error of person estimate gives an estimate of the variance of the errors, . 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 the two sets of parameter estimates is therefore That is, the disattenuated correlation estimate is obtained by dividing the correlation between the estimates by the geometric mean of the separation indices of the two sets of estimates. Expressed in terms of classical test theory, the correlation is divided by the geometric mean of the reliability coefficients of two tests. Given two random variables and measured as and with measured correlation and a known reliability for each variable, and , the estimated correlation between and corrected for attenuation is . How well the variables are measured affects the correlation of X and Y. The correction for attenuation tells one what the estimated correlation is expected to be if one could measure X′ and Y′ with perfect reliability. Thus if and are taken to be imperfect measurements of underlying variables and with independent errors, then estimates the true correlation between and . Is correction necessary? In statistical inference based on regression coefficients, yes; in predictive modelling applications, correction is neither necessary nor appropriate. To understand this, consider the measurement error as follows. Let y be the outcome variable, x be the true predictor variable, and w be an approximate observation of x. Frost and Thompson suggest, for example, that x may be the true, long-term blood pressure of a patient, and w may be the blood pressure observed on one particular clinic visit. Regression dilution arises if we are interested in the relationship between y and x, but estimate the relationship between y and w. Because w is measured with variability, the slope of a regression line of y on w is less than the regression line of y on x. Does this matter? In predictive modelling, no. Standard methods can fit a regression of y on w without bias. There is bias only if we then use the regression of y on w as an approximation to the regression of y on x. In the example, assuming that blood pressure measurements are similarly variable in future patients, our regression line of y on w (observed blood pressure) gives unbiased predictions. An example of a circumstance in which correction is desired is prediction of