If you want to build typology of agricultural holdings on the basis of some attributes, such as, standard gross margin and standard output etc., you can go in for 'Attribute-based Multi-dimensional Scaling using Discriminant Analysis'. I have used this statistical tool, but in a different context - 'Indian Merchant bankers' Perception Regarding Southeast-Asian IPO markets'.
I guess if you're interested in build typologies, I suggest you to use any hierarchical or non-hierarchical cluster technique. The issue with discriminant analysis is that it uses a-priori classification outcomes to weight and build an instrument to use it to characterize later. Thus, if you do not have any a-priori outcome, I think discriminant analysis won't be the best way to build those typologies.
In addition, I suggest reviewing some Multi-dimensional Scaling analysis, such as, correspondence analysis, which allows you to work with ordinal variables and numerical variables. In my opinion this is extremely worthy, because you could mix analysis using total hectares, education level, and/or production focus (i.e. fruit production, livestock, horticultural, etc.), for instance.
Thanks for a very detailed answer. I fully share your opinion regardingn discriminant analysis vs. Cluster techniques. As about multi-dimmensional scaling analysis, it is difficult to judge, as I am not familiar with it, unfortunately. Could you tell me what statistical package support this technique? I looked in STATA and SPSS and didn't discover any module related to MDS.
Actually both statistical packages have MDS algorithms. Personally, for exploratory multivariate analysis I prefer SPSS because its output it quite comprehensive, but no so flexible. The algorithm that SPSS uses is PROXCAL, multidimensional scaling of proximity data. Here I’ve attached a link with an explanation of this algorithm:
Additionally, SPSS has categories, which allows you to analyze categorical data. I used to work with HOMALS & CATPCA, which are a really versatile algorithm. I also recommend take a look into it. You could Google them.
Best,
Leonardo
PS: I worked analyzing farms structures and typologies, I have some literature, if you're able to read some Spanish, you could take a look into this:
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