Dear Davit,

I think it might be easier to invert odds ratios < 1 and talk about the relative likelihood of the opposite event first. It would seem to make the language easier. Also, don't forget the confidence interval for the odds ratio. If it contains 1 then there is insufficient evidence to reject the null hypothesis.

Hi Peter, 

Thank you for your quick feedback. It is highly appreciated 

Davit 

Good afternoon Davit,

I think you have the basic idea correct but some of the terminology could be improved.  If the odds ratio for having higher education is 0.34 then those farmers with a higher education have 0.34 the odds of staying in the agricultural sector as those without a higher education.   In other words, if 25 non-highly educated workers leave the agricultural sector and 100 stay than 75 highly educated workers will leave the agricultural sector if 102 stay.

You can't say that highly educated agricultural workers are 0.34 times more likely to stay and 74% more likely to leave--that is a contradiction.  The odds a highly educated person stays in the agricultural sector are 0.34 the odds of someone without a higher education. 

But you might have known this already and just needed some help making it grammatically correct.

Best,

Aran

Dear Aran, 

Thank you for your suggestions. 

Let me clarify some details here. 

If I can calculate exact probabilities of staying and exit out of odds ratio then why it is not right to interpret it in the following way: 

                             Coefficient (B)           Odds Ratio 

   High_edu            -1.067925                   0.34 

Interpretation of effect: 

So I see that, higher education is negatively associated with farmer’s decision to stay in the agricultural sector. 

Out of odds ratio I calculated exact probabilities of stay=0.2558 and exit= 0.7442. So, there is almost 25% of chances that educated farmers will stay in the sector rather then leave? Do you agree with me? 

and why I can't say that there is almost 74% less chances of staying in the agricultural sector? or more correct way would be 1-0.34=66% less likely to stay? 

Best regards, 

Davit 

Good afternoon Davit,

Odds Ratios, and Logistic Regression more generally, can be difficult to precisely articulate.  

Using the formula for probability from the odds ratio, which you correctly employed, you can say that educated farmers have approximately 25% the chance of staying compared to uneducated workers (I'm assuming that High_edu=0 is uneducated workers).  When you say there is a 25% chance the educated farmers will stay in the sector rather than leave I think you have to remember that this is compared to uneducated workers and is not an absolute figure.

Or you could say that uneducated workers had an approximately 75% higher chance of staying than educated workers.  I would hesitate on saying that educated workers had a 74% less chance of staying because the actual percentage is that they had a 0.25 the probability of staying.

You could also frame this in terms of odds ratios.  Educated workers had 0.34 times the odds of staying as uneducated workers or uneducated workers had an odds of staying 2.94 times the odds of educated workers.

However you choose to phrase the conclusions just be careful that you clarify when you are speaking of probabilities and when you are speaking of odds.  You also need to keep in mind the distinction between the absolute probability of the worker staying versus a relative probability (uneducated vs. educated)

Sincerely,

Aran

Dear Aran, 

Thank you for your quick response. It is highly appreciated 

I do agree with your suggestions and will take them into account 

Best regards,

Davit 

Dear Felix, 

Thank you for your comment. 

I just used this variable as an example. Of course, I have almost 8 predictors in my logistic regression. I just wanted to understand the best way of interpretation. 

In my example for variable high_education (1=bachelor and above; 0=otherwise) odds ratio =0.343721. How do we get this odds ratio ? Odds Ratio = Probability of staying/Probability of exit. The formula for calculating probabilities out of odds ratio is as follows P(stay in the agricultural sector) = OR/1+OR = 0.343721/1+0.343721= 0.2558 So, the probability of the alternative category (exit) will be 1-0.2558=0.7442. In this case you interpret the results in terms of probabilities. 

If you want to interpret the results in terms of odds ratios then you can interpret in the following way: 

1. Farmers with higher education level have 0.34 times the odds of staying as farmers with lower education level 

or 

Inverting the probabilities 

Farmers with lower education level had an odds of staying in the agricultural sector 2.94 times the odds of farmers with higher education level 

You mentioned the following way of interpretation: 

1-0.343721= 65.6 (Educated farmers are 65% less likely to stay in the agricultural sector compared to farmers with lower education level) 

I have seen this type of interpretation before.  But can you explain why are you deducting 1-odds ratio and interpreting in terms of percentage reduction ? 

Best regards, 

Davit 

Dear Davit, 

A very good reference is the book "Categorical Data Analysis" by Alan Agresti. It  provides readers with basic information on how to compute and interpret Odds Ratio.

Also see this link for some more detail

Dear Felix, 

Thank you for your contribution. 

What do you think about explanation given in this source 

https://stats.idre.ucla.edu/stata/faq/how-do-i-interpret-odds-ratios-in-logistic-regression/

Best regards,

Davit 

Dear Davit,

That is right.

Dear Felix, 

That is a formula I am employing. I am sure now you get better idea why I have used the formula mentioned above 

Anyway, thank you for your follow up 

Best regards, 

Davit 

Dear Davit,

The information I intended to provide is in relation to the fact that, the intercept term (constant) plays a role in the computation of the probabilities. You had left that out in your first post. In my first post, I tried to explain that. Its similar to the post you shared. I denoted the constant term as "b0"and in the post it was denoted as "a"

Cheers, 

Felix

I would like to ask that how I can decide it is less likely or more likely to occur something based on the Odd ratio?. For example, suppose I got the odd ratio for GPA score 2.45 and score math is 0.831 (at P