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st: More on autocorrelation in Poisson, some diagnostic results


From   Antonio Silva <asilva100@live.com>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: More on autocorrelation in Poisson, some diagnostic results
Date   Thu, 14 Aug 2008 14:57:47 -0400

Hello All: I fear now that I run the risk of alienating the people who have helped me with my question, but I am going to ask one more question nonetheless. In response to helpful comments I received, (see previous posts), I ran a Poisson model, following the advice of several posters. If you recall, I was concerned about autocorrelation in a Poisson model.

Here is the model I ran:

glm Y X1 X2 X3, family(poisson) link(log)

The actual results of the model are good, and they confirm the theory. But next, to look at the residuals, I did this:

predict dev
then this:
corrgram dev
Here are the results of that exercise:


LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor]

-------------------------------------------------------------------------------

1 0.9403 0.9449 38.972 0.0000 |------- |-------

2 0.8620 -0.2916 72.558 0.0000 |------ --|

3 0.7664 -0.4628 99.808 0.0000 |------ ---|

4 0.6625 -0.1638 120.72 0.0000 |----- -|

5 0.5586 -0.1633 136 0.0000 |---- -|

6 0.4575 -0.3101 146.54 0.0000 |--- --|

7 0.3369 -0.5216 152.43 0.0000 |-- ----|

8 0.2092 -0.5005 154.77 0.0000 |- ----|

9 0.0897 -0.4995 155.21 0.0000 | ---|

10 0.0007 0.2802 155.21 0.0000 | |--

11 -0.0657 0.5618 155.46 0.0000 | |----

12 -0.1220 0.4781 156.37 0.0000 | |---

13 -0.1667 0.0302 158.12 0.0000 -| |

14 -0.2122 0.5885 161.06 0.0000 -| |----

15 -0.2525 0.1082 165.38 0.0000 --| |

16 -0.2761 0.1019 170.75 0.0000 --| |

17 -0.2791 -0.3027 176.48 0.0000 --| --|

18 -0.2681 1.3390 181.98 0.0000 --| |--------



This looks pretty bad to me, as these results seem to suggest serious AC problems. Am I correct in this conclusion? My first thought was to use arpois, with an ar(1) variable in the model. Does this sound reasonable? Even when I do this, however, the results of the corrgram show big-time AC of the residuals. Moreover, there continues to be AC in the residuals, even when I use higher order ar terms in the model. I am really not sure what to do next. Give up? Run arpois with more ar parameters?


As an aside, I should also note that if I include a lagged version of the dependent variable of the model to see if there was some sort of correlation in the Poisson counts themselves, and the variable did not turn up significant.


 Again, any thoughts are helpful.
Antonio

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