[ADMB Users] difference between ADMB-RE and R/mgcv in SEs for smoother coefficients in a GAM fitted by maximum likelihood

[dave fournier]

On 12-11-29 01:16 PM, H. Skaug wrote:

Not if you are a frequentist.  Then there is no u just uhat(x).  I don't 
belong to churches.
However the frequentist approach produces numbers much closer to what 
the OP had.
> I think it is the "variance of the random effect given the data"
> data we want. Your second notion of variance,
> which in your example has var(uhat) = 0, does not not
> correspond to "the uncertainty about u", which
> is what people want.
>
> Besides, we need to be consistent internally in ADMB
> with what comes out of -mcmc, and that is the first
> variant.
>
> Conclusion: I think your variance formula is conceptually correct.
>
> Hans
>
>
> On Thu, Nov 29, 2012 at 7:45 PM, dave fournier <davef at otter-rsch.com> wrote:
>> There is also the question of the variance of what?  I was thinking of the
>> variance of the
>> random effect given the data. (At least I think I was thinking that.)
>> Another
>> way of looking at it is the variance of the estimate for the random effect
>> you would
>> get from a frquentist standpoint.   That means running the model over and
>> over with
>> data generated from the right probabilistic model.  From this point of view
>> the
>> correct answer is the variance of uhat(x) as generated from the delta
>> method.
>>
>> To see this difference suppose the model is
>>
>>     f = square(x-10.) + 0.5*square(u(1));
>>
>> Here 10 is one realization of the data.  Then uhat(x) =0 for every data
>> input so the variance of
>> uhat(x) is zero.
>>
>> To incorporate this into the model I think it is sufficient to comment out a
>> line in getbigs.cpp
>> near line 141.
>>
>>>   if (lapprox->hesstype !=2)
>>>      {
>>>        if (lapprox->saddlepointflag==2)
>>>        {
>>>          Suu-=minv;
>>>        }
>>>        else
>>>        {
>>>          //Suu+=minv;   // comment this out
>>>        }
>>>      }
>>
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