?

Thank you.

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