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I had a couple of questions about interpreting odds ratios for continuous variables in logistic regression. I feel like these are basic questions about logistic regression (and probably about regression in general), and although I'm slightly ashamed that I don't know the answers, I'm gonna swallow my pride and ask them so I know them in the future!

Here's my situation...I'm looking at a sample of adjudicated youth who, as part of their probation, were enrolled in a job/life skills training program. I wanted to see the extent to which the age at which they were released from the program predicted employment six months post-release from the program.

(Also, keep in mind that there are other predictors in the model, but I've excluded them because they are not statistically significant and I want to keep this as clear as possible.)

Predictor: Age of release from training program (Mean age = 17.4, SD=1.2, Range 14.3-20.5)

Outcome: Employed or not (Employed=1, Not Employed=0)

Result: Odds ratio 3.01 (p<.005) (I've excluded goodness of fit stats, etc. because I'm seeking answers about the interpretation of the odds ratio only; I feel comfortable w/ the evaluation of model fit, CI's, etc.)

Putting it into words: As age increases by one year, the odds of being employed six months post-discharge increase by three units.

Questions:

1) When I say, "As age increases by one year..." what is the starting point for age?

Does age start at zero? For example, "As age increases from 0 [i.e., the lowest age if you were to place this model on a graph]...”

Does age start at the the lowest age among the range of ages in the sample? For example, “As age increases from 14.3...”

OR

Does age start at the mean age of the sample? For example, “As age increases from 17.4...”,

2) Would centering help me interpret this result OR is that only effective in interpreting the y-int? If it would help, I was thinking of doing either mean centering or subtracting the lowest age in the range from all the other ages in the sample. Any suggestions?

3) Finally, is it appropriate to say that compared to a 14-year-old youth, a 17-year-old youth is nine times more likely to be employed? I ask because I know that logistic regression assumes a sigmoidal relationship, and I’m curious as to whether this 3 unit increase in odds remains consistent at any point along the regression line.

Thanks so much!

Aaron

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    $\begingroup$ You might be interested in this. $\endgroup$ – tchakravarty May 5 '14 at 10:24
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    $\begingroup$ Removal of "insignificant" variables is very problematic. $\endgroup$ – Frank Harrell May 5 '14 at 11:08
  • $\begingroup$ @FrankHarrell could you elaborate on why removing insignificant variables is very problematic in this case? $\endgroup$ – Mark White Jun 23 '17 at 15:42
  • $\begingroup$ This has been discussed at length on this site. Briefly it ruins standard errors, P-values, confidence interval coverage, etc. $\endgroup$ – Frank Harrell Jun 23 '17 at 18:57
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1) Since it is an odds ratio it doesn't matter where you start. The odds for an 18 year old are 3 times those for a 17 year old. Or the odds for a 17 year old are 1/3 those of an 18 year old. Same thing. If you want to get the probability that a person of a particular age will be employed, you can use the formula with the parameter estimates (not the ORs). Or you can get the program you are using to do it for you.

2) Whether centering helps is a matter of opinion. I don't find centered models clearer, but some people do.

3) The odds are not exactly the same as "likely" (although many people speak as if they were) and the odds for a 17 year old would be 27 times those of a 14 year old.

Finally, I'd be cautious about this model. The model assumes that the OR is the same between 14 and 15, 15 and 16 and so on. That seems unlikely to me, based on what I know about the subject.

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The average odds of enrolling in the training problem for an individual is # times the odds for another individual who are one year younger/older, after holding all other variables constant.

That's my take.

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    $\begingroup$ Can you expand on how this adds to the previous answer? $\endgroup$ – mdewey Mar 14 '17 at 21:20

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