R help - Dec 2011 - Problem with reproducing log likelihood estimated with ghyp package

I was playing around with the ghyp package and simulated series of
t-distributed variables when suddenly i was not able to reproduce the log
likelihood values reported by the package. When trying to reproduce the
likelihood values, I summed the log(dt(x,v)) values and it worked with some
simulated series but not all. 

Is there any obvious flaws with this script?

library("ghyp")
series_1=rt(10000,4) 

#simulating 10000 relation of student t variables with df=4
#Which implies a standrad deviation equal to sqrt(2)

series_2=series_1/sqrt(2)*5 

#To get student t distributed variabler with standard
#deviation equal to 5 I rescale the first series

#When i check the first series with the ghyp package, the result coincides
with
#the sum of log likelihood calculated with dt(x, df, ncp, log = FALSE)

fit_1=fit.tuv(series_1, silent=T, symmetric=T)
fit_1
sum(log(dt(series_1,coef(fit_1)$nu,0)))

#The two log likelihood estimates is approximatly equal, and the parameters
are 
#sensible. 

#When I check series 2, i get a very different result. The estimate for mu
and nu 
#is still sensible, but the log likelihood is very different from what i get
with 
#dt(x, df, ncp, log = FALSE)

fit_2=fit.tuv(series_2, silent=T, symmetric=T)
fit_2
sum(log(dt(series_2,coef(fit_2)$nu,0)))

#This is very different



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On Dec 17, 2011, at 10:57 , Steinar wrote:
> I was playing around with the ghyp package and simulated series of
> t-distributed variables when suddenly i was not able to reproduce the log
> likelihood values reported by the package. When trying to reproduce the
> likelihood values, I summed the log(dt(x,v)) values and it worked with some
> simulated series but not all. 
> 
> Is there any obvious flaws with this script?
Try rethinking your definition of the likelihood.

I would expect that the likelihood depends on the scale and position parameters
via (x-mu)/sigma or so. As far as I can tell, you are de facto setting mu=0 and
sigma=1, which might sort of work if you are simulating with mu=0 and sigma=1,
but not when sigma=5.

> library("ghyp")
> series_1=rt(10000,4) 
> 
> #simulating 10000 relation of student t variables with df=4
> #Which implies a standrad deviation equal to sqrt(2)
> 
> series_2=series_1/sqrt(2)*5 
> 
> #To get student t distributed variabler with standard
> #deviation equal to 5 I rescale the first series
> 
> #When i check the first series with the ghyp package, the result coincides
> with
> #the sum of log likelihood calculated with dt(x, df, ncp, log = FALSE)
> 
> fit_1=fit.tuv(series_1, silent=T, symmetric=T)
> fit_1
> sum(log(dt(series_1,coef(fit_1)$nu,0)))
> 
> #The two log likelihood estimates is approximatly equal, and the parameters
> are 
> #sensible. 
> 
> #When I check series 2, i get a very different result. The estimate for mu
> and nu 
> #is still sensible, but the log likelihood is very different from what i
get
> with 
> #dt(x, df, ncp, log = FALSE)
> 
> fit_2=fit.tuv(series_2, silent=T, symmetric=T)
> fit_2
> sum(log(dt(series_2,coef(fit_2)$nu,0)))
> 
> #This is very different
> 
> 
> 
> --
> View this message in context:
http://r.789695.n4.nabble.com/Problem-with-reproducing-log-likelihood-estimated-with-ghyp-package-tp4207833p4207833.html
> Sent from the R help mailing list archive at Nabble.com.
> 
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-- 
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com

Thank you very much for your answer.

I did not think about the scale influencing the log likelihood score. The
first simulation was zero mean student t distributed variables with
variance=v/(v-2). And as far as I can understand, that is exactly what
dt(x,v) assumes. This also gave me the same result as the ghyp package. 
Scaling the variance to get t distributed variables with variance=5^2 gave a
totally different likelihood score for the reason you mentioned. 



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