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From |
Maarten buis <maartenbuis@yahoo.co.uk> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Quadratic term in ZIP model |

Date |
Mon, 18 Oct 2010 09:20:09 +0100 (BST) |

--- On Sat, 16/10/10, Asaduzzaman Khan wrote: > I've fitted a zero-inflated Poisson (ZIP) model where I had > to include a significant quadratic term (e.g. age, age^2) to > have a better fit. Can anyone help me with the > interpretation of the overall effect of age on the counts? The very fact that you included a quadratic term means that there no longer is one effect of age but that the effect of age differs depending on how old one is. As a consequence it is hard to imagine how to define an "overall effect". I would just graph the effect of age. Alternatively, I would represent age as linear splines, see -help mkspline- if age is only of secondary importance so I would not want to spent an entire graph on it. That way you can interpret directly interpet the parameters. In the example below I show one way of graphing a model with a quadratic term. Below that I show the alternative with linear splines. The latter would be interpreted as follows: below mathnce score of 50 you would expect a 10 point increase in mathnce to result in a decrease of the expected count by a factor of 0.95 (i.e. (1 - 0.95)*100% = -5%), while above a mathnce score of 50 you would expect a 10 point increase in mathnce to result in in increase in the expected count by a factor of 1.07 (i.e. 7%). *--------------------- begin example ---------------------------- use http://www.ats.ucla.edu/stat/stata/notes/lahigh, clear zip daysabs i.gender i.biling mathnce langnce, inflate(i.school) est store lin zip daysabs i.gender i.biling c.mathnce##c.mathnce langnce, inflate(i.school) est store quad preserve // fix the other variables at meaningful values replace gender = 2 replace biling = 0 sum langnce if e(sample), meanonly replace langnce = r(mean) replace school = 1 // keep only one observation per unique value of mathnce // this will make the resulting graph smaller in terms of memory bys mathnce : keep if _n == 1 // predict the expected counts est restore lin predict n_lin est restore quad predict n_quad // graph the expected counts twoway line n_lin n_quad mathnce, sort /// legend(order( 1 "linear" /// 2 "quadratic")) restore // alternatively use linear splines // make the unit a bit bigger for ease of interpretation replace mathnce = mathnce / 10 mkspline math1 5 math2 = mathnce zip daysabs i.gender i.biling math1 math2 langnce, inflate(i.school) irr *----------------------- end example ----------------------------------- (For more on examples I sent to the Statalist see: http://www.maartenbuis.nl/example_faq ) Hope this helps, Maarten -------------------------- Maarten L. Buis Institut fuer Soziologie Universitaet Tuebingen Wilhelmstrasse 36 72074 Tuebingen Germany http://www.maartenbuis.nl -------------------------- * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Quadratic term in ZIP model***From:*Asaduzzaman Khan <asad1988@yahoo.com>

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