# How to show that the dependent variable decreases to a plateau over trails?

Hi,

One of my hypotheses is about the dependent variable decreasing to a plateau over trails in control and treatment conditions.
I have a regression model that shows a decrease in D.V over trails. Visually I can show that in both conditions it does reach a plateau but is there any other more sophisticated statistical method, that can help me show that reaches a plateau?

Since no one else has answered, I’ll try to point you in a useful direction, at least, though I can’t really be much more helpful. A piecewise model of some kind might be a way to model an effect reaching a plateu, as you describe. I’d suggest you have a look at this thread, which might be a good place to start (if you haven’t already): Piecewise Linear Mixed Models With a Random Change Point

Apart from that, it might be helpful to share a bit more about your data and what process you are trying to model, and for what purpose?

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Depending on the shape of the data, fitting an (decreasing) exponential, sigmoid or a similar curve could also be useful. Also I would be a bit more pedantic about the language: I don’t think you can “show” the DV reaches a plateau with just statistics. At best you can hope to show that a plateauing model is a good fit to your data, possibly also show that it is a better fit than some alternative models. In that regard posterior predictive checks and the loo package might be of interest.

Hope that helps!

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@erognli . @martinmodrak My data is pupil data.I’m trying to model a decrease in pupil size over trails a game progresses. My hypothesis is that in all the conditions they decrease to a plateau and the decrease is faster for blue than for say red(different conditions).
I did use the loo package and the pp checks, but I really don’t understand it in the case of ‘showing’ for a plateau.How should I approach this problem?
Looking forward to what you have to say. Wishing you a great Christmas.

The data you show look like they could be well fitted by an exponential curve, something like:

y_i = p + s_i \\ log(s_i) \sim N(\mu_i, \sigma) \\

Where p > 0 is a parameter for the plateau, and \mu_i is a linear function of trials and condition (as in your usual linear model). Possibly constraining the coefficient for trials to be negative to force decrease.

But, as I said, you cannot “show” a plateu - here the model assumes there is a plateau and you can show this is a good fit for the data. Does that make sense?