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mastoffel / partR2

R package to partition R2 among predictors in Generalized linear mixed models
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interpretation of confidence intervals including zero #7

Open mmcqui opened 2 years ago

mmcqui commented 2 years ago

Hello, thanks for the great package. I had a question about partial R^2 interpretation, particularly when the 'partR2' command returns a partial Rsquared value for a variable of known importance with a confidence interval that includes zero. Below is an example output. My issue is that 'Variable1' is a significant predictor in the lmer model, and also comes out as a highly significant variable in a likelihood ratio test. However, the lower CI for the partial Rsquared includes zero. Is the interpretation here that this variable does not explain a significant amount of the variation in the outcome?

Thanks for any info you can provide.

R2 (marginal) and 95% CI for the full model: 
 R2     CI_lower CI_upper nboot ndf
 0.3748 0.3378   0.425    1000  24 

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Part (semi-partial) R2:
 Predictor(s)                              R2     CI_lower CI_upper nboot ndf
 Model                                     0.3748 0.3378   0.4250   1000  24 
 Age                                       0.1852 0.1406   0.2449   1000  23 
 Sex                                       0.0073 0.0000   0.0797   1000  23 
 Variable1                                 0.0367 0.0000   0.1069   1000  23 
 Age+Sex                                   0.1977 0.1544   0.2565   1000  22 
 Age+Variable1                             0.2468 0.2054   0.3030   1000  22 
 Sex+Variable1                             0.0451 0.0000   0.1148   1000  22 
 Age+Sex+Variable1                         0.2604 0.2197   0.3162   1000  21
mastoffel commented 2 years ago

This is really an interpretation issue and my feeling is what matters here a lot is the biological background and question. Variable1 only explains 3.7% of the variation, which doesn't seem to be a lot. In partR2, we use parametric bootstrapping to calculate the CIs, which simulates new response vectors from the model, refits the model for the new response vector and re-calculates part R2. That the CI includes 0 simply means that for more than 2.5% of those models, the R2 for Variable1 was 0. This is not a significance test, and I also wouldn't interpret it as one. It simply gives you a sense of the variation of the R2. Also, it's not unusual to have a highly significant variable with a low R2. Hope that helps!

mmcqui commented 2 years ago

This is perfect, thanks so much!