I am performing a multiple regression analysis for my PhD and most of the assumptions are not met (non linear model, residuals are non normal and heteroscedastic). How much can I deviate from them before I have to resort to non parametric tests and which tests would that be? tried to transform my variables but it did not improve anything .
Have you tried taking the logarithm of all your variables? In econometrics this is a commonly applied way to get rid of some of this issues, basically because it removes the influence of variables being measured in different units (i.e. something measured in 0.1 steps, something else in 1,000s ...). You just have to be careful in the interpretation, because you basically have an elasticitiy-relationship (% change leads to % change, not absolute).
Hope this helps.
Fitting log (Y) is a good consideration. Using the Box-Cox approach to transformation is a more general approach. Non-homogeneous variance can also be due to one or more important variables not being included in the model. Plotting the residuals versus time/sequence is a good way to get insight as to other variables that should be in the model. When the linear model shows lack of fit try including cross-product (XiXj) and Squared (XiXi) terms to the model.
Regardless of any transformation, the tree based algorithms like CART, CHAID, and Exhaustive CHAID can be used when assumptions of independent variables are violated. In SPSS, follow
1. Classify >Tree......
2. Select CHAID algortihm as a growing method.
3. V fold Crossvalidation should be 10.
4. Stop when re-substition cost is become equal to crossvalidation cost!
5. Minimum number of cases in parent and child nodes should N/6 and N/12 where N is total sample size. To increase the predictive performance of CHAID, N/18 and N/16 should be assigned.
5. you will obtain a decision tree contructred via CHAID algorithm.
Please examine links of my papers on regression tree method
http://www.thejaps.org.pk/docs/v-24-1/18.pdf
http://www.thejaps.org.pk/docs/v-23-4/02.pdf
http://thejaps.org.pk/docs/v-23-3/08.pdf
http://www.zsp.com.pk/pdf47/1579-1585%20(10)%20QPJZ-0146-2015%2014-7-15%20REVISEDVERSION_FINAL.pdf
http://www.tandfonline.com/doi/abs/10.1080/09712119.2008.9706952#.VqT5WPmLTDc
https://www.researchgate.net/profile/Abdul_Waheed11/publication/233959583_Prediction_Of_Body_Weight_From_Body_Measurements_Using_Regression_Tree_%28Rt%29_Method_For_Indigenous_Sheep_Breeds_In_Balochistan/links/00b7d51d699d987b9f000000.pdf
https://www.researchgate.net/profile/Ecevit_Eyduran
Best Regards.
Assoc. Prof. Ecevit EYDURAN
Article Prediction Of Body Weight From Body Measurements Using Regre...
What is the VIF of the terms in your models? That might be part of the issue too. I'm not sure how to get SPSS to calculate VIF.
Looking at your plots I don't see much evidence of heterogeneity of variance and departures from normality are fairly mild - some negative skew and some kurtosis. There won't be much gain from switching to other methods such as robust regression or bootstrap regressions. Also transformations such as the log will make things worse (as they deal with positive not negative skew).
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