I have data assessing reaction time (RT) with 2 variables: Variable 1: 'HighLow', with 2 levels ('High' and 'Low') Variable 2: 'Condition', with 3 levels ('Predicted', 'Implausible', 'Plaus/Unpred')
I am learning about contrasts and have therefore run 2 mixed models that differ based on the contrasts used.
Contrasts for 1st Mixed Model:
HighLow is left as default coding (dummy coded with 'High' representing the intercept). Condition is simple coded with the following contrast matrix:
Predicted 1 1/3 1/3 Implausible 1 -2/3 1/3 Plaus/Unpred 1 1/3 -2/3
The first contrast (cH01) therefore represents Predicted-Implausible, and the second contrast represents Predicted-Plaus/unpred.
Contrasts for 2nd mixed model:
Contrasts for Condition is the same as the first mixed model (simple coded). The contrast for the HighLow variable is sum coded (High=-0.5, Low=0.5).
The mixed model in both cases is
lmer(RT ~ Condition*HighLow+(Condition|Pt_ID) + (Condition|SentNumb)
Fixed Effects Output For Mixed Model 1
Estimate Std. Error df (Intercept) 0.77357 0.03029 84.70182 ConditioncH01 -0.08738 0.01886 115.78438 ConditioncH02 -0.35944 0.03105 99.02833 HighLowLow -0.01422 0.01439 75.30162 ConditioncH01:HighLowLow 0.05955 0.02043 76.36148 ConditioncH02:HighLowLow 0.17244 0.04049 74.76725 t value Pr(>|t|) (Intercept) 25.539 < 2e-16 *** ConditioncH01 -4.634 9.47e-06 *** ConditioncH02 -11.576 < 2e-16 *** HighLowLow -0.988 0.32632 ConditioncH01:HighLowLow 2.915 0.00467 ** ConditioncH02:HighLowLow 4.259 5.90e-05 ***
Fixed Effects Output For Mixed Model 2
Fixed effects: Estimate Std. Error df (Intercept) 0.76647 0.02943 76.32919 ConditioncH01 -0.05760 0.01592 95.00997 ConditioncH02 -0.27322 0.02365 109.77111 HighLow1 -0.01422 0.01439 75.30164 ConditioncH01:HighLow1 0.05955 0.02043 76.36134 ConditioncH02:HighLow1 0.17244 0.04049 74.77345
My interpretation is as follows:
(Intercept) : mean of High ConditioncH01: Predicted,High-Implausible,High ConditioncH02: Predicted,High- Plaus/unpred,high HighLowLow: Low-High ConditioncH01:HighLowLow: Predicted,low-Implausible,low ConditioncH02:HighLowLow: Predicted,low- Plaus/unpred,low
(Intercept) : grand mean across all levels of both variables ConditioncH01: Predicted-Implausible (high and low combined) ConditioncH02: Predicted- Plaus/unpred (high and low combined) HighLowLow: Low-High/2 ConditioncH01:HighLowLow: (Predicted-Implausible) for high- (Predicted-Implausible) for low ConditioncH02:HighLowLow: (Predicted-plaus/unpred) for high- (Predicted-plaus/unpred)low
However, looking at the means (see below) my assumptions do not all seem to be correct? In particular, I am confused about the interpretation of HighLow in both outputs and the interactions (which are the same in both outputs)?
Predicted,High 0.6272715 Implausible,Hig 0.7055791 Plaus/Unpred,High 0.9423626 Predicted,Low 0.6861870 Implausible,Low 0.7123400 Plaus/Unpred,Low 0.8428695 Predicted 0.6564936 Implausible 0.7089290 Plaus/Unpred 0.8896377 High 0.7421962 Low 0.7426768