The traditional construction of a composite indicator is generally based on Factor analysis or Principle Component Analysis. These two methods require that individual indicators are supposed to be correlated to each other to some extent (e.g., factors in the correlation matrix are larger than 0.5). This precondition could guarantee that these individual indicators describe a similar phenomenon.
However, in my case, there are 5 individual indicators representing waste treatment behavior from different perspectives (e.g., sewage treatment methods, domestic waste treatment, agricultural production waste treatment....). These indicators are less correlated to each other, which cannot satisfy the requirement for the application of FA or PCA(cannot pass KMO test). Based on this, what should I do if I want to use one composite indicator to capture treatment behavior?
By the way, these 5 individual indicators are valued by 1,2,3, and 4. The larger the number, the more environmentally friendly the treatment method is. Do you think it is feasible if I calculate the sum of these 5 indicators directly?
Dear Xiaojie Wen
I solved a similar problem a long time ago, not using CPA analysis but MCDM, where it does not matter if indicators are or are not correlated. I also used MCDM to determine a composite index for environmental issues
With this method, you can or not evaluate the indicators. I prefer not, because in so doing you are indicating the system which are the indicators you prefer the most, which is what you want to determine mathematically
Nolberto Munier
Dear Prof. Munier,
Thank you very much for your advice. It indeed helps and gives me a new perspective to think about this question.
Dear Xiaojie Wen
You are most welcome and don't hesitate to contact me if need arises and you think that I can help
Yes it is possible if you use MCDM regardless of the correlation status of individual indicators.
Nolberto Munier
Dear Prof. Munier,
Sorry to bother you again. As your suggestion, I check some literature on MCDM, especially the TOPSIS method. I think this method could help me evaluate the performance of households on waste treatment. But I am confused about how we could weigh the sub-indicators properly. In general, we could use the same weight for each indicator. And there are also some objective weighting techniques, e.g., the entropy method or CRITIC method. Even though these weighting methods could generate objective weights based on the information from the dataset, this method could not guarantee that the results could reflect the situation in the real world.
Actually, I want to use some subjective/flexible weights to evaluate or rank the performance. For example, I have 4 sub-indicators to represent the waste treatment behavior. I could set 4 different scenarios, where there is always one sub-indicator taking the biggest weight. (if 1 is the full score, the weights for 4 indicators can be 0.4, 0.2, 0.2, and 0.2, respectively.) In this case, policymakers could see the results when they put attention to different indicators. Even, we could further study the influence of contextual variables on performance. Ideally, the influence of contextual variables on performance varies in different scenarios. Do you think it is feasible? Could you please recommend some weighting methods?
Thank you very much and sorry for this quite long question.
Xiaojie Wen
Dear Xiaojie
Thank you for your question, and rest assured that you don't bother me, quite the opposite.
I am puzzled with your conclusion at te end of the first long paragraph when you state that: 'Even though these weighting methods could generate objective weights based on the information from the dataset, this method could not guarantee that the results could reflect the situation in the real world'
At present-time, there is no MCDM method that can reflect with certainty ther situation is the real world.
TOPSIS, an excellent method, works with objective data and entropy weights that are based on that dtaa. Consequently, I believe that it can be used.
I read several times what you say about 4 different scenarios and I couldn't understand what you mean. What are 'scenarios' for you? For me a scenario is a determined problem with data. Another scenario is the same problem but with different data, and so on.
What are sub indicators? What kind of wastes are you talking about?
I am against in using weights of any kind in MCDM.
In my practice in MCDM, I don't use weights, by working with SIMUS where they are not necessary, therefore, unfortunately, I am unable to answer your question.
Nolberto Munier
Dear Prof. Nolberto,
Sorry for the unclear expression. And thank you very much for your reply.
First, I think I should not state my doubt or confusion like the statement-'Even though these weighting methods could generate... in the real world'. I am just confused about how we could ensure that the weights are consistent with policy makers' expectations if the method is only based on the information from the data, e.g., the entropy, standard deviation, or correlation. For this question, I think you already answered me, right?
With this in mind, I am wondering if it is possible to apply some subjective weighting methods which are based on the real demand of human society (e.g., the experts grading method). For instance, I have 4 indicators to reflect waste treatment behavior, which are sewage disposal approach, household solid waste separation, household soil waste disposal approach, and agricultural production waste disposal, separately. I was thinking that maybe I could set up 4 different scenarios, where we treat only one indicator as a priority (that is, this indicator has a higher weight) and other indicators share equal weights. Specifically, in the first scenario, we treat sewage disposal as the primary task for the government; in the second, waste separation is the primary task;... This idea might be nonsense, but it will be very kind and helpful if you could share your opinion about this.
Best regards,
Xiaojie
As mentioned by the other scientists, it is possible to utilize MCDM. Besides you can use other data preprocessing methods such as ICA
Dear Xiong
The fact that you don't use weights does not mean that a method like SIMUS does not consider tehm. Quite rthe opposite, SIMUS is an iterative method, and thus, the COMPLETE SET of weights are computed internally at each iteration, based on data, maybe hundreds of times. However, these weights do not correspond to experts estimates.
In SIMUS, once you get the final result completely based on certain data, either quantitative or/and qualitative, it is the DM task to analyze the result and make as many changes as as she/he wants, based not onloy on experience and know-how, but also from consultationsd with stakeholders
In this way, you estimate how the results are in agreement with what each stakeholder wants, and of course, it can be corrected many times, until reaching a compromise solution that satisfies all stakeholders.
Refernce to you question, the answer is yes, you can apply subjective weights from stakeholders. Just multiply the subjective weight, by the values of each criterion, before building the initial decision matrix. You can proceed as group decision making.
But you don't need to do as you say in the case of wastes, because thus, you are considering the value of only one criterion and leave the other criteria with a same weight. As you can see, it does not have any mathematical support. First, because thre selection of the criterion with the highest weight is arbitrary, and second, because you can't assume that the other remain equal.
In reality, what you are proposing is what SIMUS does. It takes sewage disposal as objective subject to the other criteria. Then, replace it in the matrix and uses waste separation, as a second objective, and so on, but SIMUS does not use any weight.
Nolberto Munier
Dear Prof. Munier
Thank you very much for paying attention to my questions. And many many thanks for your comprehensive explanation. I think SIMUS can help me solve my research questions very well.
Best regards,
Xiaojie
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