Logit regression

[Amber Oostrom]

Hello everyone,

As part of my thesis i look at the influence of size(that is the natural logarithm of total assets) en leverage(debt/equity) on the choice for a Big Four auditor(dummy variable 1=big4 0=non big4).
I changed log-odds into the odds-ratio, because i read on the internet that the interpretation would be easier. But could someone explain to me how i should interpret the oddsratio of 2.10 bij size when it is the natural logarithm and the odds-ratio of leverage? I also read something about using margins to explain the effect, but then i get only one outcome for all the variables

so, logit Big4 size leverage and then my control variables

Table 6. Logit regression
Dependent variable:	Predicted Sign	Coef.	Odds ratio	Z-value
Big4
CONSTANT		-13.2069***	1.84 e-6	-21.64
SIZE	+	0.7430***	2.1023	26.72
LEV	+	1.7508***	5.7594	7.86
ROA	?	-1.8180***	0.1623	-2.95
ASSETSTRUC	?	-1.0201***	0.3605	-6.31
CASHASSET	?	-0.5796	0.5601	-1.56
INDUSTRY FE		YES
YEAR FE		YES
OBS.	7743
PSEUDO R2	0.0971

[Clyde Schechter]

So to interpret this in the odds ratio metric, you would state that a unit difference in log size (i.e. a 2.718 fold difference in amount of assets) between is associated with the odds of choosing a big 4 accountant being 2.1023 times as high for the larger firm as it is for the smaller firm, adjusting for all the other variables in your model.

I'm not sure exactly what you mean by INDUSTRY FE and YEAR FE YES in your output table, but this suggests to me that you have used ordinary logit regression in panel (or perhaps even multi-level) data. Unless you first performed the panel or multi-level analysis and found that the hierarchical models were equivalent to ordinary logit, this is probably not valid and you should re-do the modeling.

If you want to do this in terms of marginal effects on probability of chosing a big 4 accounting firm (which most people will find more intuitive), the proper command is:

margins, dydx(SIZE)

This will give you the average marginal effect of SIZE. The result would be interpreted as the difference in probability of choosing a big 4 accountant associated with a 2.718 fold difference in amount of assets.

[Amber Oostrom]

Thanks for the quick response.
I did use the margin right now and for size i get 0.1380836. So should i see it as a difference of 14% in choosing a big 4 auditor?
For leverage i get 0.3293218, can i interpret this the same way a size? even if leverage is not measured by natural logarithm?

[Clyde Schechter]

For size, it would be a difference of 14 percentage points, not 14%.

For leverage, it would be a difference of 33 percentage points associated with a unit increase in leverage.