conditions of application assumption checking. assumptions for mixed models and rm anova linearity ...
Post on 18-Dec-2015
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Assumptions for mixed models and RM ANOVA
Linearity The outcome has a linear relationship with all
of the predictors Homoscedasticity
The residuals are equally variable at any level of the predictors
Normality of the residuals
Fitting the model
Fit the same model from last week:
SIGNAL = (b0 + u
0) + b
1ACCELERATION +
b2COIL + b
3COILxACCELERATION + ε
Be sure to use the long dataset, and ALL values of RESOLUTION
ACCELERATION is a covariate, not a factor
SAVE the residuals and the predicted values
Residual plots
Create a histogram of the residuals (Analyze → Descriptive Statistics → Frequencies → Chart), and a scatterplot of the residuals v.s. the predicted values (Graphs → Chart builder).
What are we testing for? Linearity (no pattern) Homoscedasticity (constant variance) Normality of residuals (bell-shaped
histogram)
Analyze the residual plots
Do our plots look okay? Scatterplot
Looks decent
Histogram Looks plausibly normal, given the sample size Weird bi-modality
Tests of normality
Check the Shapiro-Wilk and the Kolmogorov-Smirnov
Neither value is statistically significant What does that mean?
We have no evidence of non-normality We pass! Be careful, though: these tests are poor at
finding bimodality
Analyze the Q-Q plot
What are we testing? Normality of the residuals
How does it look? Decent, except for the extreme tails Probably okay
Checking Cook's D
Transform the dataset to long form Only keep ID and the Cook's D variables Plot Cook's D v.s. ID
How does it look?
Not too bad None of the points are wildly farther than the
others It looks none of the points were wildly
influential Subject 23 had a big impact, though
Now...
Check the conditions of application for the same models, only now only for subjects with RESOLUTION = 2
Tests of normality
Uh-oh We fail our tests! And they don't have a lot of power with small
samples, so this might be really bad
Residuals v.s. acceleration
This explains it: it's the weird interaction between acceleration and coil that we noticed before
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