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From |
Suryadipta Roy <sroy2138@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Interpretation of interaction term in log linear (non linear) model |

Date |
Mon, 10 Jun 2013 09:37:53 -0400 |

Dear David, Thank you very much for the wonderful suggestions! I would make sure that the writeup reflects them! In fact, I have used -margins- to reflect the contribution of x1 in the two groups as well. A related question was if the coefficient of the interaction term in the log-linear model can be interpreted as a log-odds ratio, and that an important property of odds ratios is that it is constant, i.e. does not matter what values the other independent variables take on. I believe that your suggestions (and my query here) is relevant for Poisson/NB models as well. Sincerely, Suryadipta. On Sun, Jun 9, 2013 at 1:58 PM, David Hoaglin <dchoaglin@gmail.com> wrote: > Dear Suryadipta, > > It may be helpful to focus, initially, on the fitted model in the log scale. > > The definition of the coefficient of "dummy" includes the list of > other predictors in the model (constant, x1, and dummy*x1). Also, > when you interpret the coefficient of "dummy", you should mention that > it summarizes the effect of "dummy" on log(Trade) after adjusting for > simultaneous linear change in x1 and dummy*x1. If the interpretation > of the coefficient of "dummy" does not mention those adjustments, it > gives the impression that the coefficient summarizes the change in > log(Trade) corresponding to an increase of 1 unit (i.e., 1 SD) in x1 > when the other predictors are held constant. In your model that > oversimplified interpretation is misleading, because one cannot change > "dummy" and hold dummy*x1 constant. More generally, the "held > constant" interpretation does not reflect the way multiple regression > works. > > The presence of the interaction term implies that the model makes > separate adjustments for the contribution of x1 in the two groups > defined by "dummy". It also implies (as you mentioned) that the > effect of "dummy" depends on the value of x1. It is easiest to > calculate that effect when x1 = 0. That may be an appropriate > starting point, but you should also show the mean of x1 when "dummy" = > 0 and the mean of x1 when "dummy" = 1 (and look at the relation > between the ranges of x1 in the two groups). Centering the variable > underlying x1 is likely to be a good idea, but the case for dividing > by its standard deviation is less clear. > > This discussion should clarify the interpretation and provide a basis > for translating it to the original scale of the data. It applies also > if you use quasi-likelihood, conveniently available in the glm/poisson > framework. If you want to work in terms of elasticities, please check > that any derivatives involved do not (inappropriately) assume that the > other predictors can be held constant. > > David Hoaglin > > On Sat, Jun 8, 2013 at 12:12 PM, Suryadipta Roy <sroy2138@gmail.com> wrote: >> Dear Statalisters, >> >> I was wondering if some one would be kind enough to clarify if I am on >> the right track in clarifying the coefficient of the interaction term >> when the dependent variable is in logarithm. The estimated model is of >> the form: log(Trade) = constant + 0.15dummy - 0.15x1 + 0.12dummy*x1, >> where dummy is (0,1) categorical variable, x1 is a continuous variable >> (standardized 0 - 1), and dummy*x1 is the interaction term. The result >> has been obtained from a fixed effects panel regression using -areg- >> with robust standard error option, and all the variables are >> statistically significant. Based on readings of Maarten's Stata tip >> 87: Interpretation of interactions in non-linear model, several >> Statalist postings, and the following link >> http://www.stanford.edu/~mrosenfe/soc_388_notes/soc_388_2002/Interpreting%20the%20coefficients%20of%20loglinear%20models.pdf >> , I wanted to make sure if any of the following interpretation of the >> above result is correct: >> >> 1. The coefficient of "dummy" indicates that this category (dummy >> variable = 1) has 16% (= exp(0.15) - 1) more of "Trade" compared to >> the base category (dummy variable = 0). >> 2. The effect of being in this category on "Trade" increases when the >> value of x1 increases. For every standard deviation increase in x1, >> the effect of "dummy" increases by about 13% (exp(0.12) - 1), OR there >> is a statistically significant 13% increase in "Trade" to countries >> having more of x1 relative to countries that have one standard >> deviation lower value of x1, OR the effect of being in the "dummy = 1" >> category in a country with one standard deviation more of x1 than >> average is exp(0.12)*exp(0.15) = 1.31, which means that "dummy=1" >> category has about 31% more "Trade" than "dummy=0" category. >> >> Following suggestions elsewhere in the Statalist, I have pursued other >> non-linear estimation strategies (and have asked questions to that >> effect earlier), but there is a tradition in this literature to use >> log-linear models. Any suggestion is greatly appreciated. >> >> Sincerely, >> Suryadipta Roy. > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/faqs/resources/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/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: Interpretation of interaction term in log linear (non linear) model***From:*David Hoaglin <dchoaglin@gmail.com>

**References**:**st: Interpretation of interaction term in log linear (non linear) model***From:*Suryadipta Roy <sroy2138@gmail.com>

**Re: st: Interpretation of interaction term in log linear (non linear) model***From:*David Hoaglin <dchoaglin@gmail.com>

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