I would like some help with setting up a linear mixed model with paired data.
I have a dataset where each participant is tested twice: either with a manipulation or without a manipulation. There are two types of manipulations (either 1 or 2 or no manipulation, 0) and we know in which order the manipulation was presented for each subject.
Here's example data:
data_ex <- data.frame( pnum = rep(1:10, each=2), manipulation = c(0,1,0,2,0,1,0,2,0,1,0,2,0,1,0,2,0,1,0,2), order_manipulation = c(0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1), man_onoff = c(0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1), score = floor(runif(20, min=0, max=101)))
I would like to find out what the influence of each type of manipulation is on a particular outcome measurement("score"), while controlling for the fact that each participant is tested twice (by adding + (1|pnum)). So basically, is there a significant difference between manipulation 1 and baseline on performance? As well as, is there a significant difference between manipulation 2 and baseline on performance?
mod <- lmer(score ~ as.factor(manipulation) + (1|pnum), data = data_ex) >summary(mod) Linear mixed model fit by REML. t-tests use Satterthwaite's method ['lmerModLmerTest'] Formula: score ~ as.factor(manipulation) + (1 | pnum) Data: data_ex REML criterion at convergence: 165.3 Scaled residuals: Min 1Q Median 3Q Max -1.78197 -0.43635 -0.06185 0.61631 1.26529 Random effects: Groups Name Variance Std.Dev. pnum (Intercept) 359.7 18.97 Residual 430.5 20.75 Number of obs: 20, groups: pnum, 10 Fixed effects: Estimate Std. Error df t value Pr(>|t|) (Intercept) 50.200 8.889 14.344 5.647 5.49e-05 *** as.factor(manipulation)1 -21.495 12.196 10.358 -1.762 0.107 as.factor(manipulation)2 -10.905 12.196 10.358 -0.894 0.392 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Correlation of Fixed Effects: (Intr) as.()1 as.fctr(m)1 -0.397 as.fctr(m)2 -0.397 0.158
With this model, I get p-values for the contrast between manipulation type 1 and baseline (0) as well as contrast between manipulation type 2 and baseline (0). However, the model takes all the zeroes of baseline to contrast the manipulation type with. But since I'm working with paired data, I would like the model to only contrast the manipulation data with the baseline of the participants that actually had those manipulations. Concrete this would mean that the model should only contrast manipulation vs baseline for type 1 in subjects 1,3,5,7 and 9. And only contrast manipulation vs baseline for type 2 in subjects 2,4,6,8 and 10.
How could I best re-write my model to take this paired data into account? Could I add some of my order information variables into the model and if so, as fixed and/or random effects or do I need to reshape my data?