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Re: st: 2 dimensional graph for joint distribution


From   Alfonso Sánchez-Peñalver <alfonso.statalist@gmail.com>
To   Stata List <statalist@hsphsun2.harvard.edu>
Subject   Re: st: 2 dimensional graph for joint distribution
Date   Thu, 31 Oct 2013 21:16:45 -0400

Hi Lulu,

I am concerned with your method of calculating the joint probability. From your example and your explanation 0.34 is the sample estimate of the joint probability of odo being 0.26 and bill being 0.30. Similarly 0.25 is the sample estimate of the joint probability that odo is 0.89 and bill is 0.56. You then estimate the joint probability that odo is 0.89 and bill is 0.30 by multiplying 0.34 (P of odo 0.26 and bill 0.30) by 0.25 (P of odo being 0.89 and bill being 0.56). How can you justify this?

Sorry if this doesn’t address the surface problem, but I thought this was strange.

Best,

Alfonso



On Oct 31, 2013, at 8:25 PM, Lulu Zeng <luluzengnz@gmail.com> wrote:

> Dear David and others,
> 
> Thank you for responding to my question.
> 
> "odo" and "bill" are 2 random coefficients I obtained from a fixed
> mass points nonparametric choice model, "share" is the proportion of
> observations at each point of "odo" and "bill", therefore gives the
> probability of "odo" and "bill" at each point. Share is the same for
> odo and bill, example as below (my actual model has 1,000 points).
> 
> odo     bill      share
> 0.26    0.30    0.34
> 0.89    0.56    0.25
> 0.41    0.73    0.41
> 
> To work out the joint probability (call it "jp") of odo and bill at
> each point, I multiply the colum vector "share" with its transposed
> row vector as shown in table below (jp is the centre part of the matrx
> below):
> 
>                                         bill share
> 
>                                    0.34    0.25     0.41
> 
>                      0.34       0.12    0.09     0.14
> odo share      0.25       0.09    0.06     0.10
>                      0.41       0.14    0.10     0.17
> 
> For the surface graph, I want odo on x axis, bill on y axis, and jp on
> z. I thought the graph may be bell sharped as jp is symetric.
> 
> In my previous email, I wasn't sure how to put jp in the graph as
> -surface- needs 3 variables while my jp is a matrix.
> 
> I just figured out a potential way to solve the problem but I haven't
> got the chance to try it so still unsure whether it will work. My
> approach is to reshape the data -- stack all 3 colums of jp into 1
> colum and match odo, bill, and jp as one to one relationships. Example
> below:
> 
> odo      bill        jp
> 0.26    0.30    0.12
> 0.89    0.30    0.09
> 0.41    0.30    0.14
> ...................................
> 0.26    0.56    0.09
> 0.89    0.56    0.06
> 0.41    0.56    0.10
> ...................................
> 0.26    0.73    0.14
> 0.89    0.73    0.10
> 0.41    0.73    0.17
> 
> Then I will do: surface odo bill jp
> 
> Thank you again David, please let me know if you can see any problem
> in my approach, any alternative approach greatly appreciated.
> 
> Best Regards,
> Lulu
> 
> 
> 
> On Thu, Oct 31, 2013 at 10:38 PM, David Hoaglin <dchoaglin@gmail.com> wrote:
>> Dear Lulu,
>> 
>> From your description, it appears that, for each combination of one
>> value of odo and one value of bill, you have an n by n matrix that you
>> would like to display.  Would you please explain that matrix further?
>> In your initial message, share appeared to be a column vector, so it's
>> not clear what you mean by "share multiplied by its inverse."  Also,
>> what is n?
>> 
>> Also, in an earlier message I think you said that you expected the
>> joint distribution to be bell-shaped.  Why do you expect that shape?
>> 
>> David Hoaglin
>> 
>> On Thu, Oct 31, 2013 at 5:06 AM, Lulu Zeng <luluzengnz@gmail.com> wrote:
>>> Dear Statalist,
>>> 
>>> My apologies for keep coming back with the same topic.
>>> 
>>> I am trying to use -surface- to graph the joint distribution of odo
>>> and bill. I want the value of odo on the x axis and bill on y axis,
>>> and their joint distribution jd (a square matrix) on the z axis. jd is
>>> calculated from share, which is the individual distribution of odo and
>>> bill.
>>> 
>>> I understand -surface- needs the z axis to be a singular variable,
>>> however, my jd is a n by n matrix (calculated by share multiplied by
>>> its inverse).
>>> 
>>> Could you please advise if there is a way to do this?
>>> 
>>> Best Regards,
>>> Lulu
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