Hi fellows, To introduce our research we often need to provide reasons why two independent variables may interact - or our finding of interaction may be simply data-driven. One common reason for interaction is threshold effect. Taking scientific creativity (dependent variable) for example, divergent thinking and convergent thinking are two contributors. In the method searching stage of creation, divergent thinking enables people to think in as many ways as possible, but eventually, in the choice stage, people have to rely on convergent thinking for the best solution. That is, only when convergent thinking reaches a certain "threshold" could divergent thinking affect creativity. This is one example for the underlying dynamics of interaction. However, I haven't found a comprehensive article or monograph on this topic. Could anyone offer help? Best Meng
I would reverse the argument and consider why one would expect the effect of X1 on Y to be perfectly independent of the effect of X2 on Y? In many contexts this is extremely implausible.
I found this paper helpful:
Article Understanding “It Depends” in Organizational Research: A The...
There is a lot of interest in this area across the social sciences under the label of 'intersectionality'.
Preprint Using shrinkage in multilevel models to understand intersect...
Uncovering interactions in multivariate contingency tables: a multi-level modelling exploratory approach Article Uncovering interactions in multivariate contingency tables: ...
I agree with @Thom that the stress has traditionally been on no interactions as the baseline; I wrote this in relation to this alternative concern of parsimony:
"Recognize that the need for parsimony depends on what you are doing: Parsimony is often interpreted as the simplest explanation being the correct one. In data analysis this is frequently taken to imply that the model should be kept as simple as possible and have few terms. For me, the usefulness of the criteria differs by practice. In induction, this can be useful for black-box model building as, in the need to capture signal not noise, parsimony becomes our guard against over-fitting and capturing contingent fluctuations. In deduction, simplicity is often necessary to make the mathematics tractable, but if there is poor abstraction and key processes are missing, then the model is not complex enough. In retroduction, while we might start with simple models in terms of practicality, I see no reason why models should necessarily be limited to simple ones. In panel studies of people’s changing behaviour over time, it is recommended that a separate term is put in the model for each and every person (Allison, 2009) so that each individual becomes their own ‘control’, just as if all stable unobserved variables had been measured, achieving the same function as random assignment in designed experiments. Such a model may well have thousands of terms. When the problem is complex, a complex model may well be needed. Parsimony should not be used to assert a naive view of causality, or to ignore demanding technical requirements."
in
Chapter The practice of quantitative methods
Is it possible to convert the two independent variables into a single one? After all the type of thinking is in a continuum and is it possible to create a score from, say, 0 to 100 with either extreme denoting a type of thinking? This score suggested could be a composite of various attributes that one uses to characterize the type of thinking. This way it takes the interaction issue totally out of the picture.
Srini Vasan
In general I think not - you have two conceptually different variables - being Black and being Poor and there is conceptually an effect for each , but there is also potentially an additional effect for them both in combination.
That is why I tend to fit not Black* Poor in statistical models but Black + Poor + Black* Poor so that I can appreciate/isolate this interaction.
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