The first expression is derived under the assumption that the errors in the predictor variables are homoscedastic, i.e., of constant variance.
Such measurement errors in the predictor variables will tend to reduce a true association between e.g. an eye pathology and the outcome, i.e. visual acuity, but it does not invalidate the associations that we actually find.
Turning to the mean square error of the predictor in Eq. (6) we need to acknowledge that uncertainty is introduced both by the estimation of the model parameters and by the random residual terms linked to each population element.
The state predictor is designed to track the plant states smoothly by incorporating proportional and integral error terms in the state predictor model.
The relative importance (RI) of a predictor in a Random Forest model is obtained by the out-of-bag (OOB) error estimation, which is the increase of mean squared error (MSE) when the predictor values are permuted.
As an example, previous analyses of the association between age disparity and HIV infection in this population which found no relationship for women aged under 30, 7 and decreasing risk with increasing age disparity in 30 50 year olds 37 may have suffered from error in their predictor variable.
Although flexible in its application, the RMSE is calculated with the assumption that error variance is homoscedastic across changes in the predictor variable.
In effect, the technique allows for errors on the predictor, as well as on the predicted variables.
IVs have to be highly correlated with the predictor (instrumental relevance) [ 14, 18], influence the outcome only via the predictor, be orthogonal to the error in the predictive model (instrumental exogeneity) and require large Ns [ 3– 5, 14– 14].
Separate predictors were implemented for ANGLE clock presentations, COLOR clock presentations, and INSTRUCTIONS ('A' and 'C' conjoined in one model predictor, since this predictor served only to decrease error in the general linear model).
