RE: st: factor analysis and bootstrapping

[Cameron McIntosh <cnm100@hotmail.com>]

I might also recommend some methodological papers re: resampling in FA and similar contexts:
Zhang, G., & Browne, M.W. (2006). Bootstrap fit testing, confidence intervals, and standard error estimation in the factor analysis of polychoric correlation matrices. Behaviormetrika, 33(1), 61-74.http://www.jstage.jst.go.jp/article/bhmk/33/1/61/_pdf

Zhang, G., Preacher, K. J., & Luo, S. (2010). Bootstrap confidence intervals for ordinary least squares factor loadings and correlations in exploratory factor analysis. Multivariate Behavioral Research, 45, 104-134.

Yuan, K.-H., & Hayashi, K. (2006). Standard errors in covariance structure models: Asymptotics versus bootstrap. British Journal of Mathematical and Statistical Psychology, 59(2), 397–417. 

Yuan, K.-H., Hayashi, K., & Yanagihara, H. (2007). A Class of Population Covariance Matrices in the Bootstrap Approach to Covariance Structure Analysis. Multivariate Behavioral Research, 42(2), 261-281.

Jennrich, R.I. (2008). Nonparametric Estimation of Standard Errors in Covariance Analysis Using the Infinitesimal Jackknife. Psychometrika, 73(4), 579-594.

Cam

> Date: Wed, 1 Feb 2012 01:45:27 +0000
> Subject: Re: st: factor analysis and bootstrapping
> From: njcoxstata@gmail.com
> To: statalist@hsphsun2.harvard.edu
> 
> The way -bootstrap- works hinges on taking one or more scalar results
> and looking at their distribution(s) under sampling with replacement.
> But you are trying to put a series of matrix results into a single
> variable. That won't work if only because you can't fit a matrix into
> a single value of a variable.
> 
> In addition, I don't understand why you are trying to -bootstrap-
> rotation. Where's the stochastic element in that? The same rotation of
> the same factor analysis results will give the same rotated results.
> It's like rotating from facing N to facing E, but doing it 1000 times.
> 
> I imagine what you want to do is -bootstrap- the whole shebang, i.e. a
> -factor- analysis followed by -rotate-, in which there will be
> variation because the factor analysis results will differ because of
> different samples. In that case, you would need to write a program to
> encapsulate both, and -- first point above -- taking each loading from
> the matrix and putting it into a separate scalar.
> 
> If you seek comment on Martin Weiss's advice, please give the specific URL.
> 
> Nick
> 
> On Tue, Jan 31, 2012 at 11:37 PM, Jurgen Sidgman <sidgman@uwm.edu> wrote:
> > A few months ago a post identical to the one I have here was made and answered by Martin Weiss. The problem is that I have not been able to execute following his advice. So here it goes.
> >
> > I want to bootstrap the factor loadings that I obtain after executing
> >
> > factor var1 var2…, pcf
> >
> > to determine if the loadings are statistically different from zero at conventional levels. Without attempting the bootstrapping all works well. However trying the following commands rotate does not work and I cannot seem to find a solution:
> >
> > bootstrap, reps(1000): rotate
> > bootstrap load:e(L), reps(1000): rotate
> > bootstrap e(L), reps(1000): rotate promax
> >
> > I have also tried:
> >
> > bootstrap loadings=e(L), reps(1000): rotate promax
> >
> 
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