I'm trying to perform linear mixed model with repeated measures. However, I have a difficulty with checking interaction between 3 independent variables. The data has 3 independent variables (factor1(2 levels), factor2(3 levels), factor3(2 levels)) and 1 dependent variable. The dependent variable was observed more than once (12) from 1 subject under each level of factor 1, 2, 3.
In R, I have run the commands as below:
library(nlme)
library(multcomp)
power_gap
What you are doing here, is almost correct. You are comparing a model with three main factors only against a model with interaction terms, and do an omnibus test. However, your specification of predictors in model 2 expands to:
training + ROI + freq + training:ROI + training:freq + ROI:freq + training:ROI:freq
In other word, model2 contains all two-way interactions and the three-way interaction. If the three-way interaction is your research question, you should first estimate the model with all two-way interaction, an abbreviation is:
(training + ROI + freq)^2
Then compare via anova to your model2.
In case you also want to compare different models with two-way interactions, you would have the problem that anova performs a Wald or LR test. Both only apply to nested models. In that case you may want to use information criteria (AIC) to select between models.
In either case, for linear mixed effects models Wald or LR test and information criteria are not fully valid, because the degrees of freedoms are unknown. It is generally recommended to estimate confidence limits for the parameters via MCMC.
What you are doing here, is almost correct. You are comparing a model with three main factors only against a model with interaction terms, and do an omnibus test. However, your specification of predictors in model 2 expands to:
training + ROI + freq + training:ROI + training:freq + ROI:freq + training:ROI:freq
In other word, model2 contains all two-way interactions and the three-way interaction. If the three-way interaction is your research question, you should first estimate the model with all two-way interaction, an abbreviation is:
(training + ROI + freq)^2
Then compare via anova to your model2.
In case you also want to compare different models with two-way interactions, you would have the problem that anova performs a Wald or LR test. Both only apply to nested models. In that case you may want to use information criteria (AIC) to select between models.
In either case, for linear mixed effects models Wald or LR test and information criteria are not fully valid, because the degrees of freedoms are unknown. It is generally recommended to estimate confidence limits for the parameters via MCMC.
I am published in a method for effect modification in SAS papers. If you like to read:
1) A New Effect Modification P value Test Demonstrated
2) Formulas Calculating Risk Estimates and Testing for Effect Modification and Confounding
Advantages
-high power
-multivariate
-standard error
-parametric
I can show you if you need.
You may use:
example from a W.P.I. example in my paper from above (2)
ex29b
Similarly in a passive smoke exposure data example from A New Effect Modification P Value Test Demonstrated or second paper listed:
1) proc Logistic
2) proc Mixed
Both can be used in data transformation
Data passlungexp5d;
input cases fit zxy xzy count;
datalines; 1 1 1 1 73
0 1 1 1 188
1 0 1332 101 27
0 0 5201 307 82
1 1 1 1 19
0 1 1 1 38
1 0 317 19 5
0 0 1015 60 16
1 1 1 1 137
0 1 1 1 363
1 0 4503 266 71
0 0 15793 933 249
;
run
proc logistic data=passlungexp5d descending;
Weight count;
class xzy fit cases;
model cases= fit zxy xzy / rsq lackfit;
run;
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