[R-sig-ME] Using variance components of lmer for ICC computation in reliability study

[David Duffy]

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.
________________________________________
From: R-sig-mixed-models [r-sig-mixed-models-bounces using r-project.org] on behalf of Jarrod Hadfield [j.hadfield using ed.ac.uk]
Sent: Monday, 18 June 2018 8:22 PM
To: Pierre de Villemereuil; r-sig-mixed-models using r-project.org
Subject: Re: [R-sig-ME]  Using variance components of lmer for ICC computation in reliability study

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.
>
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