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st: autocorrelation in Poisson regression


From   Antonio Silva <asilva100@live.com>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: autocorrelation in Poisson regression
Date   Wed, 13 Aug 2008 16:16:51 -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 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 indicate serious AC problems. 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? Again, any thoughts are helpful. 
Antonio

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