[R-sig-ME] ordinal regression with MCMCglmm

[Jarrod Hadfield]

Hi,

Imagine a latent variable (l) that conforms to the  standard linear  
model.

l = Xb+Zu+e

The probabilities of falling into each of the four categories are:


pnorm(-l)

pnorm(cp[1]-l)-pnorm(-l)

  pnorm(cp[2]-l)-pnorm(cp[1]-l)

1-pnorm(cp[2]-l)

where cp is the vector of cut-points with 2 elements. A 3 cut-point  
model would be over-parameterised (unless the intercept is zero, which  
I presume is what polr does (?).

The factors don't need to be ordered, the order is obtained from  
levels(resp).  In the future, I may only allowed ordered factors to  
stop any accidents.

Cheers,

Jarrod





On 14 Apr 2010, at 08:07, Kari Ruohonen wrote:

> Hi and thanks for the answer. I tried exactly that model syntax before
> posting but the output of the "fixed" part had an unexpected
> parameterisation and I thought I misspecified the model somehow. The
> parameters I got with the above model are
> - two cutpoints
> - intercept
> - effect of group B
>
> I would have expected that instead of the intercept and two  
> cutpoints I
> would have had three cutpoints as given by polr (MASS package), for
> example. Can you explain me the parameterisation in MCMCglmm and how  
> it
> connects to the one in polr that uses J-1 ordered cutpoints  
> (J=number of
> score classes) without an intercept?
>
> Also, I am uncertain do I need to convert the "resp" before MCMCglmm  
> to
> an ordered factor (with "ordered")?
>
> Many thanks,
>
> Kari
>
> On Tue, 2010-04-13 at 17:41 +0100, Jarrod Hadfield wrote:
>> Hi Kari,
>>
>> The simplest model is
>>
>>
>> m1<-MCMCglmm(resp~treat, random=~group, family="ordinal",
>> data=your.data, prior=prior)
>>
>> as with multinomial data with a single realisation, the residual
>> variance cannot be estimated from the data. The best option is to fix
>> it at some value. most programs fix it at zero but MCMCglmm will fail
>> to mix if this is done, so I usually fix it at 1:
>>
>>
>> prior=list(R=list(V=1, fix=1), G=list(G1=list(V=1, nu=0)))
>>
>> I have left the default prior for the fixed effects (not explicitly
>> specified above), and the default prior random effect variance
>> structure (G) which has a zero degree of belief parameter. Often this
>> requires some/more thought, especially if there are few groups or
>> replication within groups is low. Sections 1.2, 1.5 & 8.2 in the
>> CourseNotes cover priors for variances.
>>
>>
>> Currently there is no option for specifying priors on the cut- 
>> points -
>> the prior is flat and improper. The posterior in virtually all cases
>> will be proper though.
>>
>> Cheers,
>>
>> Jarrod
>>
>> Quoting Kari Ruohonen <kari.ruohonen at utu.fi>:
>>
>>> Hi,
>>> I am trying to figure out how to fit an ordinal regression model  
>>> with
>>> MCMCglmm. The "MCMCglmm Course notes" has a section on multinomial
>>> models but no example of ordinal models. Suppose I have the  
>>> following
>>> data
>>>
>>>> data
>>>   resp treat group
>>> 1     4     A    1
>>> 2     4     A    1
>>> 3     3     A    2
>>> 4     4     A    2
>>> 5     2     A    3
>>> 6     4     A    3
>>> 7     2     A    4
>>> 8     2     A    4
>>> 9     3     A    5
>>> 10    2     A    5
>>> 11    1     B    6
>>> 12    1     B    6
>>> 13    1     B    7
>>> 14    2     B    7
>>> 15    2     B    8
>>> 16    3     B    8
>>> 17    2     B    9
>>> 18    1     B    9
>>> 19    2     B   10
>>> 20    2     B   10
>>>
>>> and the "resp" is an ordinal response, "treat" is a treatment and
>>> "group" is membership to a group. Assume I would like to fit an  
>>> ordinal
>>> model between "resp" and "treat" by having "group" effects as random
>>> effects. How would I specify such a model in MCMCglmm? And how  
>>> would I
>>> specify the prior distributions?
>>>
>>> All help is greatly appreciated.
>>>
>>> regards, Kari
>>>
>>> _______________________________________________
>>> 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.