In my experiment i.e. RSM CCD, I have predicted R-square 95% but lack of fit is significant. Studying this problem, I came to know that if the pure error is very low as compared to residual then lack of fit will be significant. Also I use very precise instrument for measuring the responses hence the pure error is very low.
Dear Alisson Borges,
You can find this statement (difference less than 0.2) in these papers:
- https://books.google.com.br/books?id=_1wEBgAAQBAJ&pg=PA35&lpg=PA35&dq=%22Predicted+R-squared%22+0.2+difference&source=bl&ots=2WGvluQcGX&sig=C0DmuCgrrfvstaXDRR6SsvRSbQ4&hl=en&sa=X&ved=0CDwQ6AEwBWoVChMIgOHvvJyfxwIVw0GQCh2pBACw#v=onepage&q=%22Predicted%20R-squared%22%200.2%20difference&f=false
- http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.64.3468&rep=rep1&type=pdf
- http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20070003497.pdf
- http://docsdrive.com/pdfs/medwelljournals/jeasci/2010/154-162.pdf
- http://dx.doi.org/10.4236/msa.2012.32009
- http://www.scielo.br/pdf/bjce/v31n1/08.pdf
- http://www.ijeit.com/Vol%204/Issue%206/IJEIT1412201412_04.pdf
- http://iieom.org/ieom2012/pdfs/505.pdf
Both are equally important. There can me minor errors in the values which you got that's the reason for the lack of fit comes significant.
I did the experiment twice but got the same result, lack of fit is significant with very good r-square and pred. R-square values. i guess i will have to do validation experiment and the fit the model showing the %error
In one of my case R-square = 0.97 , Adj R-square =0.968, Pred R-square =0.965 and without even reducing the model the P-value of Lof = 0.001 which shows significant LOF. I tested the predictive model with 2 replicates of validation model but the average % error is around 17% which is unacceptable... the % error between the two replicates itself is 5%
In other case R-square =0.838 Adj R-square = 0.825, Pred R-square = 0.805 with same significant LOF problem, but when i did validation experiments the average % error is around 5% and checked it with another replication again i got around 5% error between actual and predicted values which seems to me as acceptable.
Both factors are important.
The non-significant lack of fit value and values for adjusted and predicted R2 close to one confirm the validity of the model.
when the adjusted or predicted R-squared is less than the actual R-squared by a value of about 0.3 or less it means that your experiment has a high likelihood of being representative of the larger population.
Both are important parameters. You will typically want to get an R-squared close to unity as much as possible and at the same time ensuring that you have insignificant lack of fit. Maybe using another test like the Fischer test to determine the goodness of fit of the generated model will help.
A Lack of Fit error generally means that there is a missing term in the model. It is possible that you need to transform the response data and re-analyze. If you are missing a significant higher order term that can cause LOF error too. Some designs allow you to look for higher order, non-standard terms.
I have seen data where the blocks form the data do not confirm the results from each other. For example, Factor A in block 1 is large and positive. In block 2, it is small and negative. This type of discrepancy can cause a LOF error too.
What happens when you take an average of the 2-trials?
Dear colleagues (specially Azubuike Chukwuka and Marius Secula)
Does anyone have the paper (or citation) about the difference recommended between R2adjusted and R2predicted ?
Should this difference less than 0.3 or 0.2? I searched in WoS and other sources but I have not found papers or books suggesting this ranges.
Thanks in advance.
Dear colleagues (specially Azubuike Chukwuka and Marius Secula)
Does anyone have the paper (or citation) about the difference recommended between R2adjusted and R2predicted ?
Should this difference less than 0.3 or 0.2? I searched in WoS and other sources but I have not found papers or books suggesting this ranges.
Thanks in advance.
Dear Alisson Borges,
You can find this statement (difference less than 0.2) in these papers:
- https://books.google.com.br/books?id=_1wEBgAAQBAJ&pg=PA35&lpg=PA35&dq=%22Predicted+R-squared%22+0.2+difference&source=bl&ots=2WGvluQcGX&sig=C0DmuCgrrfvstaXDRR6SsvRSbQ4&hl=en&sa=X&ved=0CDwQ6AEwBWoVChMIgOHvvJyfxwIVw0GQCh2pBACw#v=onepage&q=%22Predicted%20R-squared%22%200.2%20difference&f=false
- http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.64.3468&rep=rep1&type=pdf
- http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20070003497.pdf
- http://docsdrive.com/pdfs/medwelljournals/jeasci/2010/154-162.pdf
- http://dx.doi.org/10.4236/msa.2012.32009
- http://www.scielo.br/pdf/bjce/v31n1/08.pdf
- http://www.ijeit.com/Vol%204/Issue%206/IJEIT1412201412_04.pdf
- http://iieom.org/ieom2012/pdfs/505.pdf
In the case of Response Surface Methodology for optimization of Factors, both Model p Value & Lack of Fit p-value are important to diagnose the predictability of selected linear quadratic or cubic regression model.
(A) During Selection of order of polynomial: MODEL [A mathematical relationship between factors & response assisting in calculations & predictions) for Analysis of Response; ANOVA was carried out thoroughly for testing of SIGNIFICANCE of every possible MODEL (p0.1) & response surface to confirm expected shape of response behavior
(B) Lack of Fit is the variation of the data around the fitted model. If the model does not fit the actual response behavior well, this will be significant. Thus those models could not be used as a predictor of the response.
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