Bivariate model — non-linear association
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JuanJMV
Joined: 07/20/2016
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Hi All,
I am working on a bivariate model for two continuous variables (normally distributed).
I have checked the association between these variables and looking at the plots the relationship seems to be non-linear. I have run a regression model and the association is significant but it is probably better explained by a quadratic or U-shaped association.
My question is about the bivariate model. Would it be biassed? Is there any way to model these non-linear associations in a twin model? What would be the best approach for this scenario?
Thank you so much in advance.
Interesting question. Can…
Interesting question. Can you share a scatterplot of the two variables to show the non-linearity? Is there anything about the variables that would make you expect non-linearity or other distributional properties?
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In reply to Interesting question. Can… by AdminNeale
Hi Mike, Thank you so much…
Hi Mike,
Thank you so much for this.
I am working with a variable (chronotype) and testing the association with other variables (e.g. depression). The scatter plot is not very clear since the association is not too strong but in order to give you an idea of the results, I have divided the chronotype measure into deciles and calculated the mean level for each decile. You can see two examples in the attached files.
It is not unexpected to find these results since those with extreme chronotypes could have higher levels of depression, for example.
So, I am not sure how I should treat this in a bivariate model. And what to do in the future if I find non-linear associations.
Thank you so much in advance.
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In reply to Hi Mike, Thank you so much… by JuanJMV
Circumplex?
Interesting. If you were to wrap the data around, say start at D05 and plot D05...D10...D04 it would look sort of normal. It is a sort of circumplex, perhaps. There is likely some literature on circumplex models (e.g., https://www.sciencedirect.com/science/article/abs/pii/S0191886919307147) but I am not very familiar with this area. That article talks about a three-step procedure, whereas I'm more of a one-step fan as there's usually information left on the table as one moves from one step to the next. For example, MLEs of factor scores can have different standard errors, so modeling factor scores after they have been estimated uses less information than if the analysis had been done in one step within a single SEM.
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In reply to Circumplex? by AdminNeale
Thank you so much for this,…
Thank you so much for this, Mike!
The article about circumplex models is really interesting.
I have different variables, and some of them show a U-shaped association (I’ll also test other models following the suggested paper). I know that including X and X² in the model is not sufficient by itself to test for a U-shaped association, but if this pattern is confirmed, would it be appropriate to model it in a bivariate (trivariate) model including Y, X, and X²?
Could this be done using the Cholesky decomposition to examine how much of the variance in Y is explained by A13, A23, C13, C23, E13, and E23?
I’m not sure if this approach would be valid, but I’m curious about how non-linear associations can be modeled in a bivariate ACE model once they are confirmed.
Thank you so much in advance!
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