Poisson regression
Message/Author
 friederike posted on Monday, November 02, 2009 - 4:48 pm
Dear all,
I have got a problem regarding poisson regression. As predictors for the dependent count variable I have one binary variable (coded 1/0), one standardized manifest variable, and two latent continuous variables, which are standardized by fixing their means at zero and setting their variances to 1; furthermore I included several interactions. For reasons of interpretational ease I intended to recode the binary variable (into 0/1). Surprisingly, this changed the regression coefficients of – solely – the latent factors – not even of the interactions they were part of! I thought that coding of the dummy variable was arbitrary and only changed the coefficients‘ directions but not absolute values or significances of (other) coefficients… did I make a mistake? There goes my model:

MODEL:
i BY i1* i2 i3 i4 i5;
e BY e1* e2 e3 e4 e5;
i@1;
e@1;
int | i XWITH e;
int2 | country XWITH i;
int3 | country XWITH e;
n ON country i e int int2 int3 dn;
i WITH e@0;

Friederike
 Tihomir Asparouhov posted on Tuesday, November 03, 2009 - 9:10 am
Indeed when you rescale the country variable you affect the coefficients of the latent factors. If you have
... +beta1*country*i +beta2*i+...
and you subtract 1 from country the new coefficient in front of i will be beta1 + beta2. This can be seen using algebraic manipulations.
 friederike posted on Tuesday, November 03, 2009 - 11:19 am
Thank you, Tihomir, I see...

But this questions the model above, doesn't it? If coding of the dummy variable "country" changes the results as regards the influences of the latent variables "i" and "e"...

How can I arrive at a trustworthy solution?

In other words: should I recode the dummy variable (into 1 and 2 or whatsoever)? Based on the standard regression literature, however, coding with 0 and 1 is recommended...
 Linda K. Muthen posted on Tuesday, November 03, 2009 - 12:28 pm
If you don't have a reason for doing otherwise, you should use traditional dummy coding of 0 and 1.
 friederike posted on Thursday, November 05, 2009 - 1:55 am

But my question remains on how to decide whether I should code the
dummy variable 1/0 or 0/1?

And why does this re-coding only affect coefficients of the latent
variables and not of the manifest variable "dn"?

Would it be better to run the model with manifest variables only?