I have collected 20 mixed (nominal, ordinal, continuous) variables that may potentially be associated with the infestation differences of one of several insect pests among sites sampled. I also have infestation status of individual sites (i.e. 48). So, I used non-linear principal component analysis (CATPCA in SPSS) for dimension reduction purpose. Three PCs were selected and I used those PCs (independent variables) in multiple regression as infestation status as dependent variable. Multiple regression is significant, but R^2 value is ~0.20 only. Is it valid to claim that selected variables have contributed significantly on infestation status given the lower R2 value?
Spatial statistics and modeling is often more useful than the r^2 parameter. Statistically significant r^2 values of between 0.3-0.4 often occur in field studies where spatial relationships are important. Use these r^2 values as a guide to determining which variables you want to use in spatial modeling (semivariogram, correlogram, cross-semivariogram, etc).
Hello Rijal,
I think you need to do some more model digging. Have you had a look at your coefficients? how big are they? do they have high variances? Moreover, have you considered including more PCs from your original PCA?
Further, as pointed out above, maybe you should look for a more spatially structured model, in order to make use of the available spatial information.
Cheers,
Thank you all for your thoughtful comments. By the way, does anybody has or know published paper with relatively lower r2 value? If so. could you pls. provide those ref. to me? Thank you in advance!!
In some sense, you are addressing a question whose answer requires a bit more information. Are you referring to statistical significance? An R^2 value of 0.20 can be highly significant with a sufficiently large n value. For a multivariate analysis, the larger the number of terms in the analysis, the greater must be the R^2 value and or the n value to achieve statistical significance.
If one is addressing questions of evolutionary rates, economic impact or environmental quality then small but significant difference might also be biologically significant as well.
Statistical significance is relatively easily determined using standard statistical procedures. The greater the sample size, the smaller the difference between two levels within a factor a statistical test is able to indicate significance. In contrast, biological significance is an entirely different animal, so-to-speak.
I came across your posting and although it is a couple of years old, I thought it deserved another response
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