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I have a linear mixed model for predicting speed of a street crossing by a pedestrian with the factors VS (vehicle speed), GAP (selected time gap size for crossing), the interaction factors VSxGAP and a random intercept.

How can I interpret parameter estimates for the interaction effects?

Dependent Variable is Speed of Street Crossing in mm/s

I only have a random effect of the intercept - is it still correct to interpret the interaction effects as follows?:

a) At the reference VS of 60km/h, pedestrians reduce their speed by 80mm/s with increasing GAP by 1 GAP-unit.
b) Pedestrians reduce their speed by |-80+70|=10mm/s with increasing GAP at VS 30km/h - interaction effect 30km/h x GAP
c) Pedestrians reduce their speed by |-80+10|=70mm/s with increasing GAP at VS 50km/h - interaction effect 50km/h x GAP

And how can I interpret the fixed effects for VS categories 30km/h and 50km/h? Would it be correct to say:
d) The crossing speed level (mean) or intercept is lowered by 600mm/s for 30km/h
e) The crossing speed level (mean) or intercept is lowered by 60mm/s for 50km/h

And is it correct to imagine the plots for each VS to have different slopes due to the interaction effect!?
The fact that I have not determined any random effects, except for the intercept, confuses me a lot with the interpretation of the estimates - so I would be very thankful for responses.

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Generally, the explanation of fixed effect are the same regardless having or not having random effect in the model.

a), b) and c) are correct. d) and e) need to add the condition that GAP = 0. (delete "or intercept").

You do not need to imagine, you should draw that three straight lines with different slops and intercepts. From this graph, you will understand these thing very clearly.

From your description, I cannot make the judgement that random intercepts should be included in the model or not.

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