topic Re: Odds ratio for a simple distribution in Discussions

Odds ratio for a simple distribution

Jonkandonkan — Mon, 20 May 2019 12:49:04 GMT

Hi

I'm looking at the distribution of individuals participating in different events. Here, I'm looking at "thirds" (i.e., first, second, third part of the year, not sure "Tertial" is the correct word in english), could also be quarters, Q1-Q4.

When doing a distribution plot, I can also test the probability/ do a chi-2 test, and thereafter get the likelihood ratio, and its confidence intervals. However, is there a easy way of calculating the Odds Ratio for this? That is, the odds that you are placed (in this case, born) in T1 instead of T3. I've tried to look around and one can doo Odds ratios under logistic regression models but that seems inappropiate for this case?

Re: Odds ratio for a simple distribution

Mark_Bailey — Mon, 20 May 2019 13:01:03 GMT

You question is not clear. You have the counts for three groups. You can compute the marginal probability of a group. You can calcualte the odds of a group. The odds ratio would require a covariate or second variable. Do you have another set of three groups for which the external variable is different?

Re: Odds ratio for a simple distribution

Jonkandonkan — Mon, 20 May 2019 13:20:55 GMT

I can imagine!

I have alot of sets with three groups, but mostly I want to calculate the odds that you are in, for example, T1 to T3.

It's quite common practice in the context of Relative Age Effects (in sports, or other fields), in original studies and meta-analysis to calculate the odds ratio, when looking at the [skewed] distribution of participants in sport:

I want to to the same.

Re: Odds ratio for a simple distribution

Mark_Bailey — Mon, 20 May 2019 16:51:31 GMT

I will let someone else who knows more than I do. JMP does not compute the odds, as far as I know. You can calculate them from the probability estimates in Distribution that were used to test probabilities.

More could be done with scripting, but you didn't mention that option. I assumed that you were looking for an interactive solution or a solution with a column formula.

On the other hand, if you set up the example (above) in a JMP data table so you have Subject Age (group), Sport, Level of Competition, and the frequency, you can fit any logistic model you want, save the probability formulas, and then compute odds and odds ratios with table summaries and column formulas.

Re: Odds ratio for a simple distribution

Jonkandonkan — Mon, 27 May 2019 13:29:37 GMT

Hm.. So to calculate OR using my probability results (as examplified in first post) would be, for T1 to T3:

( 0.426 / (1-0.426) ) / ( 0.258 / (1- 0.258) ) = 2.13 ?

Will try your second option, but then I need to re-arrange all the data and type in frequencies etc..

Re: Odds ratio for a simple distribution

Jonkandonkan — Mon, 27 May 2019 13:48:11 GMT

So, would it be possible to calculate Odds ratio (i.e. T1 vs T3) with this dataset? Never used logistic modelling..

Re: Odds ratio for a simple distribution

Mark_Bailey — Tue, 28 May 2019 12:26:50 GMT

Yes, that is how you compute the odds and odds ratio, although I have never used it this way.

Re: Odds ratio for a simple distribution

Mark_Bailey — Tue, 28 May 2019 12:30:45 GMT

You can use the Tables > Stack command to combine the three data columns N T1 through N T3 into one column and create a second label column to capture the original column name. Use the label column for the response and the stacked data column for the frequency. You do not need the total counts for the analysis.

The logistic regression would allow you to model dependencies of the probability on the other variables. The conditional probabilities, in turn, could be used to compute the odds and odds ratios (e.g., different age groups) as you have done above.

Re: Odds ratio for a simple distribution

Jonkandonkan — Thu, 20 Jun 2019 08:08:27 GMT

Thanks. Almost there...

I stack the data & fits the model. Confused. Is it possible to do the model for the whole dataset? In addition do analysis by age group.

Im not really getting the results table, or finding any odds ratios.

Re: Odds ratio for a simple distribution

Mark_Bailey — Thu, 20 Jun 2019 14:03:37 GMT

You are there but you still have to compute the odds and odds ratios yourself. This method is just another way to get the marginal probabilities (red triangle > Save Probabilities). But it gets more interesting and useful if you want to compute conditional probabilities. Nominal Logistic still does not produce the odds or odds ratios, but you can save the probabilities and then use Tables > Summary to get a concise table of probs for the remaining manual computation.

Re: Odds ratio for a simple distribution

Jonkandonkan — Thu, 20 Jun 2019 14:10:03 GMT

Thanks for you patience!

Hm, I already have the likelihood ratios from previous analysis. However, in this format I could automatically calculate ORs using Formulas, (but what about 95% CI for OR?)

Also, for me these doesn't make sense:

T3 can't have the highest probability, with fewest individuals?

Re: Odds ratio for a simple distribution

Mark_Bailey — Thu, 20 Jun 2019 14:20:48 GMT

The model is for the marginal probability. Is it true that the group T3 is always smaller? You could use Tables > Summary to get the Sum for T1-T3 overall. Those sums are where the probabilities come from. (You did not enter any covariates so the probabilities are not estimated for each grouping.)

Re: Odds ratio for a simple distribution

Jonkandonkan — Thu, 20 Jun 2019 14:27:00 GMT

Well, almost always. But in that dataset, as you can see T3 has the fewest but highest probability.

Now, with Age as Covariate (As a model effect?) it says: Failed: Cannot Decrease Objective Function, but can proceed and now it makes some sense:

Re: Odds ratio for a simple distribution

Jonkandonkan — Thu, 20 Jun 2019 14:42:09 GMT

Then, using the formula, I get the OR, which seems correct. Then I just need to come up with the formula for calculating 95% CI using this set... Anyone?

Re: Odds ratio for a simple distribution

Mark_Bailey — Thu, 20 Jun 2019 20:06:14 GMT

There is nothing wrong with your OR calculation as far as I know but I have never used them with the marginal probabilities so I do not know how to estimate the OR with a confidence interval in your case.

You might send your request JMP Technical Support (support@jmp.com).

You can also use another software with this capability. There are many on-line calculators although the ones that I found for you did not apply to this case. If there is an R package, then you can write a short script to make JMP work with R to get the results for you.

I'm sorry that we do not have a simple and easy, ready-made solution for you.

Re: Odds ratio for a simple distribution

Jonkandonkan — Mon, 24 Jun 2019 07:29:08 GMT

Thanks.

Yea, didn't find any online calculator suitable for this approach.

Think I will try SPSS (against my will) for just this one.