In order to interpret the coefficients of your GLM, you have to consider the underlying structural regression model, including the interaction:

Basic model: Yi = b0 ​+ b1​⋅X1i ​+ b​2⋅X2i​ + b3​⋅X1i * X2i

Because both of your indicator variables X1 and X2 have 3 levels, you get the following coefficients in your model:

Specific model: Y(BAOP_TIME) = b0 ​+ b1​ ⋅ condition1 + b2 ​⋅ condition2 + b3​ ⋅ time1 + b4 ​⋅ time2 + b5 ⋅ (condition1 x time1) + b6 ​⋅ (condition1 x time2) + b7​ ⋅ (condition2 x time1) + b8​ ⋅ (condition2 x time2)

So the coefficients split in three parts:

(1) Intercept

• β0: Baseline BAOP_TIME for the reference group (Intervention_Condition=3 at TIME=3)

(2) Main (“Conditional”) effects

• β1: Change in BAOP_TIME for Intervention_Condition=1 at TIME=3 relative to Intervention_Condition=3, holding other factors constant. Interpretation: β1 = 2.432 suggests that, on average, BAOP_TIME for Intervention_Condition 1 is estimated to be 2.432 units higher than the BAOP_TIME for the reference group (Intervention_Condition 3) at TIME 3, holding other factors constant. However, the effect lacks statistical significance.
• β2: Change in BAOP_TIME for Intervention_Condition=2 at TIME=3 relative to Intervention_Condition=3, holding other factors constant.
• β3: Change in BAOP_TIME for TIME=1 relative to TIME=3 for the reference Intervention_Condition=3, holding other factors constant.
• β4: Change in BAOP_TIME for TIME=2 relative to TIME=3 for the reference Intervention_Condition=3, holding other factors constant.

(3) Interaction effects

• β5: Additional change in BAOP_TIME for Intervention_Condition=1 at TIME=1 compared to Intervention_Condition=3 at TIME=3, holding other factors constant. Interpretation: β5=−3.712 with p=0.026 indicates that for participants in Intervention_Condition 1, BAOP_TIME at TIME 1 is significantly lower by 3.712 units compared to the reference group, controlling for the main effects.
• β6: Additional change in BAOP_TIME for Intervention_Condition=1 at TIME=2 compared to Intervention_Condition=3 at TIME=3, holding other factors constant.
• β7: Additional change in BAOP_TIME for Intervention_Condition=2 at TIME=1 compared to Intervention_Condition=3 at TIME=3, holding other factors constant.
• β8: Additional change in BAOP_TIME for Intervention_Condition=2 at TIME=2 compared to Intervention_Condition=3 at TIME=3, holding other factors constant.

Because Intervention_Condition=3 and TIME=3 are the references of your indicators, all other coefficients in your model are zero, because they are redundant (as indicated by the superscript “b” in your figure).

If you want to know whether there is an overall effect of Intervention_Condition or TIME you need to test the coefficients for the respective effects together (e.g. β3 + β4 + β5 + β6 + β7 + β8 for the overall effect of TIME). Further, if you want to know whether there is a significant treatment effect (i.e., BAOP_TIME changes over time differently by intervention condition), you need to test the interaction terms together (β5 + β6 + β7 + β8). This can all be done using Wald-Tests.

Overall, as you can see above, the interpretation of the coefficients in your model is quite difficult, since you have two 3-level categorical indicators and an interaction between them. It might be much easier to compute marginal mean differences (e.g. adjusted mean differences in BAOP_TIME at any TIME between the Intervention_Condition groups). Additionally, it might be even better to plot the effects seen in your model with TIME on the X-axis, estimated BAOP-TIME on the Y-axis and one line per Intervention_Condition. This makes interpretation much easier! However, I don't know how to implement this in SPSS. In Stata, for example, you could use "margins" or "marginsplot".

Hope this helps!

Best regards,

Alex Pabst

Alexander Pabst amazing!! thank you so much for this!

The last four rows are empty because they represent redundant categories that are automatically set to zero by the model:

• [Intervention_Condition=1]*[TIME=3]
• [Intervention_Condition=2]*[TIME=3]
• [Intervention_Condition=3] for all time points (TIME=1, TIME=2, TIME=3).

Alexander Pabst I would add that the first thing to do is a likelihood ratio test to see if having the fixed effects in the model was better fitting than a model without them. I see that the two of the interaction terms may be significant but that's contingent on the overall system of variables being 'significant'. Personally I don't use Wald tests, their approximation sometimes isn't very good. I would use stepwise LRT to determine whether a term (or system of terms) should be included in the model (although for some situations in a mixed model one needs to use something like the BIC).