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Construct truncation can be defined as the failure to capture variation along the entire continuum of a construct reliably. It can occur due to suboptimal person selection or due to suboptimal item selection. In this thesis, I used a series of simulation studies coupled with real data examples to characterise the consequences of construct truncation on the inferences made in empirical research. The analyses suggested that construct truncation has the potential to result in significant distortions of substantive conclusions. Based on these analyses I developed recommendations for anticipating the circumstances under which construct truncation is likely to be problematic, identifying it when it occurs, and mitigating its adverse effects on substantive conclusions drawn from affected data.

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This thesis discusses various issues in the estimation of models for count data. In the first part of the thesis, we derive an analytic expression for the bias of the maximum likelihood estimator (MLE) of the parameter in a doubly-truncated Poisson distribution, which proves highly effective as a means of bias correction. We explore the circumstances under which bias is likely to be problematic, and provide some indication of the statistical significance of the bias. Over a range of sample sizes, our method outperforms the alternative of bias correction via the parametric bootstrap. We show that MLEs obtained from sample sizes which elicit appreciable bias also have sampling distributions which are unsuited to be approximated by large-sample asymptotics, and bootstrapping confidence intervals around our bias-adjusted estimator is preferred, as two tiers of bootstrapping may incur a heavy computational burden. Modelling count data where the counts are strictly positive is often accomplished using a positive Poisson distribution. Inspection of the data sometimes reveals an excess of ones, analogous to zero-inflation in a regular Poisson model. The latter situation has well developed methods for modelling and testing, such as the zero-inflated Poisson (ZIP) model, and a score test for zero-inflation in a ZIP model. The issue of count inflation in a positive Poisson distribution does not seem to have been considered in a similar way. In the second part of the thesis, we propose a one-inflated positive Poisson (OIPP) model, and develop a score test to determine whether there are “too many” ones for a positive Poisson model to fit well. We explore the performance of our score test, and compare it to a likelihood ratio test, via Monte Carlo simulation. We find that the score test performs well, and that the OIPP model may be useful in many cases. The third part of the thesis considers the possibility of one-inflation in zero-truncated data, when overdispersion is present. We propose a new model to deal with such a phenomenon, the one-inflated zero-truncated negative binomial (OIZTNB) model. The finite sample properties of the maximum likelihood estimators for the parameters of such a model are discussed. This Chapter considers likelihood ratio tests which assist in specifying the OIZTNB model, and investigates the finite sample properties of such tests. The OIZTNB model is illustrated using the medpar data set, which describes the hospital length of stay for a set of patients in Arizona. This is a data set that is widely used to highlight the merits of the zero-truncated negative binomial (ZTNB) model. We find that our OIZTNB model fits the data better than does the ZTNB model, and this leads us to conclude that the data are generated by a one-inflated process. / Graduate

Computational fluid dynamics (CFD) is a tool that is widely used in most industries today. It is important to have rigorous techniques to estimate the error produced when using CFD. This thesis develops techniques to estimate discretization error for unsteady flows using the unsteady error transport equation (ETE) as well as defect correction. A framework to obtain exact truncation error and estimated truncation error is also presented. The technique and results for the steady-state cases are given and the algorithm used for the steady case is extended for the unsteady case. Numerical results are presented for the steady viscous Burgers' equation, unsteady viscous Burgers' equation, steady quasi-1D Euler equations, and unsteady 1D Euler equations when applied to a shock tube. Cases using either defect correction or ETE are shown to give higher orders of accuracy for the corrected discretization error estimates when compared to the discretization error of the primal solution. / Master of Science / Computational fluid dynamics (CFD) is a tool that is widely used in most industries today. It is used to understand complex flows that are difficult to replicate using experimental techniques or by theoretical methods. It is important to have rigorous techniques to estimate the error produced when using CFD even when the exact solution is not available for comparison. This paper develops techniques to estimate discretization error for unsteady flows. Discretization error has one of the largest error magnitudes in CFD solutions. The exact physics dictates the use of continuous equations but to apply CFD techniques, the continuous equations have to be converted to discrete equations. Truncation error is, the error obtained when converting the continuous equations to discrete equations. This truncation error is in turn, the local source term for discretization error. To reduce the discretization error in the discrete equations, the exact or estimated truncation error is either added as a source term to the discrete equations or is used along with the error transport equation to get a better estimate of the solutions. A framework to obtain exact truncation error and estimated truncation error is also presented. The framework is first applied to the steady equations and is verified with results from previous studies and is then extended to the unsteady flows.

In modern wireless communication systems, such as satellite communications and wireless networks, the need for higher data rates without the need for additional transmit power has made Continuous Phase Modulation (CPM) one of the most attractive modulation schemes in band limited channels. However, as the data rates keep increasing, the spectral width of the CPM signal increases beyond the channel bandwidth and performance becomes constrained by the intersymbol interference (ISI) that results from band-limiting filters. We propose two approaches to the problem of equalization of band-limited CPM signals. First, our efforts are focused on shortening the channel impulse response so that we can use a low complexity MLSE equalizer. We implement the channel truncation structure by Falconer and Magee and adapt it to work with CPM signals. This structure uses a, a more derivable, pre-filter to shape the overall response of the channel, so that its impulse response is of shorter duration. Simulation results show that near-MLSE performance can be obtained while dramatically reducing MLSE equalizer complexity. In our second approach, we focus on eliminating the group-delay variations inside the channel passband using an FIR pre-filter. We assume the channel to be time-invariant and provide a method to design an FIR filter so that -when convolved with the band limiting filter - it results in more constant group-delay over the filter passband. Results show that eliminating the group-delay variations in the band limiting filter passband reduce the amount of ISI and improve bit error rate performance. / Master of Science

As part of a risk assessment study of the Leading Creek Watershed in Ohio, a prior Virginia Tech researcher collected pavement and subpavement sediment samples at 17 sites using the hybrid areal sampling technique with a clay adhesive. The watershed, which is heavily impacted by mining and agricultural activities, suffers from low pH, high concentrations of metals and sediment in the water column, and excessively silted streambeds. The current work presents the results of the particle size analyses performed on the hybrid samples in the context of evaluating the effectiveness of the technique itself and as a tool in future watershed/ecological studies, as well as examining possible relationships between siltation and indicators of ecological health in Leading Creek. By combining clay grid and adhesive sampling methods, the hybrid technique consistently achieved an effective particle size sampling range of 0.05 mm (1.97 x 10-3 in) to over 300 mm (11.8 in), thereby reducing the common problem of trunction. However, the overlap of the clay adhesive and natural sediment distributions and atypical sediment loading from surrounding abandoned and reclaimed mine lands obscured expected trends such as downstream fining and hindered the analysis of materials finer than 0.125 mm (4.93 x 10-3 in). Volumetric conversion of areal samples using the Modified Cube Model with a traditional exponent of -1 for clay was complicated by the large amount of fines in the Leading Creek samples. Further investigation into a more appropriate conversion technique for the evaluation of fine sediment samples is warranted. / Master of Science

HarpinPss, a proteinaceous elicitor from Pseudomonas syringae pv. syringae, is a glycine-rich, cysteine-lacking, heat-stable protein. It can elicit the hypersensitive response (HR) when delivered to the surface of plant cells. HRAP (hypersensitive response assisting protein) is an amphipathic protein purified from sweet pepper and could intensify harpinPss¡Vmediated HR in sweet pepper. In the previous research, harpinPss was present as monomer, dimer, trimer, tetramer, and ocatamer forms in neutral pH buffer. Only monomer and dimer forms of harpinPss induced hypersensitive response in nonhost plants. HRAP could cause multimeric forms of harpinPss dissociation into monomer forms. The interaction between HRAP and harpinPss is an important issue. HRAP contained three positively charged regions, a typical signal peptide and a cAMP-dependent phosphorylation site. In this study, these regions of HRAP would be truncated and identified whether these truncated HRAP fragments could promote harpinPss dissociation. Different combinations of truncated HRAP and harpinPss were used to identify the protein-interaction regions between two proteins. HarpinPss triggers HR via interaction with cAMP phosphorated region of HRAP and MAPK pathway transduction. When cAMP region of HRAP was truncated, harpinPss still triggers HR via polymerization and anchor on lipid bilayers to form an ion-conducting pore.

abstract: The aerospike nozzle belongs to the class of altitude compensating nozzles making it a strong candidate for Space Shuttle Main Engines. Owing to their higher efficiency compared to conventional bell nozzles, the aerospike nozzles are being studied extensively and are being used for many Single State to Orbit (SSTO) designs. A rocket engine nozzle with altitude compensation, such as the aerospike, consumes less fuel than a rocket engine with a bell nozzle. Aerospike nozzles are huge and are often difficult to construct and have to be truncated in order to make them feasible for application in a rocket propulsion system. Consequently, truncation of the aerospike leads to pressure loss under the base, which in-turn decreases the overall thrust produced by the rocket nozzle. To overcome this loss, a technique called base bleed is implemented in which a secondary jet is made to flow through the base of the truncated portion. This thesis uses dynamic pressure contour plots to find out the ideal base bleed mass flow rate to avoid base recirculation in 10 %, 20 % and 30 % truncated aerospike nozzles. / Dissertation/Thesis / Masters Thesis Mechanical Engineering 2017