Linear mixed model with one categorical and one continuous fixed effect possible? I'm planning on using a (linear mixed model) LMM for my analyses but am not 100% sure if it is actually suitable.
This is what my data are like:

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*I have one variable measured 4 times for each participant (let's call it dependent variable (D)). It is a subjective measure of my participants rating something.

*I have a variable indicating what participants saw before rating the dependent variable (let's call it predictor 1 (P1)). It has 4 levels (i.e. the four different things participants saw before rating D).

*I have another variable measured once (let's call it predictor 2 (P2)). It is a continuous personality measure from 0-100.

I want to investigate if D is different depending on the level of P1. Furthermore, I want to investigate if the magnitude of the effect of P1 on D is influenced by the magnitude of P2.
Here is what I planned to do:
Run an LMM with D as dependent variable and P1 and P2 as predictors specified as fixed effects (also I plan to add random effects for my participants because there is reason to believe that the effect might not be the same for everybody). Then I will have a look if P1 is a significant predictor and if there is a significant interaction between P1xP2 to answer my question.
Is that possible or am I thinking in the wrong direction?

The approach you described seems to be a reasonable way to investigate your research question(s). In particular, since you have repeated measures within subject, a mixed model with random intercepts for subject may account for the non-independence of observations within subjects, while the estimates of the fixced effects including the interaction will answer your research questions.
