Good Discussion

Following

You can do listwise deletion - omit those cases with missing data and run the analyses on what remains.

I found this:

"By far the most common approach to missing data is to simply omit those cases with missing data and to run our analyses on what remains. Thus if 5 subjects in Group 1 don't show up to be tested, that group is 5 observations short.  Or if 5 individuals have missing scores on one or more variables, we simply omit those individuals from the analysis. This approach is usually called listwise deletion, but it is also known as complete case analysis. 

Although listwise deletion often results in a substantial decrease in the sample size available for the analysis, it does have important advantages. In particular, under the assumption that data are missing completely at random, it leads to unbiased parameter estimates. Unfortunately, even when the data are missing completely at random (MCAR) there is a loss in power using this approach, especially if we have to rule out a large number of subjects. And when the data are not MCAR, bias results (for example when low income individuals are less likely to report their income level, the resulting mean is biased in favor of higher incomes)".

Ahmed Taifor

Mixed orthogonal arrays can be used for the case defined by you.

Mixed orthogonal arrays allows to study few factors at certain levels and few factors at other levels.

Few examples of mixed OA are:

L18 OA (2^1 x 3^7) = One factor at 2 levels and seven factors at 3 levels can be studied

L'32 OA (2^1 x 4^9) = One factor at 2 levels and nine factors at 4 levels can be studied

L36 OA (2^11 x 3^12) = Eleven factors at 2 levels and twelve factors at 3 levels can be studied

L'36 OA (2^3 x 3^13) = Three factors at 2 levels and thirteen factors at 3 levels can be studied

L50 OA (2^1 x 5^11) = One factor at 2 levels and eleven factors at 5 levels can be studied

L54 OA (2^1 x 3^25) = One factor at 2 levels and twenty five factors at 3 levels can be studied

Dear Ahmed,

A widely accepted guideline in the design and analysis of experiments is "Keep the design and analysis as simple as possible". Why do you not use a sequential strategy of experimentation (the RSM)?! RSM, properly understood, is a series of experiments, each one building upon the previous ones:

. The first phase is a factorial screening experiment that has two purposes. The first is to determine which of the factors postulated as critical really has a significant impact on the response or responses of interest. The second purpose is to propose a simple model to build a path of steepest ascent. .

. The second phase is this path of steepest ascent, where the experimenter performs a series of runs in the direction the model suggests will produce better results.

. The third phase is another factorial experiment built around the run in the path of steepest ascent with the best results. Generally, this experiment involves replication, usually via center runs, to allow a test for lack-of-fit. Once the experimenter believes that he or she is in the neighborhood of optimum conditions, one runs a design specifically intended to fit a

second-order model. The second order model allows the analyst to fit a second order model, which allows a useful approximation of the behavior of the response in the neighborhood of a mountain top (the optimal response).

. The final phase in RSM is a confirmation experiment based on the set of conditions recommended by the second-order design.

For further details see, as example, Geoff Vining (2011) Technical Advice: Design of Experiments, Response Surface Methodology, and Sequential Experimentation, Quality Engineering, 23:2, 217-220, DOI: 10.1080/15226514.2011.555280