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

Self-control and early adolescent antisocial behavior: A longitudinal analysis

Contains fulltext : 73179.pdf (publisher's version ) (Closed access)The article discusses a three-wave longitudinal study that investigates the relationship between self-control and aggressive and delinquent behavior of early adolescent boys and girls. The sample consists of 1,012 Dutch adolescents (mean age = 12.3) in their first year of secondary education. Structural equation modeling analyses reveal that high levels of self-control consistently decrease aggressive and delinquent behavior in the subsequent 6 months follow-up intervals. Results for the total sample do not support the hypothesis that self-control is influenced by previous levels of aggression or delinquency. For boys, the partial evidence found indicates reciprocal effects of self-control and delinquency.21 p

High-dimensional maximum marginal likelihood item factor analysis by adaptive quadrature

Although the Bock–Aitkin likelihood-based estimation method for factor analysis of dichotomous item response data has important advantages over classical analysis of item tetrachoric correlations, a serious limitation of the method is its reliance on fixed-point Gauss-Hermite (G-H) quadrature in the solution of the likelihood equations and likelihood-ratio tests. When the number of latent dimensions is large, computational considerations require that the number of quadrature points per dimension be few. But with large numbers of items, the dispersion of the likelihood, given the response pattern, becomes so small that the likelihood cannot be accurately evaluated with the sparse fixed points in the latent space. In this paper, we demonstrate that substantial improvement in accuracy can be obtained by adapting the quadrature points to the location and dispersion of the likelihood surfaces corresponding to each distinct pattern in the data. In particular, we show that adaptive G-H quadrature, combined with mean and covariance adjustments at each iteration of an EM algorithm, produces an accurate fast-converging solution with as few as two points per dimension. Evaluations of this method with simulated data are shown to yield accurate recovery of the generating factor loadings for models of upto eight dimensions. Unlike an earlier application of adaptive Gibbs sampling to this problem by Meng and Schilling, the simulations also confirm the validity of the present method in calculating likelihood-ratio chi-square statistics for determining the number of factors required in the model. Finally, we apply the method to a sample of real data from a test of teacher qualifications.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43596/1/11336_2003_Article_1141.pd

An EM algorithm for fitting two-level structural equation models

Chi-square statistic, mean and covariance structures, EM algorithm, maximum likelihood, multivariate normal distribution, two-level structural equation models,

Constructing measures for school process variables: the potential of multilevel confirmatory factor analysis

School process variables, Secondary education, Multilevel confirmatory factor analysis, Educational effectiveness research,

Evaluating estimation methods for ordinal data in structural equation modeling

Estimation, Ordinal data, Model misspecification, Small sample structural equation modeling,