# Making sense of binary logistic regression results/Interpreting odd ratio in r

I am using binary logistic with two response level, Yes and No. The results are in log odd I learned and was advised earlier (question was on multinomial logistic regression) to exponentiate my estimates and get odd ratios. Odd ratios are as guided easy to interpret when the audience is from a non statistical background which is my case. This is what I did:

exp_coef <- exp(coef(logit_model))
conf_intervals <- exp(confint.default(logit_model))


Here are the exponentiated results:

(Intercept)                       (Intercept) 1.898752e+00 0.1224433 29.444310
Age                                       Age 9.507915e-01 0.8569893  1.054861
GenderMale                         GenderMale 8.980799e-01 0.0753226 10.707909
EducationSecondary         EducationSecondary 6.013910e+00 0.4316033 83.797132
EducationTertiary           EducationTertiary 1.144236e-08 0.0000000       Inf
Access_to_resourcesYes Access_to_resourcesYes 3.924051e+00 0.2185817 70.445865


Here are the specific result interpretation I have put together considering the dependent variable Juice practice/making Juice and the independent variables; age, gender, education and access to resources for review and correction.

Intercept: The odds of making Juice is 1.898752 times. What does this mean?

Age: For every unit increase in age of respondents, the odds of making Juice increases 9.507915 times. This means the practice of Juice increases with age. This is not clear.

Gender: The likelihood of Male respondents making Juice is 8.980799 times compared to females. In the input dataset, there are 14 females vs 6 males and of those 9 female yes, and 5 No, 3 males, 3 indicated yes, and 3 No, I cannot make sense of this results. What does the 9 times really mean compared to females? Why is the confidence level 1?

Education: The likelihood of those who can make Juice with secondary education is 6.013910 times compared to those with primary education. What does this mean because in the input dataset, secondary has 7 yes whereas primary 5?

Education: The likelihood of respondents with tertiary education who can make Juice is 1.144236 times compared to those with primary education. This result is low because there was only one participant with tertiary education.

Resources Accessibility: the likelihood of respondents without access to resources to make Juice is 3.924051 times compared to those with access to resources. Also not clear.

This interpretations does not seems to make logical sense to me. How do I make sense of them, interpret them in a complete yet sensible manner. The data is about being able to make juice and factor that affects making juice. How are references used when interpreting the results? How do I explain the number of times to make sense of my interpretation? I tried doing readings on logistic regression result interpretation and was directed to some resources on interpreting the results through my question here but I am still lost https://stackoverflow.com/questions/78110101/how-to-create-dummy-variables-for-a-multinomial-logistic-regression

Here is my input dataset:

• Is that your whole dataset or just a sample from it:? Commented Apr 1 at 10:01
• I think you need to take a course in logistic regression or, at the very least, read a good book on the subject. One very good book on regression in general is Regression Modelling Strategies by Frank Harrel, who is active here as @fharrell. This covers logistic regrssion as well as other kinds of regression. A classic on logistic regression alone is Hosmer and Lemeshow Applied Logistic Regression. Commented Apr 1 at 10:06
• This is a test dataset, the idea was to identify correct method, learn how to analyze my data before going into the field but I learned that small sample size can be problematic and cause issues, e.g. large coefficient etc. I am trying to learn and perfect the procedure ideally.. My sample size is 385 households so I am looking at having a large number of respondents. Commented Apr 1 at 10:07
• This platform is very useful for specific questions and problems, but it can't substitute for a whole course or book. However, if you do get one of the books I recommended (or another one) and have questions, then this is a good site to get answers. Commented Apr 1 at 10:17
• You've linked to PDF copies of those two books which might be < 100% legal. Please don't do that. You can find the Regression Modeling Strategies (RMS) online notes here. Chapters 10, 11 & 12 are on logistic regression. Commented Apr 1 at 11:17

As other questions have noted, there are a number of issues here. First of all, one of your coefficients for education seems to have infinitely large confidence intervals, which suggests something is very wrong (maybe perfect correlation with the dependent variable?). If your N is only 385 then I do think you have an issue on sample size, especially with this many variables in your model.

But I also think your confusion partly stems from thinking that odds ratios are "easy to interpret when the audience is from a non statistical background." This is a common misconception, even from people who do have a statistical background.

In statistics, an "odds" has a very technical meaning: it is the probability of a thing happening divided by the probability of a thing not happening. So if something has a 70% chance of happening (vs 30% not) it has an odds of 2.3. In a logit model, an odds ratio tells you how the odds, not the probability of the event changes. So this sentence is wrong:

"Gender: The likelihood of Male respondents making Juice is 8.980799 times compared to females."

People misinterpret odds ratios this way all the time, even in published peer reviewed papers. But it is wrong.

The true interpretation of this odds ratio is:

"The odds of Male respondents making Juice are 898% as high as the odds for females, holding all other variables in the model constant."

Note that this doesn't tell us anything about how the probability or likelihood of making juice differs, which is what most people want to know. Unfortunately, the model can't tell you that unless you give it some more information about the baseline likelihood of making juice for different types of people. There are ways of doing that (google "average marginal effects" for example) but they require additional work.

This is why logistic regression is such a complex tool, and one that is easily misunderstood, and difficult to use well. I would be very careful about trying to use it "in the real world" without a strong background in what it is trying to do.

• My takeaway is familiarizing myself with the fundamentals especially given that my sample size can be key issue here . Thank you for your patience and generosity. The misconception came from the advise I got earlier through this question , or i misinterpreted the answer. stats.stackexchange.com/questions/642964/… I would like to learn and be guided on the right path. I am busy studying your answer and the comments recieved. Commented Apr 1 at 11:34
• Yes! But the infinite confidence levels indicate something, maybe separation ... (search this site). But, they probably comes from Wald intervals, do something better, like likelihood profiling Commented Apr 1 at 12:42