Linearity Test Using SPSS 

Linearity refers to the consistent slope of change that represents the relationship between an IV and a DV. If the relationship between the IV and the DV is radically inconsistent, then it will throw off your SEM analyses. There are dozens of ways to test for linearity. Perhaps the most elegant (easy and clear-cut, yet rigorous), is the deviation from linearity test available in the ANOVA test in SPSS. In SPSS go to Analyze, Compare Means, Means. Put the composite IVs and DVs in the lists, then click on options, and select “Test for Linearity”. Then in the ANOVA table in the output window, if the Sig value for Deviation from Linearity is less than 0.05, the relationship between IV and DV is not linear, and thus is problematic (see the screenshots below). Issues of linearity can sometimes be fixed by removing outliers (if the significance is borderline), or through transforming the data. In the screenshot below, we can see that the first relationship is linear (Sig = .268), but the second relationship is nonlinear (Sig = .003).

• If this test turns up odd results, then simply perform an OLS linear regression between each IV->DV pair. If the sig value is less than 0.05, then the relationship can be considered “sufficiently” linear. While this approach is somewhat less rigorous, it has the benefit of working every time! You can also do a curve-linear regression (“curve estimation”) to see if the relationship is more linear than non-linear.