I'm hoping someone could help with a problem that I'm sure has a simple explanation. I have conducted a visual test on 2 groups of people 1) healthy controls 2) patients (with a vision problem) using 2 different types of vision testing charts and tested both right and left eyes.

I have then used the following linear mixed model using the patient ID to account for the nested right and left eyes from each patient and the interaction term to separately analyse the healthy control group from the patient group. So LMM written as:

lmm1 <- lme4::lmer(letters read using chart 2 ~ letters read using chart 1 * group + (1|ID), data = d)

using the interact_plot function from the interaction package I have the following plot which as shown by the summary command of the interaction terms shows a significant difference between slopes.


However, if I swap the dependent and independent variables, so:

lmm2 <- lme4::lmer(letters read using chart 1 ~ letters read using chart 2 * group + (1|ID), data = d)

I obtain the following plot which shows a non-significant difference between the slopes:


I understand that from a theoretical point of view that you would normally decide which variable is the predictor and which the response but in this case both chart 1 and chart 2 are interchangable with both being the obtained from actual measured results and so there is no clear IV versus DV. I would just like to explore the association between both and the differences between controls and patients. So my question is which plot would I go with, plot 1 or plot 2. One shows a significant difference in slopes and the other doesn't.

I'm sure I'm missing something obvious here but I can't see how to analyse the association between these two variables.

Thank you

  • $\begingroup$ What are you trying to find out? What are your research questions/hypotheses? $\endgroup$
    – Peter Flom
    Commented Jul 10 at 16:30
  • $\begingroup$ Hi, I'm trying to find out if chart 1 is significantly different from chart 2 in its ability to distinguish the letter reading ability between controls vs patients. $\endgroup$
    – holmes
    Commented Jul 10 at 20:06

1 Answer 1


Your regressions do not seem to answer that question. I would, instead, see which did better.

So, the DV would be "control vs. patient" and the IVs would be letters read with each chart. Since this DV is binary, a natural starting point is logistic regression. I would do two logistic regressions, one using each chart. How exactly you operationalize "letters read" is up to you -- maybe total, maybe "left" and "right" or maybe something else.

  • $\begingroup$ Of course! Thank you very much. That makes total sense. $\endgroup$
    – holmes
    Commented Jul 11 at 18:20

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