Reminds me a bit of "Heywood cases" in structural equation modeling, where (if I recall correctly) the estimated variances are negative (but I'm confident that one or more sharp-eyed TIPSters will correct me if I'm wrong...). ...Scott
Scott O. Lilienfeld, Ph.D. Professor Editor, Scientific Review of Mental Health Practice Department of Psychology, Room 473 Psychology and Interdisciplinary Sciences (PAIS) Emory University 36 Eagle Row Atlanta, Georgia 30322 [email protected] (404) 727-1125 Psychology Today Blog: http://www.psychologytoday.com/blog/the-skeptical-psychologist 50 Great Myths of Popular Psychology: http://www.wiley.com/WileyCDA/WileyTitle/productCd-140513111X.html Scientific American Mind: Facts and Fictions in Mental Health Column: http://www.scientificamerican.com/sciammind/ The Master in the Art of Living makes little distinction between his work and his play, his labor and his leisure, his mind and his body, his education and his recreation, his love and his intellectual passions. He hardly knows which is which. He simply pursues his vision of excellence in whatever he does, leaving others to decide whether he is working or playing. To him - he is always doing both. - Zen Buddhist text (slightly modified) -----Original Message----- From: Mike Palij [mailto:[email protected]] Sent: Wednesday, April 21, 2010 1:20 PM To: Teaching in the Psychological Sciences (TIPS) Cc: Mike Palij Subject: RE: Re:[tips] Biserial r. On Wed, 21 Apr 2010 05:48:50 -0700, Rick Froman wrote: >OK, I know that some correlational techniques occasionally produce r greater >than 1 or less than -1 but I think I am on firm footing when I say that I am >not going to see a negative r-squared in the set of real numbers used in >statistical calculations (although it may occur with complex numbers > http://mathforum.org/library/drmath/view/52613.html ). Unfortunately, this is not true. A simple Google search for either "negative R squared" or "negative R square" will provide a variety of hits. A number of conditions can give rise to a negative R square but they all tend to be pathological. If you used the regression tool in pre-2003 Excel and you forced the regression through the origin (i.e., the intercept is zero), you could get a negative R-square as well as negative sum of squares, etc., (it is somewhat unusual to see a negative F-value in the output). Microsoft fixed the code that created these results in Excel 2003 and later versions; see the following website (scroll down to "Regression" or search for the word "negative" on the page): http://support.microsoft.com/default.aspx?scid=kb;en-us;829208 Negative R square can also be obtained in multilevel or HLM analyses. Consider the following that attempts to identify the variance accounted for in a heirarchial model: |Socioeconomic status explains 45% of the explainable between-unit |variance in this model using the first formula and 59% using the second |formula. Thus, it appears that socioeconomic status contributes greatly |to explaining variation between schools, but does not explain much |variance in math achievement scores. | |It should be noted that there are some potential problems with the method |described above. One possible problem is the possibility that the level-1 |variance is larger in the restricted model than the unrestricted model, which |would produce negative R-squared values. Kreft and De Leeuw (1998) point |out that the formula may not apply to situations where there are random |intercepts. This is especially true for computing the between-unit variance |explained, as there is not a single level-2 error term in models containing |random slopes. from: http://ssc.utexas.edu/software/faqs/hlm The Question is "R-squared in a Hierarchical Model" which is lower on the page. The cited reference for Kreft & De Leeuw is: Kreft, I., De Leeuw, J. (1998). Introducing Multilevel Modeling. London: Sage Publications. So, it is possible to get oddball values for statistics and for a variety of reasons, ranging from improperly programmed procedures to situations where key assumptions are violated. In either case, one has to think through what is going on. -Mike Palij New York University [email protected] --- You are currently subscribed to tips as: [email protected]. To unsubscribe click here: http://fsulist.frostburg.edu/u?id=13509.d0999cebc8f4ed4eb54d5317367e9b2f&n=T&l=tips&o=2142 or send a blank email to leave-2142-13509.d0999cebc8f4ed4eb54d5317367e9...@fsulist.frostburg.edu This e-mail message (including any attachments) is for the sole use of the intended recipient(s) and may contain confidential and privileged information. If the reader of this message is not the intended recipient, you are hereby notified that any dissemination, distribution or copying of this message (including any attachments) is strictly prohibited. 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