= Measurement Error Models =

'''Measurement Error Models''' (ISBN: 9780470316665) was written by Wayne A. Fuller in 1987.

A measurement ''X,,t,,'' is decomposed into the true value ''x,,t,,'' and the measurement error ''u,,t,,''.

When a linear model is constructed as ''Y,,t,, = β,,0,, + β,,1,,x,,t,, + e,,t,,'' but estimated as ''Y,,t,, = βˆ,,0,, + βˆ,,1,,X,,t,, = βˆ,,0,, + βˆ,,1,,(x,,t,, + u,,t,,)'', then the expected values are characterized by:

{{attachment:exp1.svg}}

{{attachment:exp2.svg}}

And the covariance matrix is specified as:

{{attachment:covar.svg}}

We assume that ''x,,t,,'', ''e,,t,,'', and ''u,,t,,'' are all independent.

The regression coefficient that has been attenuated (biased towards 0) by measurement error is represented as ''γ''.

{{attachment:gamma.svg}}

The relationship between ''γ'' and ''β,,1,,'' is characterized by ''κ''.

{{attachment:kappa1.svg}}

In more plain terms, this is:

{{attachment:kappa2.svg}}

''κ'' is the '''reliability ratio'''.



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CategoryRicottone