Hi I quickly did following SPSS simulation to see correspondence between continuous two-factor dataset and dichotomized version of same data. Results are positive for the correspondence between the two ... both retrieve 2 factor structure, although somewhat stronger for former. You can play with n (10,000 here to see results in limiting case), #r = correlation between variables and underlying construct, and #cutoff, the point of dichotomization to see more about what happens.
input program. loop o = 1 to 10000. comp #za = rv.norm(0,1). comp #zb = rv.norm(0,1). comp #r = .7071. do repeat a = a1 to a8. compute a = rv.norm(0,1)*#r + #za*sqrt(1-#r**2). end repeat. do repeat b = b1 to b8. compute b = rv.norm(0,1)*#r + #zb*sqrt(1-#r**2). end repeat. end case. end loop. end file. end input program. corr a1 to b8. factor /vari a1 to b8. *dichotomize. comput #cutoff = .5. do repeat x = a1 to b8. compute x = x > #cutoff. end repeat. corr a1 to b8 /stat. factor /vari = a1 to b8. As noted, done quickly, so perhaps check for errors (I almost posted a biggie ... due either to old age or jet lag or both). Also, I am NOT familiar with the literature on dichotomized variables, or effect of using tetrachoric, as Scott suggested. Take care Jim James M. Clark Professor of Psychology 204-786-9757 204-774-4134 Fax [email protected] >>> "Lilienfeld, Scott O" <[email protected]> 01-Aug-11 8:52:31 AM >>> Hi Annette - Actually, many researchers do conduct factor analyses on dichotomous (e.g., T-F items), although as you note doing so potentially runs afoul of some assumptions. One possibility is to convert your rs into tetrachoric correlations (this is a fairly standard approach in factor analysis with dichotomous items), which estimate what the r would be if the ratings were made an on underlying continuous scale (and as I understand it, tetrachoric rs come with some assumptions too and wouldn't be appropriate if the underlying distribution is genuinely qualitative/categorical). Here's a primer, but I'm sure there are others. http://www.john-uebersax.com/stat/tetra.htm Good luck! Scott O. Lilienfeld, Ph.D. Department of Psychology, Room 473 Emory University 36 Eagle Row, Atlanta, Georgia 30322 [email protected]<mailto:[email protected]>; 404-727-1125 From: Annette Taylor [mailto:[email protected]] Sent: Monday, August 01, 2011 9:44 AM To: Teaching in the Psychological Sciences (TIPS) Subject: [tips] factor analysis for dichotomous data Dear Tips Friends: Let me start by saying that I am a relative statistical analysis moron. That's not to say that I am a total moron...but beyond basic stats that you'd get in the highest undergrad course, I'm mostly lost. I'm not proud of it, but there you have it. {Let me pass the blame onto my last stats instructor in grad school. Up to that point, I thought I really "got" it....then it got all undone...that's another story.} Right now, the story is this: I have a dichotomous instrument with 21 items. I'd like to know if any of the items hang together. I have two hypotheses in mind as to how they "might" logically cluster, but that doesn't mean that either is correct--they are just best educated suggestions of what could be. So, here is the question: apparently I have determined that factor analysis for true/false or yes/no or forced choice between two items data is just not meaningful. These types of data violate the two main underlying assumptions of factor analysis, including continuous data, rather than discrete. Since some of you all seem very well-versed in stats I am hoping some one of you has some good advice for me, that I will be able to understand. Sigh. There is much online but I don't get it :( I mean, I get that I can't do factor analysis and why I can't do it; but when the explanations go into other domains, then I get lost. Annette Annette Kujawski Taylor, Ph. D. 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