Baibing Li

Model selection for partial least squares regression

Partial least squares (PLS) regression is a powerful and frequently applied technique in multivariate statistical process control when the process variables are highly correlated. Selection of the number of latent variables to build a representative model is an important issue. A metric frequently used by chemometricians for the determination of the number of latent variables is that of Wolds R criterion, whilst more recently a number of statisticians have advocated the use of Akaike Information Criterion (AIC). In this paper, a comparison between Wolds R criterion and AIC for the selection of the number of latent variables to include in a PLS model that will form the basis of a multivariate statistical process control representation is undertaken based on a simulation study. It is shown that neither Wolds R criterion nor AIC exhibit satisfactory performance. This is in contrast to the adjusted Wolds R criteria which is shown to demonstrate satisfactory performance in terms of the number of times the known true model is selected. Two industrial applications are then used to demonstrate the methodology. The first relates to the modelling of a product quality using data from an industrial fluidised bed reactor and the second focuses on an industrial NIR data set. The results are consistent with those of the simulation studies.

On principal component analysis in L 1

Four formulations of principal component analysis in L1 norm were developed by Galpin and Hawkins (Comput. Statist. Data Anal. 5 (1987) 305), QPmax, QPmin, LPmax, and LPmin. Choulakian (Comput. Statist. Data Anal. 37 (2001)135) claimed that of the four formulations, only QPmax produces a non-trivial solution. The objective is to present counter-examples that illustrate that the QPmin and LPmin formulations also give non-trivial solutions that may be unique except for the sign.

A study of the relationship between exit, voice, loyalty and neglect and commitment in India

Drawing on exit, voice, loyalty and neglect (EVLN) literature, this study examines direct and interactive associations between organizational-level commitment and team-level commitment and the use of EVLN by managers in India. The study is based on a survey of 200 managers and supervisors from seven Indian firms. The findings on the use of voice are consistent with the past research in Western countries, but challenge the prevailing assumption about the use of voice in high power distance societies. The results also indicate that team-level commitment moderates the association between organizational-level commitment and the use of EVLN.

Bayesian inference for origin-destination matrices of transport networks using the EM algorithm

Information on the origin-destination (OD) matrix of a transport network is a fundamental requirement in much transportation planning. A relatively inexpensive method for updating an OD matrix is to draw inference about the OD matrix based on a single observation of traffic flows on a specific set of network links, where the Bayesian approach is a natural choice for combining the prior knowledge about the OD matrix and the current observation of traffic flows. The existing approaches of Bayesian modeling of OD matrices include using normal approximations to Poisson distributions, which leads to the posterior being intractable even under some simple special cases, and using Markov chain Monte Carlo simulation, which incurs extreme demand of computational efforts. In this article, through the EM algorithm, Bayesian inference is reinvestigated for a transport network for estimating the population means of traffic flows, reconstructing traffic flows, and predicting future traffic flows. It is shown that the resultant estimates have very simple forms with minimal computational costs.

Recursive estimation based on the equality-constrained optimization for intersection origin-destination matrices

A fast constrained recursive identification (CRI) algorithm is proposed to estimate intersection origin-destination (O-D) matrices dynamically. The basic idea of the CRI algorithm is to estimate intersection O-D matrices based on equality-constrained optimization and then to adjust them by Bells correction (Bell, 1991a. The estimation of origin-destination matrices by constrained generalized least squares. Transporation Research 25B, 13-22; Bell, 1991b. The real-time estimation of origin-destination flows in the presence of platoon dispersion. Transportation Research 25B, 115-125.) for inequality constraints. Numerical results show that the accuracy of estimates by the CRI algorithm is fairly good--the solutions obtained by the CRI are optimal in majority of the cases, while the computational efforts are very limited--increment mainly lies on the evaluation of an inverse for an mxm matrix (m=4 for a typical intersection) compared with the ordinary recursive least squares method. These results mean that a properly designed recursive algorithm can indeed avoid iterative procedure in each time step to obtain highly accurate on-line estimates for intersection O-D matrices. Therefore, the CRI algorithm with its reasonable balance between accuracy and computational simplicity is very suitable for practical use.

On existence, optimality and asymptotic stability of the Kalman filter with partially observed inputs

For linear stochastic time-varying systems, we investigate the properties of the Kalman filter with partially observed inputs. We first establish the existence condition of a general linear filter when the unknown inputs are partially observed. Then we examine the optimality of the Kalman filter with partially observed inputs. Finally, on the basis of the established existence condition and optimality result, we investigate asymptotic stability of the filter for the corresponding time-invariant systems. It is shown that the results on existence and asymptotic stability obtained in this paper provide a unified approach to accommodating a variety of filtering scenarios as its special cases, including the classical Kalman filter and state estimation with unknown inputs.

Dynamic identification of origin-destination matrices in the presence of incomplete observations

Abstract It is quite often in practice that observation information of traffic flows is incomplete due to failures of facilities or insufficient installment of sensors. In this paper, we investigate problems of dynamic identification of origin–destination matrices when traffic counts are unavailable in some entrances and/or exits of a traffic system. To deal with non-linearity and inestimability problems in conventional research frameworks, identification problems with incomplete information are reformulated as optimization problems with linear equality constraints and non-negative inequality constraints. An algorithm is then suggested for identification of origin–destination matrices with incomplete observation information. Finally, numerical examples are provided to illustrate the proposed algorithm for some incomplete information patterns.

State estimation with partially observed inputs: A unified Kalman filtering approach

For linear stochastic time-varying state space models with Gaussian noises, this paper investigates state estimation for the scenario where the input variables of the state equation are not fully observed but rather the input data are available only at an aggregate level. Unlike the existing filters for unknown inputs that are based on the approach of minimum-variance unbiased estimation, this paper does not impose the unbiasedness condition for state estimation; instead it incorporates a Bayesian approach to derive a modified Kalman filter by pooling the prior knowledge about the state vector at the aggregate level with the measurements on the output variables at the original level of interest. The estimated state vector is shown to be a minimum-mean-square-error estimator. The developed filter provides a unified approach to state estimation: it includes the existing filters obtained under two extreme scenarios as its special cases, i.e., the classical Kalman filter where all the inputs are observed and the filter for unknown inputs.

Box–Tidwell transformation based partial least squares regression

Abstract Partial least squares (PLS) is a powerful and frequently applied technique for process modelling and monitoring when the data is highly correlated. In this paper, a Box–Tidwell transformation based PLS (BTPLS) algorithm is proposed to address the modelling of non-linear systems. The BTPLS algorithm provides a family of flexible regression models for data fitting, where linear and quadratic PLS are special cases. BTPLS is shown to out-perform quadratic PLS, for non-linear problems, in terms of modelling ability and prediction accuracy, and neural network based PLS algorithms with respect to computational time and model parsimony in terms of the Bayesian information criterion. Linear PLS, quadratic PLS, neural network PLS and BTPLS are compared using a benchmark data set relating to the analysis of cosmetic data, a mathematical simulation and a highly non-linear pH problem. It is shown that the BTPLS algorithm provides a pragmatic compromize between model simplicity and accuracy, and constitutes a complementary modelling technique to both existing linear and non-linear PLS approaches.

A non-linear nested partial least-squares algorithm

A nested partial least-squares (PLS) algorithm is proposed for the modelling of non-linear systems in the presence of multicollinearity. The nested algorithm comprises both an inner and outer PLS algorithm. The objective of the outer algorithm is to extract those latent variables that will form the basis of the final application whilst the role of the inner algorithm is to derive the weight vectors for the outer PLS algorithm. Wolds non-linear PLS algorithm and the error-based weight updating procedure are special cases. The nested PLS algorithm is illustrated by application to simulated data and an industrial NIR spectral data set.