# Thread: Consequences of choosing the wrong likelihood function...

1. ## Re: Consequences of choosing the wrong likelihood function...

Originally Posted by GretaGarbo

And give the cakes to Jake, who is, I believe, a “cookie scientist”.
that's part of my plan, actually. i want Jake to eat too many cookies so he can become fat :P

Originally Posted by GretaGarbo

What is the meaning of this: Dason on the Cauchy distribution:
"YOU BETTER LOOK OUT BECAUSE THIS IS SOMETHING THAT IS GOING TO GET YOU"
heh... funny story. i think, Greta, that if you come to this forum often enough you will realise that every now and then we all get very philosophical and start debating interesting thinigs. other times we get the same question asked on the forum probably hundreds of times and we, the regular contributors, twist our answers into a debate just for the fun of it. questions that are very recurrent and either get ignored or generate passionate discussions have to do with the appropriate analysis of likert and likert-type responses to surveys (are they discrete? continuous? a latent continuous variable that becomes discretised?) and our own realisation that a lot of people (particularly in my area, the social sciences) do not understand very well the assumptions around ordinary, least-squares (OLS) multiple regression.
one such misunderstanding that gets asked very often here is people being worried because their predictor variables are not normally-distributed. we have tried endlessly to repeat, over and over again, that the assumption of normality is on the residuals and the residuals only. after one of such debates Dason once casually mentioned that that is not always the case. that, sometimes, the distribution of the predictors does matter. it was a surprise (at least for me) because we have been campaining endlessly against this misconception. so when we inquired further i realized that Dason was being facetious because the example that he used was that of regression predictors which follow the Cauchy distribution. which made me sigh in relief because, at least for me, the Cauchy distribution was probably invented by Satan. or a possessed Cauchy (and yes, i know Cauchy didnt invent that distribution, it's just named after him. just in case someone wants to be smart about it :P). why? well... no first and second moments? what kind of distribution is that!?
so when i told Dason that, he replied something along the lines of being mindful that we cannot overgeneralize and say that the distribution of the predictors in multiple regression is never an issue because if they happen to be Cauchy-distributed then we can have certain problems
... but... THAT IT IS NOT SOMETHING THAT IS OUT THERE TO GET YOU. so i assumed that Dason had inside knowledge that the Cauchy distribution may be after me. which sounded funny. so i quoted him that.

Originally Posted by GretaGarbo

And what did you mean by this expression “Frequentism used to be cool but then they got a knife in their knee.” (something like this)

the right version would be " Frequentism used to be cool but then IT TOOK AN ARROW TO THE KNEE." that is a meme, an online joke that went viral on youtube and which me, being the nerd that i am, just had to use it somewhere. a good place to learn about the history of where this whole thing began is here. and i used it on frequentism because i'm starting to switch towards the Bayesian approach to statistcs. i do believe that Bayesianism will be the new paradigm of data analysis.

Originally Posted by GretaGarbo
What means:

“Workin’ for the Raptors” Does it mean: "Working for the Raptors"?

that is true. it is once again part of the inside joke on this forum of the apocalyptic war between raptors and bots. workin' is just English slang to say workinG as you correctly pointed out. the rest is... well... i dunno. i'm wondering if the whole social science side of this forum is either raptor or raptor-sympathiser.

Originally Posted by GretaGarbo
Why don't you ever use upper case letters in the beginning of a sentence?
that's a good question. in an online course i once took in highschool i was scolded BECAUSE I ALWAYS LIKED TO WRITE EVERYTHING ON UPPERCASE LETTERS UNTIL THEY TOLD ME THAT, IN ONLINE ETIQUETTE, WRITTING IN UPPERCASES AMMOUNTS TO YELLING. which is not polite. ever since then i have avoided uppercases. everywhere (even in formal essays :P)

Originally Posted by GretaGarbo
I was gooling the expression: "Maximum likelihood under a wrong model" and found many links.
thanks!! acutally googling that helped me out even more!!!

gosh, now i feel like i should be the next interviwee

Greta, just me being curious... where are you from? you have a great command of statistics. are you a statistician? biostatistician? a graduate student in math/stats?

2. ## Re: Consequences of choosing the wrong likelihood function...

Originally Posted by spunky
... predictors in multiple regression is never an issue because if they happen to be Cauchy-distributed then we can have certain problems
... but... THAT IT IS NOT SOMETHING THAT IS OUT THERE TO GET YOU.
The Cauchy distributon can haunt you when you're testing a (non-directional) null hypothesis involving the ratio of two means - where the two distributions are assumed to normally distributed with means of zero and constant variance....i.e. the problem of so-called "Type III error".

3. ## Re: Consequences of choosing the wrong likelihood function...

I believe my recommendation was that it wasn't something that will actually get you most likely but the it was something to keep in mind. My reasoning was that the Cauchy distribution isn't just some mythical beast (Dragan's example is something I believe I brought up as well in our previous discussion) but most likely you don't need to worry too much.

4. ## Re: Consequences of choosing the wrong likelihood function...

Originally Posted by Dason
I believe my recommendation was that it wasn't something that will actually get you most likely but the it was something to keep in mind..
yep... but it was the way you phrased it that i liked. the whole aspect of it coming to get me... and i was like "oh no! the Cauchy distribution is hunting me down! run! run!"

up to these days i'm still running. my approach to the Cauchy Distribution is the same as Edgar Allan Poe towards ghosts. so quoting him:

"I don't believe in the ghosts. But i have been running from them all my life"

5. ## Re: Consequences of choosing the wrong likelihood function...

Well of course the Cauchy is hunting you down. I wouldn't worry too much though - the expected amount of time until it gets you is undefined.

6. ## Re: Consequences of choosing the wrong likelihood function...

Originally Posted by Dason
Well of course the Cauchy is hunting you down. I wouldn't worry too much though - the expected amount of time until it gets you is undefined.
The Cauchy distribution is useful when deriving moment-matching simulation procedures. A good example is John Tukey's g-and-h distributions. The parameter h controls the tail-weight of the (non)normal distribution. You can easily say that when h=0 the distribution is (log)normal and as h->1 it's Cauchy...nice and easy.

7. ## Re: Consequences of choosing the wrong likelihood function...

Does it mean: “Working for the Raptors”?
I think it does Greta.

All of this can be very confusing for new readers.
I agree... although I suspect that that might be the idea...

8. ## Re: Consequences of choosing the wrong likelihood function...

I wouldn't say that confusing new readers is the idea. But aren't we allowed to have some fun every now and then?

9. ## Re: Consequences of choosing the wrong likelihood function...

Originally Posted by spunky
that's part of my plan, actually. i want Jake to eat too many cookies so he can become fat :P

heh... funny story. i think, Greta, that if you come to this forum often enough you will realise that every now and then we all get very philosophical and start debating interesting thinigs. other times we get the same question asked on the forum probably hundreds of times and we, the regular contributors, twist our answers into a debate just for the fun of it. questions that are very recurrent and either get ignored or generate passionate discussions have to do with the appropriate analysis of likert and likert-type responses to surveys (are they discrete? continuous? a latent continuous variable that becomes discretised?) and our own realisation that a lot of people (particularly in my area, the social sciences) do not understand very well the assumptions around ordinary, least-squares (OLS) multiple regression.
one such misunderstanding that gets asked very often here is people being worried because their predictor variables are not normally-distributed. we have tried endlessly to repeat, over and over again, that the assumption of normality is on the residuals and the residuals only. after one of such debates Dason once casually mentioned that that is not always the case. that, sometimes, the distribution of the predictors does matter. it was a surprise (at least for me) because we have been campaining endlessly against this misconception. so when we inquired further i realized that Dason was being facetious because the example that he used was that of regression predictors which follow the Cauchy distribution. which made me sigh in relief because, at least for me, the Cauchy distribution was probably invented by Satan. or a possessed Cauchy (and yes, i know Cauchy didnt invent that distribution, it's just named after him. just in case someone wants to be smart about it :P). why? well... no first and second moments? what kind of distribution is that!?
so when i told Dason that, he replied something along the lines of being mindful that we cannot overgeneralize and say that the distribution of the predictors in multiple regression is never an issue because if they happen to be Cauchy-distributed then we can have certain problems
... but... THAT IT IS NOT SOMETHING THAT IS OUT THERE TO GET YOU. so i assumed that Dason had inside knowledge that the Cauchy distribution may be after me. which sounded funny. so i quoted him that.

the right version would be " Frequentism used to be cool but then IT TOOK AN ARROW TO THE KNEE." that is a meme, an online joke that went viral on youtube and which me, being the nerd that i am, just had to use it somewhere. a good place to learn about the history of where this whole thing began is here. and i used it on frequentism because i'm starting to switch towards the Bayesian approach to statistcs. i do believe that Bayesianism will be the new paradigm of data analysis.

that is true. it is once again part of the inside joke on this forum of the apocalyptic war between raptors and bots. workin' is just English slang to say workinG as you correctly pointed out. the rest is... well... i dunno. i'm wondering if the whole social science side of this forum is either raptor or raptor-sympathiser.

that's a good question. in an online course i once took in highschool i was scolded BECAUSE I ALWAYS LIKED TO WRITE EVERYTHING ON UPPERCASE LETTERS UNTIL THEY TOLD ME THAT, IN ONLINE ETIQUETTE, WRITTING IN UPPERCASES AMMOUNTS TO YELLING. which is not polite. ever since then i have avoided uppercases. everywhere (even in formal essays :P)

thanks!! acutally googling that helped me out even more!!!

gosh, now i feel like i should be the next interviwee

Greta, just me being curious... where are you from? you have a great command of statistics. are you a statistician? biostatistician? a graduate student in math/stats?
Such a nice piece of detailed interview I hope you are the next one

10. ## Re: Consequences of choosing the wrong likelihood function...

Originally Posted by victorxstc
I hope you are the next one
the way it goes (i think) is that a member nominates you and then other members vote on it. but i might be wrong. i was not here when the whole interviewing thingy started...

11. ## Re: Consequences of choosing the wrong likelihood function...

The way it's been so far is basically whoever is willing to give an interview gets to go next. If nobody is willing then we use the power of peer pressure to try to get somebody to agree to tell us more about themselves. So basically what I'm saying is that you should give the next interview.

***PEER PRESSURE***

12. ## Re: Consequences of choosing the wrong likelihood function...

Originally Posted by Dason
***PEER PRESSURE***
oh no.... i'm cracking...under...the pressure. cracking...cracking.... ok, fiiiiine, i'll do it. whatever helps me avoid writting my thesis. :P

(i'm even planning on starting up with a youtube video component seeing how much in love i'm with it. i've been meaning to start something Kahn Academy-like for people doing psychometrics so i could use that as an intro video and then start talking about topics i like or how to do psychometrics/ data analysis for the social sciences in R, advanced SPSS stuff (<-- yes it can pretty interesting sometimes) and some Mplus/EQS or other latent variable modelling software. i HATE that pretty much everyone charges for these tutorials!)

13. ## Re: Consequences of choosing the wrong likelihood function...

I am sorry victorxstc, if you got the impression that it tended to some kind of interview with Spunky. I think that discussing the Cauchy distribution is relevant when talking about maximum likelihood with the normal distribution. What would be the “consequences of choosing the wrong likelihood function”? I don’t know. The Cauchy distribution is the t-distribution with one degree of freedom. What would be the consequences of estimating normal based likelihood models on data generated from t-distribution with 1, 5, 20 or 100 degrees of freedom?

That could be worth discussing.

Spunky had a very interesting thread about multilevel analysis SEM (structural equations models) and so on so I thought it was interesting to ask about frequentism and Bayesianism and so on.

But I really hope that this will not put pressure on Spunky to be an interviewee. Especially when Spunky need to write the dissertation. I would feel bad if I had been one of those who had prevented Spunky from writing.

I sometimes find it difficult to start to write. Do you find it difficult to explain in simple words what your research is about? Have you heard of “Grandmothers test”? When your grandmother asks you what your research is about then you can explain it in very simple words.

I suggest that spunky pretend that spunky is supposed to explain to “TalkStats” what the research is about. Then once you have started to write something it might flow on. For me it is easier to get started if it is not that serious like “the very big important Research”. There are many experienced people here. Maybe they can share some of their tricks.

I hope that spunky will NOT reply to this thread and NOT to be an interview victim.

Spunky said:
are you a statistician? biostatistician?
Is there a difference?
Is there a difference between biometrics, statistics, econometrics, psychometrics, technometrics, sociometrics or chemometrics? Maybe some areas are drifting away from other. It seems like psychometrics are developing new good methods, and keep an eye to general statistics, but general stats are not aware of what is going on in psychometrics so in my impression it is to the disadvantage of general stats.

Originally Posted by Dason
I wouldn't say that confusing new readers is the idea. But aren't we allowed to have some fun every now and then?

Of course we can have some fun. Actually it is both silly and quite fun. But we can also explain to newcomers what it is about now and then.

Something different: wouldn’t you classify maximum likelihood estimation as a part of “statistics” rather than “probability”?

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