The Estimation of Test Score Reliability

The method of Instrumental Variables is suggested as an alternative to traditional methods for estimating the reliability of mental test scores which avoids certain drawbacks of these methods. The consistency and efficiency of the instrumental variable method are examined empirically using data from the British National Child Development Study in an analysis of 16 year, 11 year and 7 year old scores on tests of mathematics and reading. In the simple regression model (with the usual assumptions about the error term u) y = a + fix + u, it is well known (Goldstein, 1979) that if the observed independent variable x contains errors of measurement and we wish to estimate the regression coefficient on the "true" value of x, then the ordinary least squares (OLS) estimator is inconsistent. The simplest and most common model relating the true value to the observed value of x is