I'm looking to explore the impact of freedom to choose the difficulty level of one's science courses in school has upon ability levels using data from PISA. One thing which comes up in related literature is the possibility that students who are already more able would benefit more from greater levels of choice, whereas less able students would suffer. In other words, the claim is that there is an interaction effect between choice and ability in relation to ability.
Would it be possible to simply run an OLS regression of the kind:
Ability = Choice + Choice*Ability + Controls
What potential problems could this sort of regression face? Are there any other possible approaches to investigating this interaction? I had thought of dividing my sample into quartiles based on ability level and then testing the relationship between ability and choice within each of those subsamples - but I'd be interested to hear any other suggestions!
Hi Nathan,
David is right. However, ... what you actually are interested in is a sequential relation, which you pack into an (omnibus) interaction formulation. But as it seems you have a very specific definition of how this unpacks, and you need to make this explicit in order to test it. For instance:
Ability at time point (t0) predicts an initial choice (or difficulty)
Then the choice (or difficulty) changes the ability at time point (t+1)
You see your actual hypothesis is about ability before and after the choice (and what is supposed to happen after having chosen), and you would need two measurements. This way your problem of using "the same" variable vanishes, and the model you got in the end would be some king of moderated mediation.
Hope this helps.
Best, René
No. The model you suggest won't work. You can't have a variable on both sides of a model. Please see the interaction discussion in Montgomery with this link:
https://www.google.com/search?q=Montgomery+Design+and+analysis+of+experiments&rlz=1C1CHBF_enUS874US874&oq=Montgomery+Design+and+analysis+of+experiments&aqs=chrome..69i57.30438j0j1&sourceid=chrome&ie=UTF-8
Best wishes, D. Booth
Hi Nathan,
David is right. However, ... what you actually are interested in is a sequential relation, which you pack into an (omnibus) interaction formulation. But as it seems you have a very specific definition of how this unpacks, and you need to make this explicit in order to test it. For instance:
Ability at time point (t0) predicts an initial choice (or difficulty)
Then the choice (or difficulty) changes the ability at time point (t+1)
You see your actual hypothesis is about ability before and after the choice (and what is supposed to happen after having chosen), and you would need two measurements. This way your problem of using "the same" variable vanishes, and the model you got in the end would be some king of moderated mediation.
Hope this helps.
Best, René
Hi
I think if response variable this model is ranking best used probit or lojestic regraession
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