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# Re: st: 2 dimensional graph for joint distribution

 From David Hoaglin <[email protected]> To [email protected] Subject Re: st: 2 dimensional graph for joint distribution Date Thu, 31 Oct 2013 23:42:49 -0400

```Dear Lulu,

The joint probability is already given by share.  That is, share is
the (empirical) probability of the particular combination of odo and
bill.  I see no justification for multiplying that column vector by
its transpose.

David Hoaglin

On Thu, Oct 31, 2013 at 8:25 PM, Lulu Zeng <[email protected]> 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
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