one of the standard references for assessing and correcting for regression dilution. Hughes (1993) shows that the regression dilution ratio methods apply approximately in survival models. Rosner (1992) shows that the ratio methods apply approximately to logistic regression models. Carroll et al. (1995) give more detail on regression dilution in nonlinear models, presenting the regression dilution ratio methods as the simplest case of regression calibration methods, in which additional covariates may also be incorporated. In general, methods for the structural model require some estimate of the variability of the x variable. This will require repeated measurements of the x variable in the same individuals, either in a sub-study of the main data set, or in a separate data set. Without this information it will not be possible to make a correction. Multiple x variables The case of multiple predictor variables subject to variability (possibly correlated) has been well-studied for linear regression, and for some non-linear regression models. Other non-linear models, such as proportional hazards models for survival analysis, have been considered only with a single predictor subject to variability. Correlation correction Charles Spearman developed in 1904 a procedure for correcting correlations for regression dilution, i.e., to "rid a correlation coefficient from the weakening effect of measurement error". In measurement and statistics, the procedure is also called correlation disattenuation or the disattenuation of correlation. The correction assures that the Pearson correlation coefficient across data units (for example, people) between two sets of variables is estimated in a manner that accounts for error contained within the measurement of those variables. Formulation Let and be the true values of two attributes of some person or statistical unit. These values are variables by virtue of the assumption that they differ for different statistical units in the population. Let and be estimates of and derived either directly by observation-with-error or from application of a measurement model, such as the Rasch model. Also, let where and are the measurement errors associated with the estimates and . The estimated correlation between two sets of estimates is which, assuming the errors are uncorrelated with each other and with the true attribute values, gives where is the separation index of the set of estimates of , which is analogous to Cronbach's alpha; that is, in terms of classical test theory, is analogous to a reliability coefficient. Specifically, the separation index is given as follows: where the mean squared standard