Comparing methods of measurement with analysis of covariance and mean structures - Alanen, Erkki (1996)
Validity, reliability and scaling of the measures are basic concepts in comparing different methods. The main focus of this paper is on developing a general measurement model well organized with these concepts. The questions addressed to this model are: Do the methods being compared measure the same thing and are the reliabilities and scales of measurement the same for all methods? A structural equation approach is applied and the measurement model is divided into two parts: a validity and reliability model and a measurement scale model. The basic assumption in comparing two methods is the perfect stability over measurement times in the characteristic being measured. Extensions applying to more than two methods are presented. Also multi-wave, multi-variable models with less restrictive stability assumption are considered. Another focus of this work is to clarify consequences of relaxing the normality assumption of the characteristic (T) being studied for the maximum likelihood estimates of parameters of interest. ML estimation of parameters in the model with multivariate normally distributed variables is considered to be a standard procedure. The conditions will be clarified under which ignoring distributional assumption of the characteristic to be measured results in the same estimates of parameters as the standard proceeding. One possible alternative for the normally distributed T is the approach of the functional model whereupon the true values of the characteristic to be measured are regarded as parameters of the model. The estimators for true values are presented from a point of view of both the functional and the structural model and the relationship between them is clarified.