# Response Surface Methodology Using Observational Data: A Systematic Literature Review
## 5 Synthesis and Discussion
### Advantages and Disadvantages of RSM-OD  
Based on the synthesis above, the discussion emphasized how the classic RSM concept methodologically adopts nonexperimental data as an alternative to the DoE experiment. The classic RSM has strong scientific references when integrating the three stages of its \begin{table}
\begin{tabular}{l l l l l l l l} \hline \hline \multirow{2}{*}{**Clusters**} & \multicolumn{3}{c}{**Three Stages of RSM**} & \multicolumn{3}{c}{**Additional Stage**} & \multirow{2}{*}{**References**} \\ \cline{2-2} \cline{4-7}  & **Stage 1 (Code C)** & **Stage 2 (Code E)** & **Stage 3 (Code F)** & **Code A** & **Code B** & **Code D** \\ \hline Cluster 6: & & & F4 & A3 & B2 & D4 & [2,94] \\ All obs.—linear model—other optimization technique (8.43\%) & C2 & E1 & & & B1 & [95, 96, 97] \\ \cline{3-7}  & & & F5 & A1 & B2 & D5 & [98,99] \\ \cline{3-7}  & & & & A3 & B3 & [100] \\ \hline Cluster 7: & & & F2 & A1 & & & [101] \\ All obs. – NN model—metaheuristics (7.23\%) & C2 & E2 & & & B1 & D5 & [102] \\ \hline \hline \end{tabular}
\end{table} 
Table 6: _Cont._ \begin{table}
\begin{tabular}{l l l l} \hline \hline  & & **Advantages** & **Disadvantage** \\ \hline \multirow{4}{*}{Stage 1} & \multirow{4}{*}{subset} & Selecting a subset based on specific criteria & A number of of observations will be \\  & & increases inter-factor orthogonality & excluded from the RSM analysis \\ \cline{2-2} \cline{4-5}  & & & As a potential source of information, all \\ \cline{2-2} \cline{4-5}  & & all observation & & observations will be included in the RSM \\ \cline{2-2} \cline{4-5}  & & & analysis & \\ \hline \multirow{4}{*}{Stage 2} & \multirow{4}{*}{linear model} & strong foundation with clear inference and & \\  & & interpretation & & strictly statistical assumptions \\ \cline{1-1} \cline{2-2} \cline{4-5}  & & & black-box model free of assumptions & no model interpretation and potential \\ \cline{1-1} \cline{2-2} \cline{4-5}  & & other models & Similar to neural networks, the SVM model has no required assumptions, and the Taguchi \\ \cline{1-1} \cline{2-2} \cline{4-5}  & & & method works without a pre-specified mathematical model. \\ \hline \multirow{4}{*}{Stage 3} & \multirow{4}{*}{local search} & fast iterative algorithm & potential local optimum \\ \cline{1-1} \cline{2-2} \cline{4-5}  & & metaheuristics & accommodate global optimum & highly depends on initial conditions \\ \cline{1-1} \cline{2-2} \cline{4-5}  & & other technique & Some papers with prediction purposes exclude optimization techniques; the others involve \\ \cline{1-1} \cline{2-2} \cline{4-5}  & & linear programming and Monte-Carlo. \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Summary of method combinations in consideration of the three stages of RSM. analysis (Figure 1), and each stage also gives a clear theoretical basis. Therefore, any development in RSM, including the fulfillment of assumptions during the analysis, should remain within these stages. Thus, the discussion will explore the methods and combinations used in the reference paper (Figure 13). According to Table 7, those options that combined the methods within the three stages of RSM raised some advantages and limitations. In stage 1 of the RSM, contradictions existed between the selection of all observations or their subsets. One problem relates to interfactor orthogonality and the other deals with the justification of selecting only a subset from several potentially informative observations. In stage 2, different types of RSM models, i.e., linear (or polynomial) or machine-learning type models, provided different modeling approaches with each of their consequences. The powerful and interpretable linear model works with several strict assumptions, whereas the free-assumption machine-learning-based model contains potential over-fitting and is noninterpretable. In stage 3, the ordinary local search algorithm works best for a single-optimum point linear model, whereas the metaheuristics algorithm provides a larger search area with local and global optima.