Timeline for Different ways to include pre-test performance as a covariate in a linear mixed-effect regression. Which is correct?
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 25, 2021 at 15:57 | comment | added | EdM |
@Cmagelssen that's the hope. It doesn't always work out that way. It all depends on how much more variance is explained by pre (and its interactions), versus the cost from estimating additional coefficients. Interaction terms are especially troublesome, as adding them leads to multiplicatively increasing numbers of coefficients. As with many things in statistical analysis, "it depends" and there's no single "correct" answer that fits all situations. If you want to use pre as a predictor, also consider Robert Long's multi-level approach, in the link from the footnote to my answer.
|
|
| Sep 25, 2021 at 15:36 | comment | added | Cmagelssen | @EdM But If I decide to use the ‘interaction model’, wouldn’t that model potentially explain more variance than the additive model? Hence, pre will account for more variance and therefore increase power? | |
| Sep 25, 2021 at 14:10 | comment | added | Cmagelssen | Good point. So I have to be careful about what I include in the model. I have 64 participants that took part in the experiment. | |
| Sep 25, 2021 at 14:03 | comment | added | EdM |
@Cmagelssen one tradeoff in keeping pre values as a predictor instead of just evaluating pre-post differences is the increased number of coefficients you have to estimate: at least 1 more if you don't include interactions, then 1 more for each interaction term you include with pre. With more coefficients the residual degrees of freedom decrease, and potentially also the precision in coefficient estimates. The question becomes whether any increased power you get with pre as a predictor is enough to outweigh the loss of power with more coefficient estimates.
|
|
| Sep 25, 2021 at 7:23 | history | bounty ended | Cmagelssen | ||
| Sep 25, 2021 at 7:23 | vote | accept | Cmagelssen | ||
| Sep 25, 2021 at 7:22 | comment | added | Cmagelssen | Thank you. Great explanation. My reason for using the ANCOVA approach (i.e. predicting post with pre as a covariate) was to increase the statistical power of the test.Our approach to 'wipe-out' differences in snow conditions was to do straight gliding runs each day where the skiers ski straight-down the course in a static upright position. Then we subtract the mean time in each of the three courses from the mean time of the straight-gliding runs. That's why my predictors in the model had 'diff' in them. The skiers' goal was to ski faster than their straight-gliding, which they did. | |
| Sep 24, 2021 at 19:00 | history | edited | EdM | CC BY-SA 4.0 |
added 17 characters in body
|
| Sep 24, 2021 at 18:58 | comment | added | EdM | @COOLSerdash Thanks. I considered presenting that suggestion as an offset term as you indicate, but thought that the analogy to paired t-tests might be simpler to grasp here. | |
| Sep 24, 2021 at 18:54 | history | edited | EdM | CC BY-SA 4.0 |
added note on alternate modeling approach
|
| Sep 24, 2021 at 18:49 | comment | added | COOLSerdash |
(+1). Great explanation. It's worth noticing that using the difference as outcome (without interactions) is akin to including the pre values as a predictor for the post values but fixing the coefficient at $1$. The model using pre as predictor (again without interactions) but estimating the coefficient can be interpreted as modelling an "estimated" or maybe "adjusted" difference between pre and post values.
|
|
| Sep 24, 2021 at 18:42 | history | edited | EdM | CC BY-SA 4.0 |
added 1 character in body
|
| Sep 24, 2021 at 18:36 | history | answered | EdM | CC BY-SA 4.0 |