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From |
Lauren Beresford <lberesfo@hotmail.com> |

To |
Statalist <statalist@hsphsun2.harvard.edu> |

Subject |
RE: st: Interaction model |

Date |
Fri, 10 Feb 2012 14:27:30 +0000 |

Hello Statalisters, Just a quick question here. I am running "saturated models" with higher order three-way interactions and lower order two-way interactions as David describes below (although with a binary dv using logistic regression). I am wondering if anyone knows of some good papers or books related to these sorts of models? Best,Lauren Beresford Doctoral Candidate, SociologyUC Berkeley ---------------------------------------- > Date: Wed, 8 Feb 2012 21:55:37 -0500 > Subject: Re: st: Interaction model > From: dchoaglin@gmail.com > To: statalist@hsphsun2.harvard.edu > > You're welcome, Shikha. > > It will be helpful to reproduce model (a), correcting the typo: > > (a) income= b1*program + b2*rich + b3*immi + b4*male + b5*program*rich > +b6*program*male + b7*program*immi > > If I were, mechanically, to sketch an interpretation of b1, it would > say that b1 gives the effect of the program on income, adjusting for > the contributions of [the other six predictors]. Unfortunately, if > the interaction effects are significant, it is not meaningful to > interpret a main effect in the presence of interactions between that > variable and other variables. And in model (a) each of the four > variables in involved in at least one two-factor interaction. Thus, > the model would be saying that the effect of the program differed > between rich and poor, between immigrants and non-immigrants, and > between males and females; and you would need to start with the > average income in each of those subgroups and discuss the comparisons. > A weighted average over the groups might be useful. > > You have not explained why model (a) does not contain a constant term, > which we could denote by b0. > > In such an analysis, if you have enough data, it would make sense to > start with the "saturated" model, which would contain b0 and also the > terms rich*male, rich*immi, and immi*male, program*rich*immi, > program*rich*male, program*immi*male, rich*immi*male, and > program*rich*immi*male (for a total of 16 predictors). It might then > be possible to eliminate some of the interactions, starting with the > highest-order and working down. (If a given interaction is > significant, however, the model must retain all the lower-order terms > associated with the variables involved in that interaction.) > > The easiest model to interpret is the additive model, which would > contain b0 and only the main effects for the four variables. > Departures from additivity often arise when the response variable is > not yet expressed in a suitable scale. In your analysis, data on > income are often skewed, and they behave better when transformed to a > logarithmic scale. I wonder whether analyzing income in the log scale > would lead to an analysis in which the contributions are more nearly > additive. Then, transforming back to the original scale would produce > effects that are multiplicative. > > David Hoaglin > > > > b4 is not the coefficient for both male and program*rich- it was a mistake/typo. > > > > I understand the model in (a) is a richer model compared to different > > specifications in (b). What would be the interpretation of b1 in (a)? > * > * 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/ * * 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/

**Follow-Ups**:**Re: st: Interaction model***From:*David Hoaglin <dchoaglin@gmail.com>

**st: Panel data with simultaneous equations***From:*Ayman Farahat <ayman.farahat@yahoo.com>

**References**:**st: Interaction model***From:*Shikha Sinha <shikha.sinha414@gmail.com>

**Re: st: Interaction model***From:*David Hoaglin <dchoaglin@gmail.com>

**Re: st: Interaction model***From:*Shikha Sinha <shikha.sinha414@gmail.com>

**Re: st: Interaction model***From:*David Hoaglin <dchoaglin@gmail.com>

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