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=13090.68da6e6e5325aa33287ff385b70df5d5&n=T&l=tips&o=2142 or send a blank email to leave-2142-13090.68da6e6e5325aa33287ff385b70df...@fsulist.frostburg.edu
