# Interpreting Binary Logistic Regression

#### Maartenvb

##### New Member
Hi,

This is my first time on this forum so I don't really know how this works. For this reason I will try to explain my problem as extensive as possible.

I am researching the innovativeness of different firm sizes. Beforehand I expected that their would be a positve relation between firm size and innovative output. Due to the fact that all my data is categorical I have used cross tabulations first. Via these cross tabulations a general patter was found that micro firms (1-9 employees) innovate less than small (10-49) and medium-sized firms (50-249). However, the correlation matrix shows a negative correlation of -.15.... This is a contradicting result... The same pattern was found in the binary logistic regression, where the Beta's are as follows

B S.E. Wald df Sig. Exp(B)
Micro: 1.342 .342 15.384 1 .000 3.825
Small: .749 .370 4.100 1 .043 2.116
Medium: 25.960 2 .000
Constant: .616 .346 3.171 1 .075 7.851

When I see these Betas, I interpret them as follows. Micro firms are 1.34 times as innovative als medium-sized firms and small firms are .749 times as innovative. However this is the opposite result that was found in the immediate responses by the firms.... How is this possible?

In the attachement is the logistic regression

Thanks in advance
Maarten

#### Maartenvb

##### New Member
Oh I see that the values have shifted when I posted it...
It should be like this

----------(B) ------S.E.--- Wald ----df ----Sig. --Exp(B)
Micro: ---(1.342)-- (.342) (15.384 ---1 ---(.000) --(3.825)
Small: ---(.749)--- (.370) -(4.100) ----1 --(.043) --(2.116)
Medium: -----------------(25.960) ----2 --(.000)
Constant.616) ---(.346)- (3.171) ----1 --(.075) --(7.851)

#### Karabiner

##### TS Contributor
Your original DV wasn't coded as 0/1, I suppose?

With kind regards

K.

#### Maartenvb

##### New Member
Your original DV wasn't coded as 0/1, I suppose?

With kind regards

K.
Do you mean the variables as they are in the dataset?
In the output of the logistic regression is said that

Dependent Variable Encoding
Original Value-----Internal Value
ja------------------(0)
nee----------------(1)

In the original data I have not recoded the answers of the managers. The anwers are "yes" or "no". However, they are indicated with a 0 and 1 respectively.

Should I have recoded them?

By the way congratz on the quarter final victory!

Maarten

#### Maartenvb

##### New Member
Hmm... They are of course negative because No is coded as 1, which means I have tried to predict who is not innovative.
Which is of course the micro firm. If I recode as follows: yes=1 and no=0 will the relationship turn around (is the same but is easier to interpret).
Am I right with this line of thinking?

Maarten

#### purifyz

##### New Member
Hi,
Have you checked if there is (multi)collinearity? This sometimes leads to unexpected betas.

#### JesperHP

##### TS Contributor
Hmm... They are of course negative because No is coded as 1, which means I have tried to predict who is not innovative.
Which is of course the micro firm. If I recode as follows: yes=1 and no=0 will the relationship turn around (is the same but is easier to interpret).
Am I right with this line of thinking?

Maarten
If you model the probability P(Y=1) instead of P(Y=0) the signs of coefficients will change. You should check out what probability is modelled as default or how to choose the probability you model .. (in my version of SAS it is P(Y=0) which is default and I personally find contraintuitive)

#### Maartenvb

##### New Member
Hi,
Have you checked if there is (multi)collinearity? This sometimes leads to unexpected betas.
Yes I have. This does not seem to be a problem...

#### Maartenvb

##### New Member
When I take a look at the correlation matrix, it seems that only firm size is negatively correlated with the dependent and other predictor variables.
In the data has firm size been coded as micro=1, small=2 and medium-sized=3, however in the logistic regression is it coded as micro=1, small=2 and medium-sized=0.

Is it possible that I should have given the firm sizes different values? That this is the reason I have contraintuitive results?