Timeline for False Coverage Rate for confidence intervals of positive likelihood ratios of multiple dependent tests
Current License: CC BY-SA 3.0
13 events
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| May 20, 2021 at 21:04 | comment | added | vbip | I came to this question while searching for an answer to a similar question I posted to SE. Just to get this right @JohnRos, if I construct five confidence intervals and 3 of them are significant at the 0.05 level (i.e., their 95% confidence intervals don't include zero), do I need to construct their new confidence intervals at the 𝛼𝑅/𝑚=0.05*3/5=0.03 level (which is 97% interval)? My original question is here: stats.stackexchange.com/questions/501346/… | |
| Apr 30, 2015 at 15:09 | comment | added | nominator | Actually the problem I have with this approach is that I want to select parameters based on their significance. The number of parameters to select should not be fixed a priori, and not just based on the likelihood ratios because that would ignore their significance. That's why I prefered the "FCR-Adjusted BH-Selected CIs" procedure. It selects parameters based on their p-values and then constructs 1-Rq/m CIs for them. The only problem I had, as stated in my question, was how to get p-values from likelihood ratios. But I have figured this out now. | |
| Apr 28, 2015 at 6:04 | comment | added | JohnRos | Absolutely. See the Methods/Overview subsection in [2]. | |
| Apr 27, 2015 at 20:04 | comment | added | nominator | So could I just select the likelihood ratios that are >= 2 (for example) and then construct 1 - Rq/m confidence intervals for those? | |
| Apr 26, 2015 at 14:39 | comment | added | JohnRos | For the purpose of FCR control, it does not matter. You can use hypothesis testing, or any arbitrary cutoff. | |
| Apr 26, 2015 at 14:08 | comment | added | nominator | But how do I calculate R? That is the main question. | |
| Apr 26, 2015 at 14:06 | comment | added | JohnRos | Good. Then the number of likelihood ratios you select is R. | |
| Apr 26, 2015 at 14:05 | comment | added | nominator | Basically I want to select the parameters that have high positive likelihood ratios ("significantly" above 1) with a certain level of confidence. That's why I am calculating confidence intervals for them. It seems like a multiple-testing matter to me, because there is definitely going to be selection. | |
| Apr 26, 2015 at 12:15 | comment | added | JohnRos | Regarding the selection: Are you constructing intervals for all likelihood ratios? If so, there is no selection (R=m). How to construct a marginal interval on the likelihood ratio is not a multiple-testing matter. Just construct the intervals as you would construct for inference on a single parameter. | |
| Apr 26, 2015 at 12:12 | comment | added | JohnRos | From [1]: unadjusted CIs seem more acceptable than "... they give the right coverage on average; the proportion of 95% CIs covering their respective parameters out of the intervals constructed (namely, the number covering divided by the number of parameters m) is expected to be .95, and thus only .05 will not be covered..." | |
| Apr 26, 2015 at 9:28 | comment | added | nominator | Also, it's still not clear to me how to select parameters (if R<m), as I have likelihood ratios, not p-values. | |
| Apr 26, 2015 at 9:26 | comment | added | nominator | I don't understand "If you are constructing intervals on all considered parameters, there is no need for correction. Regular intervals will control the FCR". Why would there be no need for correction in this case? (I couldn't find this in the referred article). | |
| Apr 25, 2015 at 17:24 | history | answered | JohnRos | CC BY-SA 3.0 |