Bootstrap for Mean and Covariance Structure Models

Abstract

The development of the social sciences as empirical sciences has been hampered by their great difficulties to measure variables of substantive interest to the researcher using reliable and valid instruments. Consequently, questions of scaling and measurement have been of great theoretical and practical concern. Researchers working in areas such as sociology, economics, and epidemiology usually wish to connect scales that measure some dependent variables with each other and with explanatory variables. Hence, models that incorporate measurement models and regression models simultaneously have been often applied in these areas of research. The most popular one is the LISREL model (cf. Jöreskog and Sörbom, 1988). A somewhat more general model is the following one: Y _i ,i = 1,…, n ∈ N are independent, identically distributed random R ^P -vectors, where each Y _i is distributed as

$$ y = \Lambda \eta + \in $$

(measurement model for y), and where

$$ \eta = B\eta + \varsigma $$

(structural model).