There are some works in literature in which selectivity models are developed in Minitab software by response surface methodology based on the data that have been collected by other researchers and optimization is performed to propose optimal conditions to maximize the selectivity for desirable products. I take the same data just to check how response surface methodology works, but I never get the same model that have been obtained in this works. The coefficients in the model for regressors and their interactions don't match. Even in such cases that R square and adjusted R square values are the same. Even in the case that I check some data points withy model and get the same responses as they get, but the coefficients are totally different. I don't know exactly whether I miss something or I don't use the software rightly or something else. I want to note that, in Minitab I go to Stay>DOE>Response surface and choose regressors in uncoded versions, as well as their lower and higher values, then responses at the same time. I think the problem might be in coded variables, are uncoded variables converted into coded ones in the same way, or it might be done differently? Or the problem might be with the way I interpret the results after I run RSM. What do you think, is the problem related to it or any other factors?
Dear Nurlan Amirov, I think your problem lies in the coding of the predictor variables or factors. In most articles, the model coefficients based on the coded factors are reported. But, to be sure, you should review the way the results are reported.
Dear Raúl González-García, In the articles the equation is given for converting uncoded variables to coded variables, and I am not sure is this formula the only way for conversion in Minitab, or the software can apply other formula based on the choice.
Hello Nurlan,
I think Raúl is right. If you get different results for the coefficients despite the same conditions (data, method for estimating the parameters, model, etc.), then I would assume that it is due to the coding of the factors. Usually, the parameters in DoE are determined using the least squares approach. No matter what software you use to estimate them, the differences should be minimal. I would like to clarify the following points: 1) Are significant effects given in the literature in addition to the data? If so, which ones? 2) What is the significance level alpha? 3) Are the factor levels coded? You should then compare these data with yours in Minitab.
Best regards
Dear Nurlan Amirov: Your DOE is for response surface, but you don't say what design it is. First you must determine the kind of design you use (CCD, Box-Behnken, D-optimal, etc.) and from that design there are variants that you should also know. With that information you can estimate the coding of factors that the software does. For example, in the CC design, the axial distance (alpha) influences (indirectly) the coding of the factors, since the coding of factors can be done with respect to the alpha value or with respect to the low-high levels that you chose from your factors .. According to what you describe, you do the coding with respect to alpha, but it may be that the software does so with respect to the low-high levels of the factors. Please check that aspect.
Dear Alexander Kremer
Thank you very much for the answer. In more detail, SE coefficients, F values and P values for each individual variable, as well as for their interactions are given in the literature works. R square, adjusted R square values, F-regression and F-lack of fit values are given. I want to note that at the same time several response variables are predicted and several models are developed. I presume that the differences in coefficients steam from the coded variables. Actually in Minitab software when I apply RSM I see that there are several coding options. But I am not sure that the coding formula in literature work matches with any of these choices.
Dear Raúl González-García
When I apply RSM, I choose low and high values and according to data the software itself finds ans sets low and high values for each parameter. Actually, the formula in one literature work is Z=z-[[Zmax+Zmin]/2]/[Zmax-Zmin/2]. Z is coded variable, while z is uncoded variable. I assumed that the low and high values represent these max and minimum values. There is also other formula in which uncoded value of independent variable at center point is subtracted from uncoded value of the independet variable and then divided by the step change value.
From your and others explanations I realize that I might have got the idea behind DOE method wrongly. Actually, as far as I know that DOE method is applied before conducting the experiment to decide how to collect the data throughout the experiment. But RSM as a different procedure for model development and optimisation involving multiple linear regression analysis. That's why admittedly I dont understand the real difference between DOE and RSM.
Dear Nurlan Amirov
I will try to explain the concept of Response Surface in DOE. The DOE is a strategy to generate a data matrix that contains orthogonal column vectors (or in the worst case column vectors close to being orthogonal). Each row of the matrix represents the conditions in which an experiment will be carried out, and the columns of the matrix represent the values (levels) of each factor. The ANOVA is the statistical theory used to analyze the relationship between the factors (in the matrix) and the response variable of interest, which is measured after executing each experiment. A mathematical model (equation) is indispensable to perform an ANOVA. Also, the experimental plan that is generated with the DOE is based on a mathematical model. In principle, the same model that generated the experimental plan should be used to analyze the results with the ANOVA. The models used are multivariable polynomials. If a linear equation (polynomial of degree 1) is involved in the design, then a Factorial Design is being constructed and a traditional multi-factor ANOVA analysis methodology can be used. But if a grade 2 polynomial is involved in the design, then a Response Surface Design is being constructed and an ANOVA analysis methodology with multi-variable linear regression should be used. In all cases, all the factors are scaled between + -1, but on the Response Surface the + -1 may correspond to the high-low levels of the factors OR may correspond to the + -alpha levels of the factors.
I recommend
Douglas C. Montgomery; Design and Analysis of Experiments, 10th Edition; Ed. Wiley; ISBN: 978-1-119-49244-3; June 2019; 567 Pages
Dear Raúl González-García and Alexander Kremer ,
Actually in Minitab software, there are three sections that statistical models can be developed, first one is 1. Stat>Regression>Fit regression model, other one 2. Stat>DOE>Response surface>Analyse response surface design, and the last one through 3. Assistant>multiple linear regression. If I want to fit a model to experimental data which one is actually more favorable for me? The results for all of them vary, and also the for the second one as far as I know it is not possible to choose coding, while in the first one it is possible, there are some options, and it is not clear for me which options match with the equations that I mentioned above. I attach the picture of one the model that have been constructed in the literature, and the picture of the model that I have developed on the basis of the same experimental data. I also attach the link for the reference paper: DOI: 10.1080/10916466.2016.1193521 Please let me know if I do not consider something important that cause to differences in this models. Thanks in advance!
Dear Nurlan Amirov . Your data does not come from a DOE, therefore you cannot use the DOE in Minitab. Your data does not represent an orthogonal plan, so there is a lot of covariance and an ANOVA is risky. Even so, from your data, you can still obtain a mathematical model by multivariable regression (polynomial or non-linear). Maybe in Minitab you should use Assistant> multiple linear regression. According to the model in image 6, there is no coding of the factors. The model shown in image 6 is a cubic model that has been prunned. When you apply the same model (same terms of model) in Assistant> multiple linear regression in Minitab, without coding the factors, you should obtain the same results in the model coefficients.
Dear Raúl González-García
Even using only Assistant.>multiple regression does not give the same model, one of regressors is excluded from the model, and not all interaction terms are represented in that model. R square value is 76.44% which is to below than that of in the original model (90%). There are two large residuals and as we discussed in other question I should not exclude large residuals points from data. I attach the ANOVA and coefficient results for this model from literature, I would love to ask you to compare them with the reproduced model
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