Hi, I seems to have missed your latest post. I will look up proc pls asap tomorrow (its friday afternoon in this part of the world, and there is a world outside of econometric modelling, sometimes..). It seems like an interesting way to estimate the predictive partial least squares. Your illustrative example of the relationship between those flat lines and splines helped me a lot in understanding how both the models work (as well as it explains the high fit of my spline-model described above). Thanks Best regards, Hank ... View more

Actually, I did a regression just recently from another, similar, dataset. Both the response and the predictors are almost the same as in the one we have discussed above. I increased the R2 from 0.18 (using Box-Cox transformation of the response (lambda -1)), to 0,51. In the Box-Cox regression, all diagnostics has been done (Reset-test, outliers-robustness/proc robustreg, multicollinearity, normal residuals, robust s.e. etc.). I only have in mind to look for endogeneity problems. So I feel OK with the Box-Cox model, that is, I feel it meets the assumptions of linear regression OK. However, if using mspline/spline can increase the explanatory power on, already tested, variables, it is tempting to present those results as well. But I am not sure how good it is to use this new information about monotone spline/spline, because I am afraid I am overfitting the model. What do you think? I must add, I am quite new to regression modelling on this level, and unfortunately, is the only one on my job that know how to do it. So I really appreciate all your feed-back and help! Have a nice weekend Best regards, Hank The code is shown below: proc transreg data=hem_reg2_2 solve test nomiss plots=all;       ods exclude where=(_path_ ? 'MV');       model mspline(response/ nknots=2) = identity(x1_dummy) spline(x2 x3 x4 x5 / nknots=2); run; I have reduced the nknots=2, just to reduce the possibility of overfitting the model. ... View more

Hi again, Thanks for your willingness to help, it means a lot. Above, I have posted the histogram from my original response-data, and the result from the box cox-transformation. As you can see, the response looks near-normal but is positively skewed. The real mess in the data lies in the independent variables, as indicated from the box-cox-picture aboce with lots of almost flat curves/lines. First, I tried to log-transform the response, but it failed all the normality-tests of the regression residuals. This transformation (the Box-Cox) are normal in residuals. Due to the many almost flat curves in the Box-Cox picture, I was thinking that maybe spline-regression in the predictors would do the trick. What is your thoughts from the pictures above? Best regards, Hank ... View more

Thanks once again for the input, and the book recommendation. I read more about the proc transreg procedure, and an example here: SAS/STAT(R) 9.2 User's Guide, Second Edition In my data, I have cost data as the response (which in the litterature usually is log-transformed) and a variety of continuous and discrete explanatory variables. Some are dummy and others are values from 0-100, often with a concentration of values near the range of 70-100 or 0. As I wrote in the initial question, I did a Box-Cox transformation of the response: model BoxCox(Y) = identity(x1 x2 x3 x4 x5 x6) This generated a model in which the residuals are normally distributed, but R2 is not as high as I think it could be, and my fear is that I could miss some relationships that are nonlinear in the explanatory variables. Thanks to yours, and Ricks, excellent help, I`m now thinking of doing something like the example in the link above (as shown below): -Namely using mspline in the response and spline on my predictors that range from 0-100. But the nice interpretation breaks down, and to explain the coefficients in one way or the other (for myself as well) is harder. Showing changes in low/mid/high values of the response from a change in (original value of x) is still a quite good way of explaining the relationship to non-professionals. But with different transformations on the independent variables (as shown below), now I find it really difficult to even say anything about which independent variable that explains the most, and the ratio of its affect on the response in relation to the other independent variables. Do you have any idea on how to make sense of the different relationships when explained to non-statisticans?  Best regards, Hank ******************************************************************** example from sas homepage ******************************************** * Fit the Nonparametric Model;   proc transreg data=Gas solve test nomiss plots=all;   ods exclude where=(_path_ ? 'MV');   model mspline(NOx / nknots=9) = spline(EqRatio / nknots=9)   monotone(CpRatio) opscore(Fuel);   run; Intercept 1 -15.274649 57.1338 57.1338 1227.60 <.0001 Intercept Pspline.EqRatio_1 1 35.102914 62.7478 62.7478 1348.22 <.0001 Equivalence Ratio (PHI) 1 Pspline.EqRatio_2 1 -19.386468 64.6430 64.6430 1388.94 <.0001 Equivalence Ratio (PHI) 2 Identity(CpRatio) 1 0.032058 1.4445 1.4445 31.04 <.0001 Compression Ratio (CR) Opscore(Fuel) 5 0.158388 5.5619 1.1124 23.90 <.0001 Fuel ... View more

Thanks a lot ... View more

Alright! Thanks for your input. Best regards, Hank ... View more

@ Rick and Steve: Thanks a lot for the feed-back. As a general thought, would you consider using maybe proc nlin to estimate a regression model, instead of trying to fit data to proc reg by transformations? Best regards, /Hank ... View more

Even though the answer is already posted, thanks a lot. Do you have any ideas to my questions in the second post in this thread? /Hank ... View more

Thanks for the help, much appreciated        I have a similar question maybe you can help to clarify. If the transformations are only in a subset of the independent variables, say half of the x-variables are transformed with the square root. How do I interpret that, in relation to the response variable? Shall I back-transform the beta-coefficients of the x-var. first and use these transformed values in relation to the response variable? On to the final question. I found another post by you (https://communities.sas.com/message/125380#125380) where you wrote: "If you are working on developing a predictive equation with only a single predictor, take a good look at PROC TRANSREG. This would enable you to model the dependent variable as a logit, and the independent variable in a variety of ways--class, optimal transforms, non-optimal transforms, nonlinear transforms (such as Box-Cox or penalized B-splines)." What if I do different transformations on both the y- and the x-variables, as a rule of thumb (if there is any), how can I think when I am about to translate the result (beta-coeff. and s.e.) into original terms? For example, if the response (y) are transformed via Box-Cox and the rest of the variables via the logit transformation, how would I go about to translate the results? Best regards, Hank ... View more