# Linear mixed models: how to interpret 3-way interaction if there is also repeated measures?

I performed a linear mixed models on a data set that measured 'outcome' for 4 groups of individuals at 8 different time points.

In summary, the data set is built up of 3 fixed factors:

1. Factor 1: Exercise (2 levels)
2. Factor 2: Genotype (2 levels)
3. Covariate 3: Time (1 individual is measured at 8 time points)

Individuals were modeled as random factors. Time was included as random effect in the model.

I did the analysis in SPSS and obtained the following results:

Now I am not sure how to interpret this results. I assume that four linear lines are modeled for each of the 2 factors and its two levels, describing the outcome for the 4 groups over time. However, I have problems with relating the results of the fixed effect analysis to these four lines.

My exact problem is most easy to explain while considering a simpler example: a similar analysis with only 1 factor (exercise) over time:

In this case, it is easy to relate these results to the two modeled lines created by the mixed model analysis:

1. 'Intercept' = is the intercept of the reference line
2. 'Exercise' = Does the non-reference exercise group have a significant different intercept?
3. 'Time' = Does the reference line have a significant slope?
4. 'Time * exercise' = Is the slope of the non-reference exercise group significantly different from the slope of the reference group?

So let's now consider the results with the three factors.

Is it correct to say:

1. Intercept = intercept reference line
2. Exercise = Does the non-reference exercise group have a significant different intercept?
3. Genotype = Does the non-reference genotype group have a significant different intercept?
4. Does the reference line have a significant slope?
5. Exercise * Genotype = ?????
6. Exercise * time = Is the slope of the non-reference exercise group significantly different from the slope of the reference group?
7. Genotype * time = Is the slope of the non-reference genotype group significantly different from the slope of the reference group?
8. Exercise * genotype * time = ????

I really hope you can help me! Many thanks in advance!!