[R] [FORGED] How to find the likelihood, MLE and plot it?
peter dalgaard
pdalgd at gmail.com
Thu Nov 19 16:29:39 CET 2015
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
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