We have a three-level model with time-of-day (binary: morning versus afternoon, Level 1) nested in days (Level 2) nested in persons (Level 3). We want to test a cross-level interaction with the Level-1 variable moderating the relationship between a Level-2 predictor variable and the Level-1 outcome variable. Note: this cross-level interaction is different from the "usual" cross-level interaction where the Level-2 variable is the moderator.
In MLwiN we can build an interaction term between the Level-2 predictor and the Level-1 moderator, this is straightforward. But we are wondering how we should treat fixed versus random slopes: in our model the effect from the Level-2 predictor variable on the Level-1 outcome is contingent on the score of the Level-1 moderator. Thus, would it make sense to specify a random slope of the Level-2 predictor (i.e., the slope varying at Level 1)? It is possible in technical terms, but appears strange within the multilevel logic.
cross-level interaction with Level-1 moderator
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Re: cross-level interaction with Level-1 moderator
It typically doesn't make sense to predict a level 1 outcome using something defined at level 2. It can be specified but what happens is that such a model effectively induces dependencies among level 1 residuals. Also not easy to interpret.
Harvey Goldstein
Harvey Goldstein
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Re: cross-level interaction with Level-1 moderator
Ignore previous post - should have read that it is inappropriate to predict a level 2 using a level 1 variable - this seems implicitly what is happening in your model.
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Re: cross-level interaction with Level-1 moderator
Hi Harvey,
thank you very much for your quick reply. How would you then specify the slopes? As fixed? Because content-wise it makes sense to propose that time of day (Level 1) influences the relationship between a day-spefic variable (e.g., sleep quality during the previous night; Level 2) and momentary affect (Level 1) - i.e., sleep quality would matter more for for affect in the morning than for affect in the afternoon.
Also Aguinis et al. (2013) briefly mention a situation of a Level-1 variable moderating the relationship between a Level-2 variable and a Level-1 outcome. But is seems that there are not many studies capturing this.
Best
Sabine
thank you very much for your quick reply. How would you then specify the slopes? As fixed? Because content-wise it makes sense to propose that time of day (Level 1) influences the relationship between a day-spefic variable (e.g., sleep quality during the previous night; Level 2) and momentary affect (Level 1) - i.e., sleep quality would matter more for for affect in the morning than for affect in the afternoon.
Also Aguinis et al. (2013) briefly mention a situation of a Level-1 variable moderating the relationship between a Level-2 variable and a Level-1 outcome. But is seems that there are not many studies capturing this.
Best
Sabine
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Re: cross-level interaction with Level-1 moderator
If I understand your model it seems to me that what you call the level 1 classification (am/pm) is actually a predictor variable and if you treat it as such then your analysis is straightforward, isn't it?