3

I want to predict a binary outcome $Y$ with two predictors, one is continuous ($X$) and the other is categorical ($G$) and has $n$ levels. I believe relationship between $Y$ and $X$ varies among the $n$ groups so I've built a logistic regression model $Y \sim X + G + X*G$ (which is called if I understand well a random slopes model).

I've also heard about multilevel analysis but I'm not sure if it's different or not of my above model. Can someone help me to understand if there is a difference or not. Is the random slopes model just a specific kind of MLM?

Patrick
  • 393
  • 1
  • 9

1 Answers1

2
  1. No, your model is not a random slopes model.
  2. Yes, A random slopes model is a specific multilevel model.

In your model, you allow for each group $G$ to have a unique slope, which I will call $S_G$. A random slopes model would assume that the distribution of slopes $S_G$ across groups is normal with some mean and variance. You do not make this assumption. Thus, this is not a random slopes model.

Julian Karch
  • 1,433
  • 1
  • 13
  • 26
  • Thank you for your help Julian. So what's the name of my model? Linear with interaction term? And about random slopes model, I understand that it's more constrained than mine, so it's maybe more appropriate for parsimony reasons (if the assumption of normal distribution of slopes is valid). Am I correct? – Patrick May 01 '19 at 18:14
  • Yes, I would simply call it an interaction term. If the assumption of the normal distribution of slopes is valid, your estimates will be better. Even if this is not the case, they might be better. But this is not guaranteed. – Julian Karch May 01 '19 at 18:20
  • Thank you for clarifying! And one last thing: is mixed effects also a kind of multilevel model? – Patrick May 01 '19 at 18:30
  • Mixed effects and multilevel model are two names for the same thing :). – Julian Karch May 01 '19 at 18:33
  • 1
    @Patrick I would say that multilevel models are a *type* of mixed effects models. The latter are more general. See the answer to [this](https://stats.stackexchange.com/questions/171313/difference-between-multilevel-modelling-and-mixed-effects-models) question for details. – Robert Long May 02 '19 at 11:54
  • @RoberLong interesting and good point, which makes a lot of sense when looking at the words. However, at least in psychology multilevel and mixed effects model seem to be used interchangeably. Especially, multilevel models are not understood to be limited to nested factors. – Julian Karch May 02 '19 at 13:29