Logistic regression_interpretation

[thomas25]

Hey!

I would like to ask you to help me how to correctly interpret the results of logistic regression test. I have 3 predictor variables, namely age, following politics and left-right self placemenet. The outcome variable is "bulding a new shopping mall in a town" (coded as 0 disagree and 1 agree).

Odds ratio of age is 0.85, following politics is 1.20 and left-right self placement is 1.05. I would interpret these results as follows:

if citizens’ age increases by one unit (one year), their odds of supporting the bulding of shopping mall (as opposed to not support the building of shopping mall) are 0.85 times lower (OR if citizens' age increases by one unit (one year), they are 0.85 times less likely to support the building of shopping mall)

if citizens’ following politics increases by one unit, their odds of supporting the bulding of shopping mall (as opposed to not support the building of shopping mall) are 1.20 times higher (OR if citizens' following politics increases by one unit, they are 1.20 times more likely to support the building of shopping mall)

if citizens’ left-right self placement increases by one unit, their odds of supporting the bulding of shopping mall (as opposed to not support the building of shopping mall) are 1.05 times higher (OR if citizens' left-right self placement increases by one unit, they are 1.05 times more likely to support the building of shopping mall)

In the extant literature I found both interpretations but I am still not sure whether they are appropriate. Are my interpretations correct (both of them)? I really appreciate your help

Thank you

[Max]

@thomas25

their odds of supporting the building of shopping mall (as opposed to not support the building of shopping mall) are 0.85 times lower

One small tip: You can say that the odds are decreased by 17% (since 1/0.85 = 1.176471).

@thomas25

likely

Be careful here. Some would argument that the odds-ratio is not an indicator of likelihood. It is safer to say that "the odds of this event occurring are X-fold higher"

[thomas25]

@Max

so if I understood you it is safer to interpret the odds ratio as: if X (independent variable) increases by one unit, the odds of Y (dependent variable) are x-times higher/lower

or to use the percentage as you recommended

[Yarnabrina]

I'm adding a few comments.

1. As far as I know, you can't define odds ratio for a continuous independent variable and a binary dependent variable. Both need to be dichotomous, which is not the case here. In my opinion, odds ratio of age etc. makes no sense.

2. In logistic regression, you model the logarithm of odds of success, not the odds ratio. May be I'm misunderstanding what you've mentioned your question, but it seemed to me that you're trying to interpret similar to linear regression, with age, etc as independent variable and odds ratio as the dependent variable.

3. I think what Max meant is that an unit increase in independent variable will increment the logit by the coefficient of that variable in the fitted logistic model, and that implies that the odds of success of the dependent variable will increase by exponential of that coefficient.

[thomas25]

@Yarnabrina

Now I am little bit confused because what I am trying to interpret is basically how many times lower or higher are the odds of supporting the building of shopping mall (dependent variable) if age, following politics and left-right self placement (independent variables) change by one unit

[Yarnabrina]

That's exactly what I said:

@Yarnabrina

odds of success of the dependent variable will increase by exponential of that coefficient.

The increment in logit will be in addition sense, but the increase in odds will be in multiplication sense.

Suppose the fitted model is:

log(\frac{p}{1-p})=\hat\beta_1x_1+\hat\beta_2x_2+\hat\beta_3x_3

If you increase x_1 by 1 unit, keeping x_2 fixed, log(\frac{p}{1-p}) will increase by \beta_1 amount.

That will mean that \frac{p}{1-p} is multiplied by e^{\beta_1} and hence the increase in the odds.

I hope I've made myself clear.

[thomas25]

unfortunately, I cannot get your point. It seems to me that we are talking about two different things, such as log odds (which can be interpreted through regression coeffcient) and odds ratio which is in RStudio calculated through exp function

because it seems to me that I interpreted it correctly, when odds ratio of age is 0.85 than following that interpretation if citizens’ age increases by one unit (one year), their odds of supporting the bulding of shopping mall (as opposed to not support the building of shopping mall) are 0.85 times lower

although I bear in mind your statement that we cannot define odds ratio for continuous and binary dependent variable

[Yarnabrina]

According to the title of this thread, I'm answering regarding interpretation of the coefficients of the fitted logistic model.

@thomas25

odds ratio of age is 0.85 than following that interpretation if citizens’ age increases by one unit (one year), their odds of supporting the bulding of shopping mall (as opposed to not support the building of shopping mall) are 0.85 times lower

I'm not sure whether odds ratio can be interpreted this way.

I'll refrain myself from further comments and I hope Max or someone else will help you regarding the problem.