How do I determine the number of participants needed to achieve X power, with a small effect size (assuming f2 of .02), for a multivariate regression?
As far as I can tell G*Power can only do this for univariate regression. Is there some modification I can make to its output? Is there another program I can use?
Note that I have no data in hand, I am only going off of the assumption that the effect size is small.
Hi David,
you could try R with the simsem package. Using this package (in combination with the SEM-package lavaan), you can easily run a Monte-Carlo-Simulation to find the necessery N for given parameters of a model. I do not actually know how to get the power for f-square or r-square.
Take a look:
- Simsem guide
https://github.com/simsem/simsem/wiki/Vignette
- Paper how to apply simsem for power analysis
http://bit.ly/2juIsN5
Having said that, I actually do not really buy the reasons for conducting a power analysis. The philosophy behind it seems to be "how much data do I have to gather to reach the holy grail of statistical significance". Beyond mere significance, gathering more data (above that border) means higher precision in estimating the population parameter which in my point of view is a goal that is at least as important as significance. :)
Best,
Holger
David, in addition to Holger's suggestion Daniel Soper provides several online sample size calculators, and among these is also an a-priori sample size calculator for multiple regression:
https://www.danielsoper.com/statcalc/calculator.aspx?id=1
HTH, Karin
There exists a distinction between multiple and multivariate regeression. for instance, a regression analysis with one dependent variable and 8 independent variables is NOT a multivariate regression. It’s a multiple regression. on the other hand, When you’re jointly modeling the variation in multiple response variables, that is Multivariate regression modeling.
On top of the excellent suggestion from excellent Holger Steinmetz, there are two points to consider when we are talking more pragmatically. The question is for what do you want this?
If you want it to use in ethics application, usually what is presented (wrongly) is the sample size calculation for simple prevalences of the condition of interest. For instance, you want to see factors associated with HIV+. Then, the sample size usually presented is the sample size to find an expected prevalence of HIV+ and some error.
The other use is to obtain a sample size that would allow you to find some effect with reasonable power.
For the first case, I don't recommend Holger solution, although it is correct. But the committee will probably not understand it and will send it back to you if they don't reject it directly. So, play the game with the rules of the game and send the sample size for the prevalence (or both, if you want to try something new).
For the second case, the described approach is awesome, although you would need to make some assumptions about data structure and covariance. And, in the end, you will probably discover that the sample size is too big, and you will need to grab whatever you can collect. But to explore the suggestion and then go back to it after data collection is a terrific way to understand your data better.
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