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

[David Winsemius]

> On Nov 19, 2015, at 7:35 AM, C W <tmrsg11 at gmail.com> wrote:
> 
> ah.  Let me fix that and get back to you.
> 
> On a side note, why can't I put fn inside curve(), why do I have to use
> Vectorize()?
> 
> Here's the code and the message:

>>>>> fn <- function(theta){
>>>>> 
>>>>> sum(0.5 * (xvec - rep(theta, 7)) ^ 2 / 1 + 0.5 * log(1))
>>>>> 
>>>>> }

> 
>> curve(fn, -5, 20)
> Error in curve(fn, -5, 20) :
>  'expr' did not evaluate to an object of length ’n’


The sum function is not vectorized. In oder for a function to be considered “vectorized”, it needs to return a vector of the same length as its input.

— 
David.
> 
> 
> On Thu, Nov 19, 2015 at 10:29 AM, peter dalgaard <pdalgd at gmail.com> wrote:
> 
>> 
>> 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
>>>> 
>>> 
>>>      [[alternative HTML version deleted]]
>>> 
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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
>> 
>> 
>> 
>> 
>> 
>> 
>> 
>> 
>> 
>> 
> 
> 	[[alternative HTML version deleted]]
> 
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

David Winsemius
Alameda, CA, USA