- Disattenuation
In
measurement andstatistics , disattenuation of acorrelation between two sets of parameters or measures is the estimation of the correlation in a manner that accounts for measurement error contained within the estimates of those parameters.Background
Correlations between parameters are diluted or weakened by measurement error. Disattenuation provides for a more accurate estimate of the correlation between the parameters by accounting for this effect.
Let and be the measures of two attributes of person "n" and let be a
maximum likelihood estimate of derived from application of a measurement model, such as theRasch model . Also, let:::
where is the measurement error associated with the estimate , as per
Fisher information theory. Specifically, thevariance of the maximum likelihood estimate of a personparameter is given by the negative of the reciprocal of the secondderivative of the log-likelihood function with respect to the parameter. The person parameter represents the theoretical measure of the person for the relevant attribute or trait.Derivation of the formula
The correlation between two sets of estimates is
:
:::::
which, assuming the errors are uncorrelated with each other and with the estimates, gives
:
:::::
:::::
where is the "separation index" of the set of estimates of , , which is analogous to
Cronbach's alpha ; this is, in terms ofClassical test theory , is analogous to a reliability coefficient. Specifically, the separation index is given as follows::
where the mean squared standard error of person estimate gives an estimate of the variance of the errors, , across persons. The standard errors are normally produced as a by-product of the estimation process (see
Rasch model estimation ).The disattenuated estimate of the correlation between two sets of parameters or measures is therefore
:
That is, the disattenuated correlation is obtained by dividing the correlation between the estimates by the square root of the product of the separation indices of the two sets of estimates. Expressed in terms of Classical test theory, the correlation is divided by the square root of the product of the reliability coefficients of two tests.
ee also
*
Regression dilution
*Errors-in-variables model External links
* [http://www.rasch.org/rmt/rmt101g.htm Disattenuating correlations]
* [http://pareonline.net/getvn.asp?v=8&n=11 Disattenuation of correlation and regression coefficients: Jason W. Osborne]
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