Mixture of latent trait analyzers for model-based clustering of categorical data

Model-based clustering methods for continuous data are well established and commonly used in a wide range of applications. However, model-based clustering methods for categorical data are less standard. Latent class analysis is a commonly used method for model-based clustering of binary data and/or categorical data, but due to an assumed local independence structure there may not be a correspondence between the estimated latent classes and groups in the population of interest. The mixture of latent trait analyzers model extends latent class analysis by assuming a model for the categorical response variables that depends on both a categorical latent class and a continuous latent trait variable; the discrete latent class accommodates group structure and the continuous latent trait accommodates dependence within these groups. Fitting the mixture of latent trait analyzers model is potentially difficult because the likelihood function involves an integral that cannot be evaluated analytically. We develop a variational approach for fitting the mixture of latent trait models and this provides an efficient model fitting strategy. The mixture of latent trait analyzers model is demonstrated on the analysis of data from the National Long Term Care Survey (NLTCS) and voting in the U.S. Congress. The model is shown to yield intuitive clustering results and it gives a much better fit than either latent class analysis or latent trait analysis alone

Linked Markov sources: Modeling outcome-dependent social processes

Many social processes are adaptive in the sense that the process changes as a result of previous outcomes. Data on such processes may come in the form of categorical time series. First, the authors propose a class of Markov Source models that embody such adaptation. Second, the authors discuss new methods to evaluate the fit of such models. Third, the authors apply these models and methods to data on a social process that is a preeminent example of an adaptive process: (encoded) conversation as arises in structured interviews. © 2007 Sage Publications

Isolating Stock Prices Variation with Neural Networks

In this study we aim to define a mapping function that relates the general index value among a set of shares to the prices of individual shares. In more general terms this is problem of defining the relationship between multivariate data distributions and a specific source of variation within these distributions where the source of variation in question represents a quantity of interest related to a particular problem domain. In this respect we aim to learn a complex mapping function that can be used for mapping different values of the quantity of interest to typical novel samples of the distribution. In our investigation we compare the performance of standard neural network based methods like Multilayer Perceptrons (MLPs) and Radial Basis Functions (RBFs) as well as Mixture Density Networks (MDNs) and a latent variable method, the General Topographic Mapping (GTM). As a reference benchmark of the prediction accuracy we consider a simple method based on the average values over certain intervals of the quantity of interest that we are trying to isolate (the so called Sample Average (SA) method). According to the results, MLPs and RBFs outperform MDNs and the GTM for this one-to-many mapping problem

QED_3 theory of underdoped high temperature superconductors II: the quantum critical point

We study the effect of gapless quasiparticles in a d-wave superconductor on the T=0 end point of the Kosterlitz-Thouless transition line in underdoped high-temperature superconductors. Starting from a lattice model that has gapless fermions coupled to 3D XY phase fluctuations of the superconducting order parameter, we propose a continuum field theory to describe the quantum phase transition between the d-wave superconductor and the spin-density-wave insulator. Without fermions the theory reduces to the standard Higgs scalar electrodynamics (HSE), which is known to have the critical point in the inverted XY universality class. Extending the renormalization group calculation for the HSE to include the coupling to fermions, we find that the qualitative effect of fermions is to increase the portion of the space of coupling constants where the transition is discontinuous. The critical exponents at the stable fixed point vary continuously with the number of fermion fields $N$, and we estimate the correlation length exponent (nu = 0.65) and the vortex field anomalous dimension(eta_Phi=-0.48) at the quantum critical point for the physical case N=2. The stable critical point in the theory disappears for the number of Dirac fermions N > N_c, with N_c ~ 3.4 in our approximation. We discuss the relationship between the superconducting and the chiral (SDW) transitions, and point to some interesting parallels between our theory and the Thirring model.Comment: 13 pages including figures in tex

Deconfining Phase Transition as a Matrix Model of Renormalized Polyakov Loops

We discuss how to extract renormalized from bare Polyakov loops in SU(N) lattice gauge theories at nonzero temperature in four spacetime dimensions. Single loops in an irreducible representation are multiplicatively renormalized without mixing, through a renormalization constant which depends upon both representation and temperature. The values of renormalized loops in the four lowest representations of SU(3) were measured numerically on small, coarse lattices. We find that in magnitude, condensates for the sextet and octet loops are approximately the square of the triplet loop. This agrees with a large $N$ expansion, where factorization implies that the expectation values of loops in adjoint and higher representations are just powers of fundamental and anti-fundamental loops. For three colors, numerically the corrections to the large $N$ relations are greatest for the sextet loop, $\leq 25$; these represent corrections of $\sim 1/N$ for N=3. The values of the renormalized triplet loop can be described by an SU(3) matrix model, with an effective action dominated by the triplet loop. In several ways, the deconfining phase transition for N=3 appears to be like that in the $N=\infty$ matrix model of Gross and Witten.Comment: 24 pages, 7 figures; v2, 27 pages, 12 figures, extended discussion for clarity, results unchange

Some Aspects of Latent Structure Analysis

Latent structure models involve real, potentially observable variables and latent, unobservable variables. The framework includes various particular types of model, such as factor analysis, latent class analysis, latent trait analysis, latent profile models, mixtures of factor analysers, state-space models and others. The simplest scenario, of a single discrete latent variable, includes finite mixture models, hidden Markov chain models and hidden Markov random field models. The paper gives a brief tutorial of the application of maximum likelihood and Bayesian approaches to the estimation of parameters within these models, emphasising especially the fact that computational complexity varies greatly among the different scenarios. In the case of a single discrete latent variable, the issue of assessing its cardinality is discussed. Techniques such as the EM algorithm, Markov chain Monte Carlo methods and variational approximations are mentioned

High Involvement Management, High Performance Work Systems and Well-being

Studies on the impact of high-performance work systems on employees' well-being are emerging but the underlying theory remains weak. This paper attempts to develop theory of the effects on well-being of four dimensions of high-performance work systems: enriched jobs, high involvement management, employee voice, and motivational supports. Hypothesized associations are tested using multilevel models and data from Britain's Workplace Employment Relations Survey of 2004 (WERS2004). Results show that enriched jobs are positively associated with both measures of well-being: job satisfaction and anxiety–contentment. Voice is positively associated with job satisfaction, and motivational supports with neither measure. The results for high involvement management are not as predicted because it increases anxiety and is independent of job satisfaction

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

Broad-scale patterns of body size in squamate reptiles of Europe and North America

Aim To document geographical interspecific patterns of body size of European and North American squamate reptile assemblages and explore the relationship between body size patterns and environmental gradients. Location North America and western Europe. Methods We processed distribution maps for native species of squamate reptiles to document interspecific spatial variation of body size at a grain size of 110 x 110 km. We also examined seven environmental variables linked to four hypotheses possibly influencing body size gradients. We used simple and multiple regression, evaluated using information theory, to identify the set of models best supported by the data. Results Europe is characterized by clear latitudinal trends in body size, whereas geographical variation in body size in North America is complex. There is a consistent association of mean body size with measures of ambient energy in both regions, although lizards increase in size northwards whereas snakes show the opposite pattern. Our best models accounted for almost 60% of the variation in body size of lizards and snakes within Europe, but the proportions of variance explained in North America were less than 20%. Main conclusions Although body size influences the energy balance of thermoregulating ectotherms, inconsistent biogeographical patterns and contrasting associations with energy in lizards and snakes suggest that no single mechanism can explain variation of reptile body size in the northern temperate zone