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Simple LR as part of a mediation analysis follows the theoretical model: M = i3 + aX + e3.

pnorm of simple linear regression jpeg

One of the models in the stacked analysis is fine... the other one is a bit strange. Why do my residuals look like this?

So, the dependent variable is a continuous latent. The original 10 questions that are used to construct the continuous latent are dichotomous. It is of a non-normal distribution (see below). I have never seen this stepped pattern in the reisiduals. Just the wonder of random-ness or can I understand something about my data from this?

Histogram of response (dependent)

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They look like that because your independent variable takes on only 10 numbers (not sure why, but you probably know). So, there can only be 10 predicted values. But your DV is continuous, so it can take on any value and the residuals will look like a step function.

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    $\begingroup$ Thank you, ever helpful Peter Flom. This is what I intuitively thought. Tbh, I don't know why they chose that question design. With a latent in mind, I would always go for something a bit more fine-grained, with some nominals to reduce fatigue, but there you are. $\endgroup$ – MissD Feb 24 '17 at 13:29

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