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From |
Nick Cox <[email protected]> |

To |
"[email protected]" <[email protected]> |

Subject |
Re: st: 2 dimensional graph for joint distribution |

Date |
Fri, 1 Nov 2013 15:33:15 +0000 |

Note that David's recommendation is essentially that recommended earlier in the thread in terms of -tabplot- (SSC). Nick [email protected] On 1 November 2013 12:01, David Hoaglin <[email protected]> wrote: > Dear Lulu, > > I have not had contact with the literature of choice models, but I > looked at the paper by Train. (Thank you for including the link.) > > I do not recall seeing an explanation of why odo and bill are independent draws. > > In your initial message you said that you had estimated those > coefficients "from a nonparametric choice model using fixed mass point > method following Kenneth Train's approach in his 2008 paper." > According to the text of that paper, Figure 5 and Figure 6 show the > joint distribution of two pairs of coefficients (out of the seven > coefficients in his model). That is, the height of each bar is the > sum of the values of share for the combinations of values of the two > coefficients that fall in that particular bin. The pattern of heights > of the bars in the two figures does not seem compatible with taking > the product of independent marginal distributions. Indeed, I would > not expect the distributions of a pair of coefficients to be > independent. > > I don't know whether your data will produce a reasonably smooth > surface, but Train's Figure 5 and Figure 6 are definitely based on > (estimated) joint probabilities. In your last paragraph, your data > will determine whether you have the joint probability for odo = 0.26 > and bill = 0.30 and also the joint probability for odo = 0.26 and bill > = 0.56. You have displayed share as a column vector. For a figure > like those in Train's paper, however, you should think of it as the > height of the bar for the particular combination of values of odo and > bill. The combinations of values of odo and bill in your data will > determine the "grid" (which may be reduced to the bins of a > histogram). > > As I recall, you have 1,000 combinations of odo and bill (with the > share for each). It may be useful to look at the marginal > distribution of odo and the marginal distribution of bill, to choose a > reasonable set of bins for each (i.e., not leave the choice to a > histogram command), and then produce (as panels of the same display) a > separate histogram of bill for each category of odo. This approach is > not elegant, but it avoids the shortcomings of 3D in Train's Figure 5 > and Figure 6. > > David Hoaglin > > On Fri, Nov 1, 2013 at 12:04 AM, Lulu Zeng <[email protected]> wrote: >> Dear David, Alfonso and others, >> >> Thank you for your comments. >> >> My understanding of the fixed mass point choice model (using EM >> algorithm) is that -- share here is the individual probability of odo >> and bill (share is the same for odo and bill), not the joint >> probability. >> >> odo and bill are independent draws (using the mdraws command), >> therefore the joint probability is the product of their individual >> probability. >> >> Please let me know if I have misunderstood the model. But if share is >> the joint probability, then it would be just a colum vector, not a >> grid (e.g., I can only have the joint probability for odo of 0.26 and >> bill of 0.30, can't have the joint probability for odo of 0.26 and >> bill of 0.56?) how can I produce a surface graph version of Train's >> graph on page 65 of http://elsa.berkeley.edu/~train/EMtrain.pdf? >> >> It would be really appreciated if I could have your advice on this. * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

**References**:**Re: st: 2 dimensional graph for joint distribution***From:*David Hoaglin <[email protected]>

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