I have a dataset composed of several subjects. Each subject has a series of binary indicators where 1 indicates that a the subject presents an indicator and 0 means that the indicator is not present. These indicators are grouped into 5 categories each one composed of a different number of the aforementioned indicators. If a subject has more indicators present at a category it means that the category is stronger in that subject.
I want to aggregate all the binary indicators in each category into a single real value for each subject. The method that came to my mind is using the number of indicators with a value of 1 divided by the total number of indicators. That way a subject with all the indicators equal to 1 in one category will get a maximum value of 1.0 in that category, likewise, a subject with half the indicators with a value of 1 and the other half with a value of 0 has an aggregate value of 0.5 in that category. I am new to data science and I am not sure if this is the best approach. What do you think ? Does this aggregation makes sense to you ? Do you know any other possible aggregations ?
Below I attach a sample toy dataset with 3 subjects, 2 categories and 2 indicators per category to further explain my problem:
| | Indicator1.1 | Indicator1.2 | Indicator2.1 | Indicator2.2 | |----------|--------------|--------------|--------------|--------------| | Subject1 | 1 | 0 | 1 | 1 | | Subject2 | 1 | 1 | 0 | 0 | | Subject3 | 0 | 1 | 1 | 1 |
In the example above, Indicator1.1 and Indicator1.2 belong to the same category, likewise, Indicator2.1 and Indicator2.2 also belong to the same category. With the aforementioned aggregation method of the ratio the categories real values will be:
| | Category 1 | Category 2 | |---------- |------------ |------------ | | Subject1 | 0.5 | 1.0 | | Subject2 | 1.0 | 0.0 | | Subject3 | 0.5 | 1.0 |
Hello Ángel Panizo Lledot ,
If you'd like for each of the indicators to have equal nominal weight in the aggregate/composite score and you wish to report descriptive results for the category composites, then the method you suggest will work just fine to accomplish that goal. Note that the actual weight for an indicator in this type of composite is proportional to its standard deviation.
On the other hand, if you have a very different research goal in mind, perhaps some other method (which possibly: (a) weights indicators differentially; and/or (b) recombines indicators within/across categories) would be preferred.
As well, if there exists already some standard method for generating category composites with this set of variables, it might be wise to consider whether that would fit your research goal/s.
Good luck with your work.
Hello Ángel Panizo Lledot ,
If you'd like for each of the indicators to have equal nominal weight in the aggregate/composite score and you wish to report descriptive results for the category composites, then the method you suggest will work just fine to accomplish that goal. Note that the actual weight for an indicator in this type of composite is proportional to its standard deviation.
On the other hand, if you have a very different research goal in mind, perhaps some other method (which possibly: (a) weights indicators differentially; and/or (b) recombines indicators within/across categories) would be preferred.
As well, if there exists already some standard method for generating category composites with this set of variables, it might be wise to consider whether that would fit your research goal/s.
Good luck with your work.
Are the different indicators the same for each person? For example, does each person trying to identify a road in the same 5 photos, or are the indicators different for the different people. If the indicators are the same for each individual, methods from item response theory (IRT, also called latent trait modeling) might be worth exploring (most packages call the individual estimates theta). The different categories would be testlets. Alternatively, multilevel (perhaps cross classified, but more info is necessary to determine that) models with indicators nested within categories crosses with people might be worth doing. The conditional modes can then be estimated (conditional modes rather than conditional means since this would be a logistic multilevel model).
Hi Ángel Panizo Lledot
For the given problem statement, your solution (i.e. the average) sounds suitable. I don’t believe there is anything better to do, especially because your problem is binary.
keep up the good work!
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