Various fit indices exist in structural equation models. Most of these indices are related to the noncentrality parameter (NCP) of the chi-square distribution that the involved test statistic is implicitly assumed to follow. Existing literature suggests that few statistics can be well approximated by chi-square distributions. The meaning of the NCP is not clear when the behavior of the statistic cannot be described by a chi-square distribution. In this paper we define a new measure of model misfit (MMM) as the difference between the expected values of a statistic under the alternative and null hypotheses. This definition does not need to assume that the population covariance matrix is in the vicinity of the proposed model, nor does it need for the test statistic to follow any distribution of a known form. The MMM does not necessarily equal the discrepancy between the model and the population covariance matrix as has been assumed in existing literature. Bootstrap approaches to estimating the MMM and a related quantity are developed. An algorithm for obtaining bootstrap confidence intervals of the MMM is constructed. Examples with practical data sets contrast several measures of model misfit. The quantile-quantile plot is used to illustrate the unrealistic nature of chi-square distribution assumptions under either the null or an alternative hypothesis in practice.
This paper presents a comprehensive nonlinear model of the controlled constant voltage transformer also known as the ferroresonant transformer. Saturation is a normal mode of operation for this device. This paper derives an equivalent electrical circuit that relates to the physical structure of a typical design. The level of detail includes winding resistances, continuously nonlinear magnetizing inductances, tapped windings, and leakage inductances. The paper describes methods to extract the winding resistances, leakage inductances, and hysteresis loops of the transformer and how to fit the latter into single-valued nonlinear functions. The paper compares computer simulation results of the model with those obtained analytically and experimentally. The results show that the derived circuit will be very useful for designers of the ferroresonant transformer, which is used in uninterruptible power supplies. 相似文献