# Multinomial regression: how to interpret results

#### GiuliaCarbone

##### New Member
Hello Everyone,

I'm currently writing my master's dissertation and i'm having two main issues.

1) The first one is related to the attached picture: as you can see, both the variables "deal value" and "N employees" are signicative, but the B and the Exp(B) are zero. This way they are not included in the model, so I don't understand how they can be significative! Do you think there is an explanation to that?

2) The second one is about the interpretation of the results when both the Y and the X variables are categorial.

Y (financing for M&A) can be Debt or Shares, while X(sector) yes or no (yes= same sector for target and acquiror, no=different sectors).

If the ODDS is 1,5, when the X is a value I say that the ODDS of paying with debt is 1,5 times the ODDS of paying with shares, for each one-unit increase in the variable X (also this case is not so clear to me, so I would be grateful if you could explain it better).

But I really don't understand what to say when the X is categorial: I need to say which is the correlation between debt and sector=yes and between debt and sector=no, is it possible?

I hope you can help me, since I really don't understand how to proceed. Thank you in advance.

Best regards,

Giulia Carbone

#### Junes

##### Member
1) Presumably the b is smaller than 0.0005, but not equal to 0. Then it will be printed as .000. The reason being that the effect of employees is such that an extra employee doesn't affect the regression very much. To see it in your table, compute a transformed variable by dividing by a sensible number.

2) for categorical variables it works the same with respect to a reference level (b is set to 0 for that level), so the odds with sector=0 is .489 of the odds with sector=1.

#### GiuliaCarbone

##### New Member
Thank you Junes, I finally could solve the first problem.

Though, I still don't understand clearly the second point.. if I apply the odds to the x, what can I say about the y? Y=debt and Yreference=equity, so if the odds of x0 is 0.4 does it mean that the odds of paying by debt when x=0 is 0.4 than when x=1, so when x=o is less probable paying by debt and more with equity?

Thanks again,

Giulia

#### Junes

##### Member
Glad to help. I think that's correct, if I understand you correctly. Let's take a concrete example again:

Cross-border = 1 is the reference for X
Equity is the reference for Y (it is the 0 outcome), so odds are expressed for debt (1) vs. equity (0). So an odds of 3 means debt is 3 times as likely as equity.

The odds-ratio for cross-border=0 is 0.274. So odds(debt vs. equity|cross-border=0)/odds(debt vs. equity|cross-border=1)=0.274

In order words, the odds for debt when cross-border is 0 is about a fourth of the odds for debt when cross-border=1 (keeping everything else constant).

By the way, for binary variables, it's probably a good idea to use the levels coded with 0 as your reference. This is more common and more intuitive (0=factor is absent, 1=factor is present). You can recode if necessary.

This may be a useful page, especially the part "Logistic regression with a single dichotomous predictor variables".

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#### gianmarco

##### TS Contributor
As for Logistic Regression in general, I found Pampel's book on LR very useful, informative, and easy to follow. It has a nice section which provides a step-by-step guide to the interpretation of the results using a worked example. It also devoted some room to the interpretation of the fitted model results when some predictors are categorical.

Best
Gm