I've been listening to the excellent podcast "quantitude" with Greg Hancock and Patrick Curran, which if you haven't done yet you should check out. In Episode 2, (Power Struggles). Patrick made the (hyperbolic) statement that all power analysis is useless. Lest you think I'm exaggerating, his exact quote is: "I think all power analysis is useless."
I was listening while washing dishes and ran across the house with wet hands to find a pen to write this quote down, because I am a power analysis believer. It's true that it can sometimes be fuzzy, and maybe more effort goes into them than is necessary, but ultimately I believe they are a good tool. I've broken down Greg and Patrick's arguments against a-priori power analysis into three basic parts:
1) Some models are so complex that there is no one pathway that represents the "effect" you need to power
They argue, essentially that if you're running a complex model that Cohen's ideas about what an effect size represents doesn't even really apply. If you have a complex multi-indicator latent factor model, there are too many pathways to consider."Take a simple growth model with five indicators... what is the power of that?? Are you interested in the intercept, the slope, the correlation between the two... "
When I'm running power analyses, I am often planning an analysis with complex, multi-indicator latent factor models, with students nested in classrooms. Sometimes there is a planned missing data design also housed within that latent model. These are extremely complicated. But in the end, my research questions, my hypotheses, can almost all be confirmed or refuted based on the statistical significance of a particular pathway (or pathways). If I can't, then I need to go back and re-state and re-think my question.
2) Power is specific to the analysis you want to run
Yes. This is why the specificity is even more important. Do you want to know if third graders grow in their language skills less than second graders do? Then you need to fit a growth model, and you need to estimate the power you have to detect the pathway that represents that difference. Maybe that's a predictor of the latent slope. You can power for that. Maybe it's a multiple group model, and you'll constrain to see if the slope factor should be forced to be equal across your groups or allowed to vary. You can power for that too.
I do this with simulations. Where the values of those simulations are seeded by pilot work or other large scale studies that have used the same or similar measures. I use the variance almanac to determine the intra-class correlation due to schools (when that is relevant). I use this delightful article to determine whether my effect sizes are meaningful or important or at all interesting.
3) Power is specific to features of the data: "Power depends on the communality estimates; the multiple R-squared. It increases the higher your R-squared is for your indicator"
Agreed, and this is why I always present a power analysis under multiple scenarios. I will always estimate my power to detect the critical pathway for a given hypothesis both with and without covariates included, for different levels of attrition, for different key variables of that particular construct.
To sum up, I do agree that running a power analysis for an entire model is useless. But it is useless because if the only power analysis you can think to run is one for the model itself, then you probably don't have a very well defined question. For any one study, I will report two to three power analyses for each and every hypothesis.
I think our differences in opinion can be boiled down to differences in funding mechanisms. The NIH gives you one paragraph, while IES, who I write most of my grants for, expects something closer to a page with a table dedicated to the power analysis. It's also different because I have the luxury of frequently working with randomized control trials. Usually a primary aim of the study is to determine whether a treatment group is different from a control group.
Don't get me wrong. A lot of my time is spent on power analysis. If Patrick and Greg can convince the federal funders to drop power, or to switch to an emoji-based system, I could learn to knit or something with all of the extra time I would have on my hands. But for now, if you're in need of a power analysis, try mapping your research question on to the actual equation or latent path model you intend to run. Where in that equation or on that diagram could your hypothesis be disproven? If you don't know, try writing a better, more specific question.