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I have two separate and heterogeneous measurements of the same object. I wish to make predictions about the object state using both sets of measurements.

What ways can the measurements be combined within a regression framework in order to improve inference?


What I mean by "heterogeneous" is that the measurements are disparate and incommensurate. Two different devices were used to observe the object, which measured different aspects of its state.

In relation to improved inference, I wish to predict the object state using the two measurements using regression. Ideally, using both measurements should lead to a more accurate prediction than using either of the measurements separately.

How should the state predictions be based on the measurements? At the moment I am learning a mapping from the measurement input space to the output space using ridge regression.

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Assuming the only differences in the measurements is due to error, you could treat the underlying construct of interest as latent and use the multiple measurements as indicators of that latent construct. – Andy W Jun 24 '11 at 14:13
No, the measurements refer to different physical attributes of the object's state. – Josh Jun 24 '11 at 15:01
The question is too vague to answer. What kind of inference is desired? How exactly should it be based on the measurements? What do you mean by "heterogeneous"? – whuber Jun 24 '11 at 15:28
@whuber I have updated my question. Please let me know if it is still unclear. – Josh Jun 24 '11 at 16:12
Thanks. It is clearer. Be aware, though, that many radically different answers are conceivable, any of them potentially correct. Selecting a good approach depends on understanding (or analyzing) the relationships among the measurements and the object state, which may be nonlinear, have heteroscedastic and correlated errors, etc. Therefore, the more information of this nature you can provide, the better you can hope the replies will be. – whuber Jun 24 '11 at 16:25

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