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- All Subjects: Design of Experiments
- All Subjects: Magnetic resonance imaging
- Creators: Pan, Rong
Description
Random Forests is a statistical learning method which has been proposed for propensity score estimation models that involve complex interactions, nonlinear relationships, or both of the covariates. In this dissertation I conducted a simulation study to examine the effects of three Random Forests model specifications in propensity score analysis. The results suggested that, depending on the nature of data, optimal specification of (1) decision rules to select the covariate and its split value in a Classification Tree, (2) the number of covariates randomly sampled for selection, and (3) methods of estimating Random Forests propensity scores could potentially produce an unbiased average treatment effect estimate after propensity scores weighting by the odds adjustment. Compared to the logistic regression estimation model using the true propensity score model, Random Forests had an additional advantage in producing unbiased estimated standard error and correct statistical inference of the average treatment effect. The relationship between the balance on the covariates' means and the bias of average treatment effect estimate was examined both within and between conditions of the simulation. Within conditions, across repeated samples there was no noticeable correlation between the covariates' mean differences and the magnitude of bias of average treatment effect estimate for the covariates that were imbalanced before adjustment. Between conditions, small mean differences of covariates after propensity score adjustment were not sensitive enough to identify the optimal Random Forests model specification for propensity score analysis.
ContributorsCham, Hei Ning (Author) / Tein, Jenn-Yun (Thesis advisor) / Enders, Stephen G (Thesis advisor) / Enders, Craig K. (Committee member) / Mackinnon, David P (Committee member) / Arizona State University (Publisher)
Created2013
Description
With the rapid development of mobile sensing technologies like GPS, RFID, sensors in smartphones, etc., capturing position data in the form of trajectories has become easy. Moving object trajectory analysis is a growing area of interest these days owing to its applications in various domains such as marketing, security, traffic monitoring and management, etc. To better understand movement behaviors from the raw mobility data, this doctoral work provides analytic models for analyzing trajectory data. As a first contribution, a model is developed to detect changes in trajectories with time. If the taxis moving in a city are viewed as sensors that provide real time information of the traffic in the city, a change in these trajectories with time can reveal that the road network has changed. To detect changes, trajectories are modeled with a Hidden Markov Model (HMM). A modified training algorithm, for parameter estimation in HMM, called m-BaumWelch, is used to develop likelihood estimates under assumed changes and used to detect changes in trajectory data with time. Data from vehicles are used to test the method for change detection. Secondly, sequential pattern mining is used to develop a model to detect changes in frequent patterns occurring in trajectory data. The aim is to answer two questions: Are the frequent patterns still frequent in the new data? If they are frequent, has the time interval distribution in the pattern changed? Two different approaches are considered for change detection, frequency-based approach and distribution-based approach. The methods are illustrated with vehicle trajectory data. Finally, a model is developed for clustering and outlier detection in semantic trajectories. A challenge with clustering semantic trajectories is that both numeric and categorical attributes are present. Another problem to be addressed while clustering is that trajectories can be of different lengths and also have missing values. A tree-based ensemble is used to address these problems. The approach is extended to outlier detection in semantic trajectories.
ContributorsKondaveeti, Anirudh (Author) / Runger, George C. (Thesis advisor) / Mirchandani, Pitu (Committee member) / Pan, Rong (Committee member) / Maciejewski, Ross (Committee member) / Arizona State University (Publisher)
Created2012
Description
No-confounding designs (NC) in 16 runs for 6, 7, and 8 factors are non-regular fractional factorial designs that have been suggested as attractive alternatives to the regular minimum aberration resolution IV designs because they do not completely confound any two-factor interactions with each other. These designs allow for potential estimation of main effects and a few two-factor interactions without the need for follow-up experimentation. Analysis methods for non-regular designs is an area of ongoing research, because standard variable selection techniques such as stepwise regression may not always be the best approach. The current work investigates the use of the Dantzig selector for analyzing no-confounding designs. Through a series of examples it shows that this technique is very effective for identifying the set of active factors in no-confounding designs when there are three of four active main effects and up to two active two-factor interactions.
To evaluate the performance of Dantzig selector, a simulation study was conducted and the results based on the percentage of type II errors are analyzed. Also, another alternative for 6 factor NC design, called the Alternate No-confounding design in six factors is introduced in this study. The performance of this Alternate NC design in 6 factors is then evaluated by using Dantzig selector as an analysis method. Lastly, a section is dedicated to comparing the performance of NC-6 and Alternate NC-6 designs.
To evaluate the performance of Dantzig selector, a simulation study was conducted and the results based on the percentage of type II errors are analyzed. Also, another alternative for 6 factor NC design, called the Alternate No-confounding design in six factors is introduced in this study. The performance of this Alternate NC design in 6 factors is then evaluated by using Dantzig selector as an analysis method. Lastly, a section is dedicated to comparing the performance of NC-6 and Alternate NC-6 designs.
ContributorsKrishnamoorthy, Archana (Author) / Montgomery, Douglas C. (Thesis advisor) / Borror, Connie (Thesis advisor) / Pan, Rong (Committee member) / Arizona State University (Publisher)
Created2014
Description
In this era of fast computational machines and new optimization algorithms, there have been great advances in Experimental Designs. We focus our research on design issues in generalized linear models (GLMs) and functional magnetic resonance imaging(fMRI). The first part of our research is on tackling the challenging problem of constructing
exact designs for GLMs, that are robust against parameter, link and model
uncertainties by improving an existing algorithm and providing a new one, based on using a continuous particle swarm optimization (PSO) and spectral clustering. The proposed algorithm is sufficiently versatile to accomodate most popular design selection criteria, and we concentrate on providing robust designs for GLMs, using the D and A optimality criterion. The second part of our research is on providing an algorithm
that is a faster alternative to a recently proposed genetic algorithm (GA) to construct optimal designs for fMRI studies. Our algorithm is built upon a discrete version of the PSO.
exact designs for GLMs, that are robust against parameter, link and model
uncertainties by improving an existing algorithm and providing a new one, based on using a continuous particle swarm optimization (PSO) and spectral clustering. The proposed algorithm is sufficiently versatile to accomodate most popular design selection criteria, and we concentrate on providing robust designs for GLMs, using the D and A optimality criterion. The second part of our research is on providing an algorithm
that is a faster alternative to a recently proposed genetic algorithm (GA) to construct optimal designs for fMRI studies. Our algorithm is built upon a discrete version of the PSO.
ContributorsTemkit, M'Hamed (Author) / Kao, Jason (Thesis advisor) / Reiser, Mark R. (Committee member) / Barber, Jarrett (Committee member) / Montgomery, Douglas C. (Committee member) / Pan, Rong (Committee member) / Arizona State University (Publisher)
Created2014
Description
Functional or dynamic responses are prevalent in experiments in the fields of engineering, medicine, and the sciences, but proposals for optimal designs are still sparse for this type of response. Experiments with dynamic responses result in multiple responses taken over a spectrum variable, so the design matrix for a dynamic response have more complicated structures. In the literature, the optimal design problem for some functional responses has been solved using genetic algorithm (GA) and approximate design methods. The goal of this dissertation is to develop fast computer algorithms for calculating exact D-optimal designs.
First, we demonstrated how the traditional exchange methods could be improved to generate a computationally efficient algorithm for finding G-optimal designs. The proposed two-stage algorithm, which is called the cCEA, uses a clustering-based approach to restrict the set of possible candidates for PEA, and then improves the G-efficiency using CEA.
The second major contribution of this dissertation is the development of fast algorithms for constructing D-optimal designs that determine the optimal sequence of stimuli in fMRI studies. The update formula for the determinant of the information matrix was improved by exploiting the sparseness of the information matrix, leading to faster computation times. The proposed algorithm outperforms genetic algorithm with respect to computational efficiency and D-efficiency.
The third contribution is a study of optimal experimental designs for more general functional response models. First, the B-spline system is proposed to be used as the non-parametric smoother of response function and an algorithm is developed to determine D-optimal sampling points of a spectrum variable. Second, we proposed a two-step algorithm for finding the optimal design for both sampling points and experimental settings. In the first step, the matrix of experimental settings is held fixed while the algorithm optimizes the determinant of the information matrix for a mixed effects model to find the optimal sampling times. In the second step, the optimal sampling times obtained from the first step is held fixed while the algorithm iterates on the information matrix to find the optimal experimental settings. The designs constructed by this approach yield superior performance over other designs found in literature.
First, we demonstrated how the traditional exchange methods could be improved to generate a computationally efficient algorithm for finding G-optimal designs. The proposed two-stage algorithm, which is called the cCEA, uses a clustering-based approach to restrict the set of possible candidates for PEA, and then improves the G-efficiency using CEA.
The second major contribution of this dissertation is the development of fast algorithms for constructing D-optimal designs that determine the optimal sequence of stimuli in fMRI studies. The update formula for the determinant of the information matrix was improved by exploiting the sparseness of the information matrix, leading to faster computation times. The proposed algorithm outperforms genetic algorithm with respect to computational efficiency and D-efficiency.
The third contribution is a study of optimal experimental designs for more general functional response models. First, the B-spline system is proposed to be used as the non-parametric smoother of response function and an algorithm is developed to determine D-optimal sampling points of a spectrum variable. Second, we proposed a two-step algorithm for finding the optimal design for both sampling points and experimental settings. In the first step, the matrix of experimental settings is held fixed while the algorithm optimizes the determinant of the information matrix for a mixed effects model to find the optimal sampling times. In the second step, the optimal sampling times obtained from the first step is held fixed while the algorithm iterates on the information matrix to find the optimal experimental settings. The designs constructed by this approach yield superior performance over other designs found in literature.
ContributorsSaleh, Moein (Author) / Pan, Rong (Thesis advisor) / Montgomery, Douglas C. (Committee member) / Runger, George C. (Committee member) / Kao, Ming-Hung (Committee member) / Arizona State University (Publisher)
Created2015
Description
One of the premier technologies for studying human brain functions is the event-related functional magnetic resonance imaging (fMRI). The main design issue for such experiments is to find the optimal sequence for mental stimuli. This optimal design sequence allows for collecting informative data to make precise statistical inferences about the inner workings of the brain. Unfortunately, this is not an easy task, especially when the error correlation of the response is unknown at the design stage. In the literature, the maximin approach was proposed to tackle this problem. However, this is an expensive and time-consuming method, especially when the correlated noise follows high-order autoregressive models. The main focus of this dissertation is to develop an efficient approach to reduce the amount of the computational resources needed to obtain A-optimal designs for event-related fMRI experiments. One proposed idea is to combine the Kriging approximation method, which is widely used in spatial statistics and computer experiments with a knowledge-based genetic algorithm. Through case studies, a demonstration is made to show that the new search method achieves similar design efficiencies as those attained by the traditional method, but the new method gives a significant reduction in computing time. Another useful strategy is also proposed to find such designs by considering only the boundary points of the parameter space of the correlation parameters. The usefulness of this strategy is also demonstrated via case studies. The first part of this dissertation focuses on finding optimal event-related designs for fMRI with simple trials when each stimulus consists of only one component (e.g., a picture). The study is then extended to the case of compound trials when stimuli of multiple components (e.g., a cue followed by a picture) are considered.
ContributorsAlrumayh, Amani (Author) / Kao, Ming-Hung (Thesis advisor) / Stufken, John (Committee member) / Reiser, Mark R. (Committee member) / Pan, Rong (Committee member) / Cheng, Dan (Committee member) / Arizona State University (Publisher)
Created2019
Description
Optimal design theory provides a general framework for the construction of experimental designs for categorical responses. For a binary response, where the possible result is one of two outcomes, the logistic regression model is widely used to relate a set of experimental factors with the probability of a positive (or negative) outcome. This research investigates and proposes alternative designs to alleviate the problem of separation in small-sample D-optimal designs for the logistic regression model. Separation causes the non-existence of maximum likelihood parameter estimates and presents a serious problem for model fitting purposes.
First, it is shown that exact, multi-factor D-optimal designs for the logistic regression model can be susceptible to separation. Several logistic regression models are specified, and exact D-optimal designs of fixed sizes are constructed for each model. Sets of simulated response data are generated to estimate the probability of separation in each design. This study proves through simulation that small-sample D-optimal designs are prone to separation and that separation risk is dependent on the specified model. Additionally, it is demonstrated that exact designs of equal size constructed for the same models may have significantly different chances of encountering separation.
The second portion of this research establishes an effective strategy for augmentation, where additional design runs are judiciously added to eliminate separation that has occurred in an initial design. A simulation study is used to demonstrate that augmenting runs in regions of maximum prediction variance (MPV), where the predicted probability of either response category is 50%, most reliably eliminates separation. However, it is also shown that MPV augmentation tends to yield augmented designs with lower D-efficiencies.
The final portion of this research proposes a novel compound optimality criterion, DMP, that is used to construct locally optimal and robust compromise designs. A two-phase coordinate exchange algorithm is implemented to construct exact locally DMP-optimal designs. To address design dependence issues, a maximin strategy is proposed for designating a robust DMP-optimal design. A case study demonstrates that the maximin DMP-optimal design maintains comparable D-efficiencies to a corresponding Bayesian D-optimal design while offering significantly improved separation performance.
First, it is shown that exact, multi-factor D-optimal designs for the logistic regression model can be susceptible to separation. Several logistic regression models are specified, and exact D-optimal designs of fixed sizes are constructed for each model. Sets of simulated response data are generated to estimate the probability of separation in each design. This study proves through simulation that small-sample D-optimal designs are prone to separation and that separation risk is dependent on the specified model. Additionally, it is demonstrated that exact designs of equal size constructed for the same models may have significantly different chances of encountering separation.
The second portion of this research establishes an effective strategy for augmentation, where additional design runs are judiciously added to eliminate separation that has occurred in an initial design. A simulation study is used to demonstrate that augmenting runs in regions of maximum prediction variance (MPV), where the predicted probability of either response category is 50%, most reliably eliminates separation. However, it is also shown that MPV augmentation tends to yield augmented designs with lower D-efficiencies.
The final portion of this research proposes a novel compound optimality criterion, DMP, that is used to construct locally optimal and robust compromise designs. A two-phase coordinate exchange algorithm is implemented to construct exact locally DMP-optimal designs. To address design dependence issues, a maximin strategy is proposed for designating a robust DMP-optimal design. A case study demonstrates that the maximin DMP-optimal design maintains comparable D-efficiencies to a corresponding Bayesian D-optimal design while offering significantly improved separation performance.
ContributorsPark, Anson Robert (Author) / Montgomery, Douglas C. (Thesis advisor) / Mancenido, Michelle V (Thesis advisor) / Escobedo, Adolfo R. (Committee member) / Pan, Rong (Committee member) / Arizona State University (Publisher)
Created2019
Description
Nonregular designs are a preferable alternative to regular resolution four designs because they avoid confounding two-factor interactions. As a result nonregular designs can estimate and identify a few active two-factor interactions. However, due to the sometimes complex alias structure of nonregular designs, standard screening strategies can fail to identify all active effects. In this research, two-level nonregular screening designs with orthogonal main effects will be discussed. By utilizing knowledge of the alias structure, a design based model selection process for analyzing nonregular designs is proposed.
The Aliased Informed Model Selection (AIMS) strategy is a design specific approach that is compared to three generic model selection methods; stepwise regression, least absolute shrinkage and selection operator (LASSO), and the Dantzig selector. The AIMS approach substantially increases the power to detect active main effects and two-factor interactions versus the aforementioned generic methodologies. This research identifies design specific model spaces; sets of models with strong heredity, all estimable, and exhibit no model confounding. These spaces are then used in the AIMS method along with design specific aliasing rules for model selection decisions. Model spaces and alias rules are identified for three designs; 16-run no-confounding 6, 7, and 8-factor designs. The designs are demonstrated with several examples as well as simulations to show the AIMS superiority in model selection.
A final piece of the research provides a method for augmenting no-confounding designs based on a model spaces and maximum average D-efficiency. Several augmented designs are provided for different situations. A final simulation with the augmented designs shows strong results for augmenting four additional runs if time and resources permit.
The Aliased Informed Model Selection (AIMS) strategy is a design specific approach that is compared to three generic model selection methods; stepwise regression, least absolute shrinkage and selection operator (LASSO), and the Dantzig selector. The AIMS approach substantially increases the power to detect active main effects and two-factor interactions versus the aforementioned generic methodologies. This research identifies design specific model spaces; sets of models with strong heredity, all estimable, and exhibit no model confounding. These spaces are then used in the AIMS method along with design specific aliasing rules for model selection decisions. Model spaces and alias rules are identified for three designs; 16-run no-confounding 6, 7, and 8-factor designs. The designs are demonstrated with several examples as well as simulations to show the AIMS superiority in model selection.
A final piece of the research provides a method for augmenting no-confounding designs based on a model spaces and maximum average D-efficiency. Several augmented designs are provided for different situations. A final simulation with the augmented designs shows strong results for augmenting four additional runs if time and resources permit.
ContributorsMetcalfe, Carly E (Author) / Montgomery, Douglas C. (Thesis advisor) / Jones, Bradley (Committee member) / Pan, Rong (Committee member) / Pedrielli, Giulia (Committee member) / Arizona State University (Publisher)
Created2020