Don't forget about the interaction (which includes the covariate). Because it's significant, the "effect" of the covariate cannot, and should not, be considered or interpreted on its own (that is, you cannot look solely at the p-value for the parameter estimate - the 'effect' of that variable is also seen in the parameter estimate of the interaction term).
Original Message:
Sent: Fri September 09, 2022 08:26 AM
From: Yann Bou
Subject: Parameter estimates of fixed effects in multilevel analysis with interactions
Hi,
Thank you very much for this enlightening answer, it helps me!
Just to make sure I'm not forgetting something: Because ACS is a covariate, it is thus not possible to get matched results (between the two tables) for the effect of the covariate itself, right? (As it is a covariate, we cannot use it in the EMMEANS subcommand) I still don't understand why the Type III and parameter estimate p_value are not the same in both tables regarding the covariate and how to fix it.
Thank you in advance for helping me figure this out.
Best,
Yann
------------------------------
Yann Bou
Original Message:
Sent: Thu September 08, 2022 04:51 PM
From: Rick Marcantonio
Subject: Parameter estimates of fixed effects in multilevel analysis with interactions
FYI - I contacted one of our statisticians, and received this reply:
While this is with regard to the fixed effects in an analysis in MIXED, but the principles would apply in GLM/UNIANOVA or GENLIN as well (as well as for fixed effects in GENLINMIXED).
The first table contains Type III tests of the fixed effects resulting from the parameter estimates shown in the next table. The parameters are the fundamental quantities in the model, and the tests are based on the estimates of the parameters. The linear combinations of the parameters from the second table that are used to form the tests in the first table can be shown by printing out the L matrices for the effects (in the Statistics dialog, check Contrast coefficient matrix, which will paste the LMATRIX keyword on the PRINT subcommand).
The relevant model contains an intercept, a binary factor (Condition), a covariate (ACS_Preoc_z, just ACS below), a factor with five levels (Time), and the interaction between the Condition factor and the covariate.
Because the Time effect appears only as a main effect, the F test for that is a true main-effects test of the set of parameters represented in the second table, in all cases adjusted for the other effects in the model, but estimable and testable without specific reference to particular levels of the other factor or covariate. You can verify this by specifying EMMEANS with COMPARE for the Time main effect, and seeing that you get that same F test result, regardless of the value at which the ACS covariate is fixed.
Because Condition interacts with ACS, test results for it reflect the choice of where to fix ACS in comparing the two conditions. In order to reproduce that F test in the table you need to specify WITH(ACS=0) on the EMMEANS subcommand for the Condition "main effect". The quotes are to call out the fact that because Condition is involved in an interaction, you can't get a single estimate of a main effect for it; the effect depends upon where you fix the covariate. That's implied by the model. The Type III tests fix ACS at 0. Note that the denominator degrees of freedom for the Condition parameter estimate match those for the Condition "main effect" in the first table, the t statistic is the square root of the F statistic, and the significance levels or p values match.
------------------------------
Rick Marcantonio
Quality Assurance
IBM
Original Message:
Sent: Wed September 07, 2022 06:41 AM
From: Yann Bou
Subject: Parameter estimates of fixed effects in multilevel analysis with interactions
Hi,
I went into the same confusing problem for interpreting results of one experiment with this following design: 1 between condition (2 modalities) + 1 continuous variable (ACS_preoc_z) + 5 time measures + interaction condition x ACS.
I have a follow up question. Is it possible to get the estimates of the first table (type III tests) as I would like to report main fixed effect and not the simple effects.
Best,
Yann
------------------------------
Yann Bou
Original Message:
Sent: Tue September 21, 2021 04:12 PM
From: Rick Marcantonio
Subject: Parameter estimates of fixed effects in multilevel analysis with interactions
Hi. I'm no expert in this kind of modeling so perhaps I'm misunderstanding but what if you were to specify in your /FIXED subcommand:
MIXED ... /FIXED=color claim product_set color*claim color*product_set claim*product_set color*claim*product_set | SSTYPE(3)
When I do that, the Fixed Effects parameter table includes the non-redundant estimates for each effect in the Type III Tests table:
------------------------------
Rick Marcantonio
Quality Assurance
IBM
Original Message:
Sent: Tue September 21, 2021 08:14 AM
From: Lotte Hallez
Subject: Parameter estimates of fixed effects in multilevel analysis with interactions
Hello,
We conducted an experiment with a 2 x 2 x 4 design, where the first 2 factors are within-subjects and the third factor was manipulated between-subjects.
As fixed effects, I included the three factors, the two-way interactions and the three-way interaction.
As random effect, I included the participant ID (and intercept).
The results in the 'type III tests of fixed effects' table seem to be correct, and correspond with the results I get from a repeated measures ANOVA.
However, the results from this table do not correspond with the 'parameter estimates of fixed effects' in the output.
I know that this is because I added interactions to the model. The first table (type III tests) reports main effects, while the second table (parameter estimates) reports simple effects.These simple effects are influenced by the higher order effects of the interactions. So, adding interactions changes the parameter estimates for the three manipulations.
I was wondering whether there is a possibility to change this so that the parameter estimates do correspond with the results from the type III fixed effects table? I don't want to exclude my interactions, because they are important elements in the model. For instance, could I add something to the /TEST field in the syntax?
------------------------------
Lotte Hallez
------------------------------
#SPSSStatistics