Effects of measurement errors in predictor selection of linear regression model

Measurement errors may affect the predictor selection of the linear regression model. These effects are studied using a measurement framework, where the variances of the measurement errors can be estimated without setting too restrictive assumptions about the measurement model. In this approach, the problem of measurement is solved in a reduced true score space, where the latent true score is multidimensional, but its dimension is smaller than the number of the measurable variables. Various measurement scales are then created to be used as predictors in the regression model. The stability of the predictor selection as well as the estimated predicted validity and the reliability of the prediction scales is examined by Monte Carlo simulations. Varying the magnitude of the measurement error variance four sets of predictors are compared: all variables, a stepwise selection, factor sums, and factor scores. The results indicate that the factor scores offer a stable method for predictor selection, whereas the other alternatives tend to give biased results leading more or less to capitalizing on chance.