The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform

Michael J Zickar - One of the best experts on this subject based on the ideXlab platform.

  • some common myths about centering predictor variables in moderated multiple Regression and Polynomial Regression
    Organizational Research Methods, 2012
    Co-Authors: Dev K Dalal, Michael J Zickar
    Abstract:

    Additive transformations are often offered as a remedy for the common problem of collinearity in moderated Regression and Polynomial Regression analysis. As the authors demonstrate in this article,...

  • some common myths about centering predictor variables in moderated multiple Regression and Polynomial Regression
    Organizational Research Methods, 2012
    Co-Authors: Dev K Dalal, Michael J Zickar
    Abstract:

    Additive transformations are often offered as a remedy for the common problem of collinearity in moderated Regression and Polynomial Regression analysis. As the authors demonstrate in this article, mean-centering reduces nonessential collinearity but not essential collinearity. Therefore, in most cases, mean-centering of predictors does not accomplish its intended goal. In this article, the authors discuss and explain, through derivation of equations and empirical examples, that mean-centering changes lower order Regression coefficients but not the highest order coefficients, does not change the fit of Regression models, does not impact the power to detect moderating effects, and does not alter the reliability of product terms. The authors outline the positive effects of mean-centering, namely, the increased interpretability of the results and its importance for moderator analysis in structural equations and multilevel analysis. It is recommended that researchers center their predictor variables when thei...

Dev K Dalal - One of the best experts on this subject based on the ideXlab platform.

  • some common myths about centering predictor variables in moderated multiple Regression and Polynomial Regression
    Organizational Research Methods, 2012
    Co-Authors: Dev K Dalal, Michael J Zickar
    Abstract:

    Additive transformations are often offered as a remedy for the common problem of collinearity in moderated Regression and Polynomial Regression analysis. As the authors demonstrate in this article,...

  • some common myths about centering predictor variables in moderated multiple Regression and Polynomial Regression
    Organizational Research Methods, 2012
    Co-Authors: Dev K Dalal, Michael J Zickar
    Abstract:

    Additive transformations are often offered as a remedy for the common problem of collinearity in moderated Regression and Polynomial Regression analysis. As the authors demonstrate in this article, mean-centering reduces nonessential collinearity but not essential collinearity. Therefore, in most cases, mean-centering of predictors does not accomplish its intended goal. In this article, the authors discuss and explain, through derivation of equations and empirical examples, that mean-centering changes lower order Regression coefficients but not the highest order coefficients, does not change the fit of Regression models, does not impact the power to detect moderating effects, and does not alter the reliability of product terms. The authors outline the positive effects of mean-centering, namely, the increased interpretability of the results and its importance for moderator analysis in structural equations and multilevel analysis. It is recommended that researchers center their predictor variables when thei...

Weng Kee Wong - One of the best experts on this subject based on the ideXlab platform.

  • t optimal designs for multi factor Polynomial Regression models via a semidefinite relaxation method
    Statistics and Computing, 2019
    Co-Authors: Yuguang Yue, Lieven Vandenberghe, Weng Kee Wong
    Abstract:

    We consider T-optimal experiment design problems for discriminating multi-factor Polynomial Regression models where the design space is defined by Polynomial inequalities and the Regression parameters are constrained to given convex sets. Our proposed optimality criterion is formulated as a convex optimization problem with a moment cone constraint. When the Regression models have one factor, an exact semidefinite representation of the moment cone constraint can be applied to obtain an equivalent semidefinite program. When there are two or more factors in the models, we apply a moment relaxation technique and approximate the moment cone constraint by a hierarchy of semidefinite-representable outer approximations. When the relaxation hierarchy converges, an optimal discrimination design can be recovered from the optimal moment matrix, and its optimality can be additionally confirmed by an equivalence theorem. The methodology is illustrated with several examples.

  • t optimal designs for multi factor Polynomial Regression models via a semidefinite relaxation method
    arXiv: Computation, 2018
    Co-Authors: Yuguang Yue, Lieven Vandenberghe, Weng Kee Wong
    Abstract:

    We consider T-optimal experiment design problems for discriminating multi-factor Polynomial Regression models where the design space is defined by Polynomial inequalities and the Regression parameters are constrained to given convex sets. Our proposed optimality criterion is formulated as a convex optimization problem with a moment cone constraint. When the Regression models have one factor, an exact semidefinite representation of the moment cone constraint can be applied to obtain an equivalent semidefinite program. When there are two or more factors in the models, we apply a moment relaxation technique and approximate the moment cone constraint by a hierarchy of semidefinite-representable outer approximations. When the relaxation hierarchy converges, an optimal discrimination design can be recovered from the optimal moment matrix, and its optimality is confirmed by an equivalence theorem. The methodology is illustrated with several examples.

Yuguang Yue - One of the best experts on this subject based on the ideXlab platform.

  • t optimal designs for multi factor Polynomial Regression models via a semidefinite relaxation method
    Statistics and Computing, 2019
    Co-Authors: Yuguang Yue, Lieven Vandenberghe, Weng Kee Wong
    Abstract:

    We consider T-optimal experiment design problems for discriminating multi-factor Polynomial Regression models where the design space is defined by Polynomial inequalities and the Regression parameters are constrained to given convex sets. Our proposed optimality criterion is formulated as a convex optimization problem with a moment cone constraint. When the Regression models have one factor, an exact semidefinite representation of the moment cone constraint can be applied to obtain an equivalent semidefinite program. When there are two or more factors in the models, we apply a moment relaxation technique and approximate the moment cone constraint by a hierarchy of semidefinite-representable outer approximations. When the relaxation hierarchy converges, an optimal discrimination design can be recovered from the optimal moment matrix, and its optimality can be additionally confirmed by an equivalence theorem. The methodology is illustrated with several examples.

  • t optimal designs for multi factor Polynomial Regression models via a semidefinite relaxation method
    arXiv: Computation, 2018
    Co-Authors: Yuguang Yue, Lieven Vandenberghe, Weng Kee Wong
    Abstract:

    We consider T-optimal experiment design problems for discriminating multi-factor Polynomial Regression models where the design space is defined by Polynomial inequalities and the Regression parameters are constrained to given convex sets. Our proposed optimality criterion is formulated as a convex optimization problem with a moment cone constraint. When the Regression models have one factor, an exact semidefinite representation of the moment cone constraint can be applied to obtain an equivalent semidefinite program. When there are two or more factors in the models, we apply a moment relaxation technique and approximate the moment cone constraint by a hierarchy of semidefinite-representable outer approximations. When the relaxation hierarchy converges, an optimal discrimination design can be recovered from the optimal moment matrix, and its optimality is confirmed by an equivalence theorem. The methodology is illustrated with several examples.

Dharma P Agrawal - One of the best experts on this subject based on the ideXlab platform.

  • Using Polynomial Regression for data representation in wireless sensor networks
    2015
    Co-Authors: Torsha Banerjeez, Kaushik R Chowdhury, Dharma P Agrawal
    Abstract:

    Unlike conventional sensor networks, wireless sensors are limited in power, have much smaller memory buffers, and possess relatively slower processing speeds. These characteristics necessitate minimum transfer and storage of information in order to prolong the network lifetime. In this paper, we exploit the spatio-temporal nature of sensor data to approximate the current values of the sensors based on readings obtained from neighbouring sensors and itself. We propose a tree based Polynomial Regression algorithm (TREG), that addresses the problem of data compression in wireless sensor networks. Instead of aggregated data, only the coefficients computed by the Regression function, TREG are passed to achieve the following goals: (i) the sink can get attribute values in the regions devoid of sensor nodes, and (ii) readings over any portion of the region can be obtained at one time by querying the root of the tree. As the size of the data packet from each tree node to its parent remains constant, the proposed scheme scales very well with growing network density or increased coverage area. Since physical attributes exhibit a gradual change over time, we propose an iterative scheme, UPDATE COEFF, which obviates the need to perform the Regression function repeatedly and uses approximations based on previous readings. Extensive simulations are performed on real world data to demonstrate the effectiveness of the aggregation algorithm, TREG. Results reveal that for a network density of 0.0025, a complete binary tree of depth 4 could provide th

  • using Polynomial Regression for data representation in wireless sensor networks
    International Journal of Communication Systems, 2007
    Co-Authors: Torsha Banerjee, Kaushik R Chowdhury, Dharma P Agrawal
    Abstract:

    Unlike conventional sensor networks, wireless sensors are limited in power, have much smaller memory buffers, and possess relatively slower processing speeds. These characteristics necessitate minimum transfer and storage of information in order to prolong the network lifetime. In this paper, we exploit the spatio-temporal nature of sensor data to approximate the current values of the sensors based on readings obtained from neighbouring sensors and itself. We propose a tree based Polynomial Regression algorithm (TREG), that addresses the problem of data compression in wireless sensor networks. Instead of aggregated data, only the coefficients computed by the Regression function, TREG are passed to achieve the following goals: (i) the sink can get attribute values in the regions devoid of sensor nodes, and (ii) readings over any portion of the region can be obtained at one time by querying the root of the tree. As the size of the data packet from each tree node to its parent remains constant, the proposed scheme scales very well with growing network density or increased coverage area. Since physical attributes exhibit a gradual change over time, we propose an iterative scheme, UPDATE_COEFF, which obviates the need to perform the Regression function repeatedly and uses approximations based on previous readings. Extensive simulations are performed on real world data to demonstrate the effectiveness of the aggregation algorithm, TREG. Results reveal that for a network density of 0.0025, a complete binary tree of depth 4 could provide the absolute error to be less than 6%. A data compression ratio of about 0.02 is achieved using our proposed algorithm, which is almost independent of the tree depth. In addition, our proposed updating scheme makes the aggregation process faster while maintaining the desired error bounds. Copyright © 2006 John Wiley & Sons, Ltd.

  • tree based data aggregation in sensor networks using Polynomial Regression
    International Conference on Information Fusion, 2005
    Co-Authors: Torsha Banerjee, Kaushik R Chowdhury, Dharma P Agrawal
    Abstract:

    In this paper, we propose a tree based Regression algorithm, (TREG) that addresses the problem of data compression in wireless sensor networks. By function approximation based on multivariable Polynomial Regression and passing only the coefficients returned by the Regression function instead of aggregated data, TREG achieves the following goals: (1) the sink can get attribute values in regions devoid of sensor nodes for attribute values that show smooth spatial gradation (2) readings over any portion of the region can be obtained at one time by querying the root instead of flooding those regions, thus incurring significant energy savings. As size of the data packet transmitted, from one tree node to another remains constant, the proposed scheme scales well with growing network density. Extensive simulations are performed on real world data to demonstrate the effectiveness of our aggregation algorithm. Results reveal that for a network density of 0.0025, the optimal tree-depth should be 4 in order to restrict the absolute error to less than a threshold of 6%. A data compression ratio of about 0.02 is achieved using our proposed algorithm, which is almost independent of tree depth.