In many papers that used regression model, we found econometric model used during analysis. But, when I analyze the methodoly used to draw conclusion, I find that most of the papers did not consider the possible interaction between the indepenent variables. Is it a right way to do thing or a partial conclusion?
Hi Paul, tank you for the link. I ask that question, because that is the way many researchers used to do. I think they should test and includ the interaction of variables.
Interaction variables moderate the effect of one IV on DV.It is extremely necessary to include interaction variable since it can change our results.For example we might not find any significant effect of education on growth in a study but when interacted with improved curriculum/overall governance of the state,education can have significant effect on growth.In my opinion it would not be wise to drop the analysis of interaction from conclusion.
Hi, Ibrahim, you are right. But, when you try to read many articles, you can find few of them consider the analysis of the interaction. They assume the lack of interaction without testing it.
Hello Antonie
Well the the plausible explanation behind the estimated coefficient/elasticity attached to the interaction term not being analyzed could be due to it not being statistically significant. The statistical invalidity would make no sense for it to be analyzed. However, it is critically pertinent to augment interaction terms into the model since the overall impact of one independent variable on the dependent variable could be conditional on another independent variable. Hence, the interaction terms provide a better understanding on the conditional marginal impacts.
Hope this clarifies your query.
Regards
I suspect one reason you don't see interaction terms in regression models very often is that many people find them difficult to interpret. There are various reasons for this. One has to do with interpretation of coefficients. Typically, people learn simple linear regression first, then multiple linear regression with two variables, first order effects only, like this:
Y = b0 + b1X1 + b2X2 + e
In that model, they learn the following interpretations of the two coefficients:
b1 = change in Y-hat for a one unit increase in X1 with X2 held constant
b2 = change in Y-hat for a one unit increase in X2 with X1 held constant
But that simple approach to interpreting coefficients gets loused up when you add X1*X2 to the model:
Y = b0 + b1X1 + b2X2 + b3X1X2 + e
In particular, people cannot understand how X1*X2 can increase by one unit with both X1 and X2 held constant! On top of that, I would argue that some of the most popular stats packages have only recently started including tools to help users plot and understand the nature of interactions in regression models--and some of those packages are still rather weak in this area.
But I would also caution you not to go overboard and include every conceivable interaction term in your model. Consider this excerpt from Mike Babyak's 2004 article on overfitting (https://people.duke.edu/~mababyak/papers/babyakregression.pdf), for example. (Emphasis was added by me).
--- start of excerpt ---
Assuming we have selected a reasonably representative sample from the population and have used reliable and valid measures of the variables of interest, we can use 1 of these models to make a guess at what the true model, or at least part of it, might look like. To achieve a model that will replicate in a new sample, we need to have an adequate sample size to generate reasonably accurate estimates of the unknowns (eg, b-weights in multiple regression). If we try to estimate too many unknowns—or, more technically speaking, if we use up too many degrees of freedom[2]—with respect to the number of observations, we will end up including predictor variables, or finding complicated relations (interactions, nonlinear effects) between the predictors and the response that indeed exist in the sample, but not in the population.
[Footnote 2] I use the term degrees of freedom throughout this article in the sense of the number of unknowns in a system that are free to vary. The number of degrees of freedom available for estimation in a regression model is roughly the number of unique bits of information (observations or cases) minus the number of unknowns (regression weights) to be estimated. In other words, each unknown uses up a degree of freedom. The notion of using too many degrees of freedom given the amount of information is a key idea in many branches of science and is directly related to the concepts of parsimony and falsification, or disconfirmation, in the philosophy of science. See Mulaik (26), for example.
--- end of excerpt ---
I'm sure I've also seen other sources that talk about overfitting due to inclusion of complex terms, but cannot lay my hands on them right now. Perhaps other followers of this thread will remember some of them.
HTH.
Cheers,
Bruce
Interactions can be very interesting, but you need quite a lot of statistical power to be able to detect reliably. if you have enough data, then explore on one subset, and confirm on the other. Why should there be no interactions?
Bruce and Jones,thank you so much for your interesting explanation. As Bruce said, there are some packages in R for instance, that detect automatically the possible interaction. However, in the final model, one must check for multicollineality issues.
Best.
You may want to have a look at this paper where evaluating interactions is the aim
Article Uncovering interactions in multivariate contingency tables: ...
]and this paper which gives some insight into the surge of interest in social epidemiology into what is called intersectionality
Preprint Using shrinkage in multilevel models to understand intersect...
Actually, models should be parsimonious, which means that they must contain as few variables as possible. This leads us to detect interaction (correlation) between variables and remove the most necessary ones. One manner to detect correlation between variables is matrix correlation. We can also poceed to ANOVA test in order to eliminate useless variables.
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