I constructed an index on Stata using "pca rotate predict". When I produced the summary statistics table, I noticed that the index has a mean of zero and a standard deviation of 1. The index is composed of five pollutants, where all pollutants are measured in the same scale μg/m3. Therefore, I am not sure whether standardisation is necessary in this case.
The API index takes values between -3 and 5. Can I interpret these values in a cardinal way, i.e. large values represent a high level of pollution. What about negative values?
Moreover, I have panel data. The dependent variable "hospital admissions" is specified in logs, and the main explanatory variable is the API. I'm not sure how to interpret coefficients.
Thank you in advance!