Re: st: Power Analysis in 2-Level Hierarchical Linear Model

[Jeph Herrin <stata@spandrel.net>]

I am often called upon to do power calculations for 2 and 3 level HLMs. There are two approaches I usually use:

1. If trying to detect a main effect (ie, make a comparison between two groups), I use the methods of [Donner A, Klar D, 
The Design and Analysis of Cluster Randomized Trials. 2000. Arnold] and others to calculate sample size based on a 
t-test or chi-square test, adjusted for clustering via a variance inflation factor (VIF). In essense, one makes the 
usual power calculation but inflates the variance by a factor of VIF=(1+rho*(m-1)) where m is the average number of 
observations per group and rho is the (usually estimated) intra-cluster correlation. Then I will assume (or at least 
claim...) that actual power will likely be greater using a model.
2. For more complicated models, or situations where I know enough to do so, I use simulation. See 
http://www.stata-journal.com/sjpdf.html?articlenum=st0010 (or if the link doesn't work, The Stata Journal (2002) 2, 
Number 2, pp. 107–124 : Power by simulation). Basically, simulate a large number of data sets using known effects of 
interest and some reasonable assumptions about the distributions, estimate the model on each, and count the number of 
times that P< 0.05, where P is the p-value for the test of interest. The main drawback to doing this is that xtmixed can 
take a few minutes to converge, and 1000 x a few minutes ~ 2 days.
hope this helps,
Jeph




On 4/16/2013 2:04 AM, Anthony Fulginiti wrote:
> Hello Statalist,
>
> I have enjoyed following the creative and informative insights and guidance on Statalist over the past few months.
>
> I am interested in performing a power analysis in a 2-level hierarchical linear model (more specifically, a growth curve model).
>
> Let's use the example of 80 clusters (individuals) with 10 per cluster (observations). If it is helpful, the code for the model is:
>
> xtmixed Self-Esteem time time2 Program ProgramBytime ProgramBytime2|| id: time, covariance(un) variance mle
>
> I ran a basic search in the Statalist archives and searched for power analysis options in Stata but did not find any information on the subject for hierarchical linear models. I have been reviewing material that recommends the use of Optimal Design software or PinT (Power in Two-level Designs) for power analysis in hierarchical linear modeling.  However, I have a Mac and both programs seem to run on Windows (my Windows platform has been giving me problems).
>
> Is it possible to perform a power analysis with a 2-level hierarchical linear model in Stata?
>
> If not, I would welcome any further recommendations for performing the analysis.
>
> Thanks in advance for feedback.
>
> Respectfully, Anthony
>
>
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