# Combining proxy variables to estimate true underlying variable

#### Svezt

##### New Member
Dear all,

suppose you have several (~3-4) measures of an economic variable. These measures all come with some degree of measurement error (noise) and it is a-priori unclear which one best represents the underlying phenomen (which one intents to capture). To complicate things, the samples of the measures only partially overlap.

Is there a method to combine the measures to arrive at "a best measure" (i.e. less noisy)? Ideally, the method would result in a point estimate and a confidence intervall.

Alternatively, where would you look for an answer?

Any help would be appreciated,
Svezt

#### hlsmith

##### Less is more. Stay pure. Stay poor.
So you have two instruments which can collect data. Both have variability in their repeated use and you have no true gold standard to compare the accuracy of the instrument to, right?

#### Svezt

##### New Member
Yes, I suppose that would be another way to phrase it.

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Not sure how you would weight them without knowing the truth. You could maybe weight them if you had a validation study on how much they may be biased. But you may run into extrapolation issues if you don't know how well the proxy values differ across all possible values.

#### noetsi

##### Fortran must die
I think the only way to do this would be to have theory to build on to tell you what the correct answer is. There are various ways to reduce variability in the method, but I don't think that addresses your basic question.

#### Svezt

##### New Member
Thanks for your answers. So, I guess my options are i) finding a theoretical argument in favor of one measure and ii) simply using the arithmetic mean.

#### noetsi

##### Fortran must die
I strongly recommend i or a literature review that supports ii especially if this is for a journal or degree.