Applications of the grade of membership technique to event history analysis: Extensions to multivariate unobserved heterogeneity

Analyses of the event histories of social and service utilization processes are often difficult because of a lack of adequate theory to specify the distributional form of any latent heterogeneity [J. Heckman and B. Singer, The identifiability of the proportional hazards model. Rev. Econ. Studies 51, 231-241 (1984); ibid., A method for minimizing the impact of distributional assumptions in econometric models for duration data. Econometrics 52, 271-320 (1984).] or the form of the basic hazard rate [J. Trussel and C. Hammerslough, A hazards-model analysis of the covariates of infant and child mortality in Sri Lanka. Demography 20, 1-26 (1983).]. In this study we present an analytic strategy that deals with both questions nonparametrically using a conditional likelihood approach. The model is illustrated using 24 months of follow-up data on Supplemental Security Income beneficiaries in Type D (Nursing Home) living arrangements. The parameter estimates can be used in standard life table computations to determine the amount of time expected to be spent in different residential and payment statuses for different analytically identified classes of beneficiaries

A functional generalized F‐test for signal detection with applications to event‐related potentials significance analysis

International audienceMotivated by the analysis of complex dependent functional data such as event-related brain potentials (ERP), this paper considers a time-varying coefficient multivariate regression model with fixed-time covariates for testing global hypotheses about population mean curves. Based on a reduced-rank modeling of the time correlation of the stochastic process of pointwise test statistics, a functional generalized F-test is proposed and its asymptotic null distribution is derived. Our analytical results show that the proposed test is more powerful than functional analysis of variance testing methods and competing signal detection procedures for dependent data. Simulation studies confirm such power gain for data with patterns of dependence similar to those observed in ERPs. The new testing procedure is illustrated with an analysis of the ERP data from a study of neural correlates of impulse control

Ranking by competence using a fuzzy approach

Heterogeneity, Competence, Fuzzy partition, Convex sets,

Using the conditional grade-of-membership model to assess judgment accuracy

nominal classification, incidental parameters, extreme profiles, mixtures,

Efficient rank-one residue approximation method for graph regularized non-negative matrix factorization

Nonnegative matrix factorization (NMF) aims to decompose a given data matrix X into the product of two lower-rank nonnegative factor matrices UV T. Graph regularized NMF (GNMF) is a recently proposed NMF method that preserves the geometric structure of X during such decomposition. Although GNMF has been widely used in computer vision and data mining, its multiplicative update rule (MUR) based solver suffers from both slow convergence and non-stationarity problems. In this paper, we propose a new efficient GNMF solver called rank-one residue approximation (RRA). Different from MUR, which updates both factor matrices (U and V) as a whole in each iteration round, RRA updates each of their columns by approximating the residue matrix by their outer product. Since each column of both factor matrices is updated optimally in an analytic formulation, RRA is theoretical and empirically proven to converge rapidly to a stationary point. Moreover, since RRA needs neither extra computational cost nor parametric tuning, it enjoys a similar simplicity to MUR but performs much faster. Experimental results on real-world datasets show that RRA is much more efficient than MUR for GNMF. To confirm the stationarity of the solution obtained by RRA, we conduct clustering experiments on real-world image datasets by comparing with the representative solvers such as MUR and NeNMF for GNMF. The experimental results confirm the effectiveness of RRA. © 2013 Springer-Verlag