Structural Equation Modeling: Applications Using Mplus

Appendix 3.A Influence of Measurement Errors

Measurement errors are known to behave nonrandomly, randomly, or both. When the nonrandom component of the error in a variable is the same for all respondents, it affects the central tendency or the mean of the response distribution, but not the relation of the variable with other variables. However, it is difficult to deal with nonrandom errors that vary across individuals. Random errors, on the other hand, increase unexplainable variation, and can obscure potential relations among variables (Alwin, 1989; Alwin and Krosnick, 1991). SEM typically assumes random measurement errors. Here we briefly review the effect of random measurement error on regression analysis. Appendix 2.B shows that reliability is defined as the extent to which the variance of an observed variable is explained by the true scores that the variable is supposed to measure:

(3.15)

where Var () and Var (x) are the variances of the random measurement error and the observed variable x, respectively. Reliability that is less than 1.0 indicates the existence of measurement error. However, imperfect reliability or measurement error in dependent and independent variables has ...