7 messages · David Duffy, Pierre de Villemereuil, Jarrod Hadfield
Thing is: there is nothing like this for GLMMs. The lowest level of "residual variance" is basically the distribution variance. You could think there would be such a thing with a threshold model, but it turns out that the total variance of the liability scale is non identifiable, so nothing there either.
There is some information when there are multiple thresholds.
Hi David,
Thing is: there is nothing like this for GLMMs. The lowest level of "residual variance" is basically the distribution variance. You could think there would be such a thing with a threshold model, but it turns out that the total variance of the liability scale is non identifiable, so nothing there either.
There is some information when there are multiple thresholds.
You mean information to measure e.g. additive over-dispersion? I agree but wouldn't you need quite a lot of thresholds (categories) for this to be measurable and not poses numerical issues? I have no practical experience in trying to account for that, so I'm curious if you have any experience in this. Best, Pierre.
Hi, I think the residual variance is still non-identifiable with multiple thresholds. In fact,? this paper: https://gsejournal.biomedcentral.com/track/pdf/10.1186/1297-9686-27-3-229 uses the non-identifiability in a 3 category problem to fix the thresholds but estimate the residual variance because this is the same as fixing the residual variance and estimating the free threshold. Cheers, Jarrod
Hi David,
Thing is: there is nothing like this for GLMMs. The lowest level of "residual variance" is basically the distribution variance. You could think there would be such a thing with a threshold model, but it turns out that the total variance of the liability scale is non identifiable, so nothing there either.
There is some information when there are multiple thresholds.
You mean information to measure e.g. additive over-dispersion? I agree but wouldn't you need quite a lot of thresholds (categories) for this to be measurable and not poses numerical issues? I have no practical experience in trying to account for that, so I'm curious if you have any experience in this. Best, Pierre.
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The situations I have most experience with is where there are fixed effects/multiple groups and the thresholds vary across groups - eg "spreading" of the thresholds in one group compared to the others may be interpretable as variance difference etc. In multidimensional setups, one tests the goodness of fit of the single threshold model by fitting one-factor models to triads of variables at a time eg Muthen B, Hofacker C (1988): Testing the assumptions underlying tetrachoric correlations. Psychometrika 53:563-578. Maybe there is information about the residual variances in the 2-threshold model in such a setup? Cheers, David.
Hi, I think the residual variance is still non-identifiable with multiple thresholds. In fact, this paper: https://gsejournal.biomedcentral.com/track/pdf/10.1186/1297-9686-27-3-229 uses the non-identifiability in a 3 category problem to fix the thresholds but estimate the residual variance because this is the same as fixing the residual variance and estimating the free threshold. Cheers, Jarrod On 18/06/2018 11:11, Pierre de Villemereuil wrote: > Hi David, > >>> Thing is: there is nothing like this for GLMMs. The lowest level of "residual variance" is basically the >>> distribution variance. >>> You could think there would be such a thing with a threshold model, but it turns out that the total variance of >>> the liability scale is non identifiable, so nothing there either. >> There is some information when there are multiple thresholds. > You mean information to measure e.g. additive over-dispersion? > > I agree but wouldn't you need quite a lot of thresholds (categories) for this to be measurable and not poses numerical issues? I have no practical experience in trying to account for that, so I'm curious if you have any experience in this. > > Best, > Pierre. > > _______________________________________________ > R-sig-mixed-models at r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models -- The University of Edinburgh is a charitable body, registered in Scotland, with registration number SC005336. _______________________________________________ R-sig-mixed-models at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
Hi,
Maybe there is information about the residual variances in the 2-threshold model in such a setup?
Maybe, but it would be quite hard (if possible at all) to distinguish from changes in the mean, wouldn't it? Unless the changes in the "spreading" are quite dramatic and located in the extreme categories with a strong "depletion" from the central one. It's interesting to think about it though. Cheers, Pierre.
Hi, No - the residual variance is non-identifiable in a threshold model irrespective of the number of thresholds unless the thresholds are constrained in some way (e.g. fully constrained as in the paper I previously referenced). Strong depletion from the central category would simply mean the two thresholds are close together. Cheers, Jarrod
Hi,
Maybe there is information about the residual variances in the 2-threshold model in such a setup?
Maybe, but it would be quite hard (if possible at all) to distinguish from changes in the mean, wouldn't it? Unless the changes in the "spreading" are quite dramatic and located in the extreme categories with a strong "depletion" from the central one. It's interesting to think about it though. Cheers, Pierre.
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Yes, but would an assumptions that thresholds are conserved between the groups you compare reasonable (depends on the "groups" of course)? In that case (with "fixed" thresholds assumptions), you might be able to start talking about the variance, no? Of course, it's still non identifiable, in the sense that you need to assume fixed thresholds to talk about this. I figured it was the assumption David was making. Cheers, Pierre. Le mardi 19 juin 2018, 10:04:22 CEST Jarrod Hadfield a ?crit :
Hi, No - the residual variance is non-identifiable in a threshold model irrespective of the number of thresholds unless the thresholds are constrained in some way (e.g. fully constrained as in the paper I previously referenced). Strong depletion from the central category would simply mean the two thresholds are close together. Cheers, Jarrod On 19/06/2018 08:38, Pierre de Villemereuil wrote:
Hi,
Maybe there is information about the residual variances in the 2-threshold model in such a setup?
Maybe, but it would be quite hard (if possible at all) to distinguish from changes in the mean, wouldn't it? Unless the changes in the "spreading" are quite dramatic and located in the extreme categories with a strong "depletion" from the central one. It's interesting to think about it though. Cheers, Pierre.
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-- The University of Edinburgh is a charitable body, registered in Scotland, with registration number SC005336.