Hello? I'm a researcher in Korea. I'm major in the Management discipline.
I really want to know how to rigorously measure the distance among entities. (absolute measure, not relative measure) I only have data; ratio of attributes.
With the ratio data, how do I measure absolute distance among entities? The distance means the similarity of entities.
I have tried a heuristic approach. First, I selected 3 representative attributes which reasonably explain the whole. And gave a grade from A to E to each attribute. Lastly I made categories from three attributes' grades, just by rule of thumb. These processes are not science, I think. Could you recommend how to solve it rigorously?
Please let me know the best idea or solution. And forgive me for my poor English if you hardly understood.
Thank you.
One way of approach is using ways of transforming your features into a lower dimensional space. In your case, you have around 25~35 features, for each entity. You could look at Principal Component Analysis (link is added below), as a preliminary approach to reduce the features.
Once you have obtained the "scores" for each sample from your principal components, you could look at distances as Euclidean distances between scores.
This could be your preliminary approach to look at the distances between entities.
Regards,
https://en.wikipedia.org/wiki/Principal_component_analysis
I agree that Principal Component Analysis is the way to proceed.
But if your data consists of ratios, then your data is relative, and it is unlikely that the entity separation could be considered "absolute".
If by "absolute" you mean that the distance should be quantitative and objectively defined, then principal component analysis should work for you.
You can also use multivariate analysis or multidimensional analysis. You'll have Euclidean distance also ...
see on my RG profile those publications:
Competitive position multivariate analysis of 1000 top EU companies in 2013 - Research and Development perspective
or
MULTIVARIATE COMPETITVE POSITION ANALYSIS IN
BANKING SECTOR: POLISH BANKS VERSUS PEER GROUP PERSPECTIVE
If I understand you correct: you have a set of items which correspond to certain entities (in our case I would use the word "construct"). Now you want to measure, whether there is a difference among them and how high it is.
If so, then:
1. You have to aggregate he items to factors. This is made by, e.g., Principal Component Analysis (as mentioned by Abhishek Sivaram above). In SPSS you go to Analyze -> Dimension reduction -> Factor. You choose PCA and restrict the number of components by 1. Save the Result as a regression.
2. Then the best option would be to use T-Test (Analyze -> Compare means -> one sample T-Test). This Test will show you, how different your factors are.
It can also be useful:
3. You can also perform a bivariate correlation which will show you how "related" the factors are. Since it is not completely clear what you mean by "different". Thse factors which are correlated are definitely "closer" than those which are not correlated.
4. If you have singe items than it would be statistically problematic. You can still compare means but the results might not be publishable/useful since single item scales should be treated differently (e.g. be dychotomized).
I hope it helped!
Best,
Eugene
YOu can also try multi-criteria decision analysis such as AHP.
Also, check out morphological analysis technique at YouTube: https://youtu.be/x4zAniSP0FY
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