# Aggregation of propensity scores with varying reliability

When trying to estimate the number of sampling units with an attribute, is there a good algebraic way to aggregate over propensity scores for that attribute which each have their own error? For example, when the propensity scores may be calculated with varying amounts of information from each sampling unit and each has its own standard error on that propensity.

Or they could be expected values of beta distributions.

In the latter case I know I can simulate beta-bernoulli outcomes from each sampling unit and add up the results many times; but is there a consistent estimator of the result of this difficult to scale process?

In short, how do people aggregate propensity scores of varying reliabilities?

Edit:

I suppose I worded it poorly; the data I have is all either binary or categorical and each observation is accompanied by the probability it was observed correctly. So suppose I have 5 persons; 3 of which had a value of 1 for an attribute, 2 of which had a value of 0 for that attribute, each of which had a probability .8,.81,.82.,.83,.84 respectively of being observed correctly. What is the expected value of p(having that attribute)?

• I don't understand what you're trying to do here. To estimate propensity scores you need to know whether each individual received the treatement or not, in which case you can simply count up how many received the treatment. Why do you want to aggregate propensity scores? – onestop Nov 14 '10 at 14:04
• I suppose I worded it poorly; the data I have is all either binary or multinomial and each observation is accompanied by the probability it was observed correctly. So suppose I have 5 persons; 3 of which had a value of 1 for an attribute, 2 of which had a value of 0 for that attribute, each of which had a probability .8,.81,.82.,.83,.84 respectively of being observed correctly. What is the p(having that attribute)? – Patrick McCann Nov 16 '10 at 17:27