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From |
David Hoaglin <dchoaglin@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Interaction model |

Date |
Wed, 8 Feb 2012 21:55:37 -0500 |

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/

**Follow-Ups**:**RE: st: Interaction model***From:*Lauren Beresford <lberesfo@hotmail.com>

**RE: st: Interaction model***From:*Cameron McIntosh <cnm100@hotmail.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>

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