[R] [FORGED] How to find the likelihood, MLE and plot it?

[peter dalgaard]

On 19 Nov 2015, at 16:17 , C W <tmrsg11 at gmail.com> wrote:

> Hi Rolf,
> 
> I think the MLE should be 1.71, no?  And yes, I am aware of the
> maximum=TRUE argument.  I still feel something is wrong here.
> 

Just read more carefully what Rolf said: Your fn is MINUS the log-likelihood. So the graph is upside-down.

-pd


> Thanks!
> 
> On Wed, Nov 18, 2015 at 6:23 PM, Rolf Turner <r.turner at auckland.ac.nz>
> wrote:
> 
>> On 19/11/15 11:31, C W wrote:
>> 
>>> Dear R list,
>>> 
>>> I am trying to find the MLE of the likelihood function.  I will plot the
>>> log-likelihood to check my answer.
>>> 
>>> Here's my R code:
>>> 
>>> xvec <- c(2,5,3,7,-3,-2,0)
>>> 
>>> fn <- function(theta){
>>> 
>>> sum(0.5 * (xvec - rep(theta, 7)) ^ 2 / 1 + 0.5 * log(1))
>>> 
>>> }
>>> 
>>> gn <- Vectorize(fn)
>>> 
>>> curve(gn, -5, 20)
>>> 
>>> optimize(gn, c(-5, 20))
>>> 
>>> $minimum
>>> 
>>> [1] 1.714286
>>> 
>>> $objective
>>> 
>>> [1] 39.71429
>>> 
>>> 
>>> The MLE using optimize() is 1.71, but what curve() gives me is the
>>> absolute
>>> minimum.
>>> 
>>> I think 1.71 is the right answer, but why does the graph showing it's the
>>> minimum?  What is going on here?
>>> 
>> 
>> Your graph shows that there is indeed a *minimum* at 1.71.  And optimise()
>> is correctly finding that minimum.
>> 
>> If you want optimise() to find the maximum, set maximum=TRUE.  In which
>> case it will return "20" (or something very close to 20).
>> 
>> Your function fn() appears not to be the log likelihood that you had in
>> mind.  Perhaps you the negative of fn()???
>> 
>> cheers,
>> 
>> Rolf Turner
>> 
>> --
>> Technical Editor ANZJS
>> Department of Statistics
>> University of Auckland
>> Phone: +64-9-373-7599 ext. 88276
>> 
> 
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> 
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-- 
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Office: A 4.23
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com