Linear indices in nonlinear structural equation models: best fitting proper indices and other composites

Best fitting proper indices, Generalized canonical variables, Partial least squares, Latent factor scores, Indices, Interaction, Flat maximum,

An Algorithm for Nonlinear, Nonparametric Model Choice and Prediction

International audienceWe introduce an algorithm which, in the context of nonlinear regression on vector-valued explanatory variables, aims to choose those combinations of vector components that provide best prediction. The algorithm is constructed specifically so that it devotes attention to components that might be of relatively little predictive value by themselves, and so might be ignored by more conventional methodology for model choice, but which, in combination with other difficult-to-find components, can be particularly beneficial for prediction. The design of the algorithm is also motivated by a desire to choose vector components that become redundant once appropriate combinations of other, more relevant components are selected. Our theoretical arguments show these goals are met in the sense that, with probability converging to 1 as sample size increases, the algorithm correctly determines a small, fixed number of variables on which the regression mean, g say, depends, even if dimension diverges to infinity much faster than n. Moreover, the estimated regression mean based on those variables approximates g with an error that, to first order, equals the error which would arise if we were told in advance the correct variables. In this sense, the estimator achieves oracle performance. Our numerical work indicates that the algorithm is suitable for very high dimensional problems, where it keeps computational labor in check by using a novel sequential argument, and also for more conventional prediction problems, where dimension is relatively low

Partial possibilistic regression path modeling

This paper introduces structural equation modeling for imprecise data, which enables evaluations with different types of uncertainty. Coming under the framework of variance-based analysis, the proposed method called Partial Possibilistic Regression Path Modeling (PPRPM) combines the principles of PLS path modeling to model the network of relations among the latent concepts, and the principles of possibilistic regression to model the vagueness of the human perception. Possibilistic regression defines the relation between variables through possibilistic linear functions and considers the error due to the vagueness of human perception as reflected in the model via interval-valued parameters. PPRPM transforms the modeling process into minimizing components of uncertainty, namely randomness and vagueness. A case study on the motivational and emotional aspects of teaching is used to illustrate the method