# Interpretation of a classic multinomial logit vs. BMA of multinomial logit

EDIT #1

Most likely I have set up the function bic.mlogit in a wrong way. @Jesper Hybel, hopefully, directed me in the right way. With the new setup I get two sets of coefficients for both of my alternative dependent variables. Results are below. The only problem is, that now I do not know how to interpret the results...

ORIGINAL POST

I have a multinomial logit model with 13 IVs and a dependent with three levels cash, stock, mix. cash is the base dependent variable.

The IVs are - COLLATERAL - a proportion of the acquirer's fixed assets to its total assets, CASH is a ratio of its cash balance to the deal's value, LEVERAGE is acquirer's leverage ratio (debt to equity), CONTROL is the acquirer's biggest shareholder stake, CONTROLLOSS is a product between CONTROL and deal's value to the acquirer's market cap, RELSIZE is a ratio of deal's value and acquirer's market cap, QRATIO is acquirer's q-ratio, RUNUP is acquirer's stock return over year preceding transaction, REVENUEGROWTH is the acquirer's compunded revenue growth three years before a transaction. Dummies are INDUSTRY (1 if acquirer and target are from the same industry), DOMESTIC (1 if both from the same country), PRIVATETARGET if the target is privately held and COMMON_LAW if the acquirer is domiciled in UK or Ireland. All my IVs are individual-specific, no alternative-specific IVs here.

Data are available here.

As far as I know, we interpret results of a multinomial logit always as a comparison to the base dependent variable - so if I have as a base dependent cash, I interpret the coefficients in comparison to this base. This means that the result of a multinomial logit gives me two sets of coefficients - one for stock and one for mix - as shown below on the output of multinom function of nnet package in R.

Here, we get two sets of coefficients - one for stock, one for mix - and we interpret the coefficients as changes in the probability of stock or mix occuring vs. cash occuring (loosely put).

Nevertheless, the output of bayesian model averaging of multinomial logit, which is done with the mlogitBMA package in R, is following:

In this output, there is only one set of coefficients - the column EV. So how do we interpret this output? Am I missing something? Thank you! I can provide you with my code and data if necessary.

• Is your data in wideform? There should be one record for each individual. Alternative-specific variables occupy single column per alternative. And I also think you need to provide and index of alternative specific variables see the help page for bic.mlogit that states that "Indices of variables within data that are alternative-specific." is set by the variable "varying" in the call. Dec 5, 2018 at 12:42
• If I understand it right, I do not have any alternative-specific variables. My data concern M&A transactions, which were either paid by in cash, stock or mix (of these). My independent variables are financial and other characteristics of the acquirer in the particular transaction. Hence, I do not have any alternative-specific variables like in logit models studying mode of transport etc. Or am I wrong? Dec 5, 2018 at 13:08
• A variable is alternative-specific if it displays variation across alternatives. So from what you're writing my guess would be no. Because you only have porperties of the individual engaged in the transaction. Maybe you could provide a minimum example including you're data. Dec 5, 2018 at 13:20
• Yes, but in my case there are none, are they? This STATA post deals with alternative-specific and individual-specific variables. According to it, if I get it right, I do not have any alternative-specific IV. My IVs are, as I said, only individual financial characteristics (leverage, cash balance, qratio, etc.) and other dummies reflecting if the acquirer and target are from the same country, industry, if the target is a private/public company. Dec 5, 2018 at 13:24
• Well you only have individual specific variables. Dec 5, 2018 at 14:02

 response ~ x1 + x2 | y1 + y2

• OK, got your point and it works. The formula specification is following PAYMENT_TYPE~-1|COLLATERAL + CASH + LEVERAGE + CONTROL + CONTROLLOSS + RELSIZE + RUNUP + QRATIO + REVENUEGROWTH + INDUSTRY + DOMESTIC + PRIVATETARGET + COMMON_LAW. The variables after | will have different coefficients for each alternative, i.e. I will get my desired two sets of coefficients - one for stock, one for mix. Dec 5, 2018 at 16:41