The Factor Analysis of Ipsative Measures

This article deals with the problem of analyzing sets of ipsative variables using the common factor model. We demonstrate that the usual assumptions of the common factor model, especially the assumption of uncorrelated disturbances, are not appropriate for sets of ipsative variables. We develop a common factor model that takes into account the ipsative properties of such data and show how this model can be applied to any set of ipsative measures using the methods of confirmatory factor analysis. We then suggest that the application of this model may be useful in modeling the latent content of sets ofrankings and other measures that have the ipsative property as a result of the measurement procedure. Finally, we apply the model to Kohn's measures of parental values, using sample data from the General Social Surveys.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68736/2/10.1177_004912418000900206.pd

Multivariate Small Area Estimation of Multidimensional Latent Economic Well-being Indicators

© 2019 The Authors. International Statistical Review © 2019 International Statistical Institute Factor analysis models are used in data dimensionality reduction problems where the variability among observed variables can be described through a smaller number of unobserved latent variables. This approach is often used to estimate the multidimensionality of well-being. We employ factor analysis models and use multivariate empirical best linear unbiased predictor (EBLUP) under a unit-level small area estimation approach to predict a vector of means of factor scores representing well-being for small areas. We compare this approach with the standard approach whereby we use small area estimation (univariate and multivariate) to estimate a dashboard of EBLUPs of the means of the original variables and then averaged. Our simulation study shows that the use of factor scores provides estimates with lower variability than weighted and simple averages of standardised multivariate EBLUPs and univariate EBLUPs. Moreover, we find that when the correlation in the observed data is taken into account before small area estimates are computed, multivariate modelling does not provide large improvements in the precision of the estimates over the univariate modelling. We close with an application using the European Union Statistics on Income and Living Conditions data

Relation Between Chiral Susceptibility and Solutions of Gap Equation in Nambu--Jona-Lasinio Model

We study the solutions of the gap equation, the thermodynamic potential and the chiral susceptibility in and beyond the chiral limit at finite chemical potential in the Nambu--Jona-Lasinio (NJL) model. We give an explicit relation between the chiral susceptibility and the thermodynamic potential in the NJL model. We find that the chiral susceptibility is a quantity being able to represent the furcation of the solutions of the gap equation and the concavo-convexity of the thermodynamic potential in NJL model. It indicates that the chiral susceptibility can identify the stable state and the possibility of the chiral phase transition in NJL model.Comment: 21 pages, 6 figures, misprints are correcte