The advantages of Multilevel Item Response Theory (MLIRT) model have been studied by several researchers, and even the impact of ignoring a higher level of data structure in multilevel analysis has been studied and discussed. However, due to the technical complexity of modeling and the shortage in function of dealing with multilevel data in traditional IRT packages (e.g., BILOG and PARSCALE), researchers may not be able to analyze the multilevel IRT data accurately. The impact of this type of misspecification, especially for MLIRT models, has not yet been thoughtfully examined. This dissertation consists of two studies: one is a Monte Carlo study that investigates the impact of this type of misspecification and the other one is a study with real-world data to validate the results obtaining from the simulation study. In Study One (the simulation study), we investigate the potential impact of several factors, including: intra-class correlation (ICC), sample size, cluster size and test length, on the parameter estimates and corresponding test of significance under two situations: when the higher level nesting structure is appropriately modeled (i.e., true model condition) versus inappropriately modeled (i.e., misspecified model condition). Three-level straightly hierarchical data (i.e., items are nested within students who are further nested within schools) were generated. Two person-related and school-related covariates were added at the second level (i.e., person-level) and the third level (i.e., school-level), respectively. The results of simulation studies showed that both parameter estimates and their corresponding standard errors would be biased if the higher level nesting structure was ignored. In Study Two, a real data from the Programme for International Student Assessment with purely hierarchical structure were analyzed by comparing parameter estimates when inappropriate versus appropriate IRT models are specified. The findings mirrored the results obtained from the first study. The implication of this dissertation to researchers is that it is important to model the multilevel data structure even in item response theory models. Researchers should interpret their results in caution when ignoring a higher level nesting structure in MLIRT models. What's more, the findings may help researchers determine when MLIRT should be used to get an unbiased result. Limitations concerning about some of the constraints of the simulation study could be relaxed. For instance, although this study used only dichotomous items, the MLIRT could also be used with polytomous items. The test length could be longer and more variability could be introduced into the item parameters’ values.

Natural gas is stored as compressed natural gas (CNG) in heavy steel cylinders under pressures of 200-250 atm. However, such a method of storage has certain disadvantages which include multistage compression costs, limited driving range and safety aspects. Hence, alternative methods of storage such as adsorbed natural gas (ANG) which involve adsorbing natural gas at moderate pressures and room temperatures in a suitable nanoporous material are currently being explored. In this thesis, we have isolated model carbon nanostructures and defect geometries most likely to be found in these materials and investigated their specific interactions with methane. The thesis is concerned with ab-initio density functional theory calculations on these various model carbon nanostructures in order to identify the potential candidates that enhance methane adsorption. The adsorption energies of methane on graphite and graphene sheets were similar, with a value of 12.3 kJ/mol for graphene. The Stone-Wales defect in graphene was found to increase the methane adsorption energy to 37.2 kJ/mol, and small surface undulations on the graphene sheet resulted in a smaller increase (16 kJ/mol) in the adsorption energy relative to graphene. The presence of an interstitial carbon was found to significantly reduce the adsorption energy to 5.2 kJ/mol. The enhanced adsorption energy in the case of the Stone-Wales defect was attributed to the significant charge redistribution in the vicinity of the defect. A variety of functional groups such as carboxylic acid (COOH), carbonyl (CO), phenol (OH), pyran (-O-), phenone (=O), peroxide (OOH) and amine (NH2) groups have been observed on carbon surfaces. Extensive density functional calculations of methane adsorbed on various chemically functionalized graphene nanoribbons were carried out to evaluate their methane adsorption energies. A significant finding in this study, is the increased adsorption energies (relative to graphene) that occur for the functional groups containing the OH moiety. The adsorption energies for edge functionalized graphene nanoribbons are 27.6 and 69.7 kJ/mol for COOH and OOH functionalization. Additional computations reveal a strong correlation between the induced dipole moment on methane and the strength of the adsorption energies obtained for the extended nanoribbons. Adsorption isotherms for methane were obtained using grand canonical Monte Carlo simulations for slit-like graphitic pores with and without functional groups. For both OH and COOH functionalized graphite, we observe more than a 40 % increase in the volumetric loading over bare graphite for the highest weight % of the functional group and smallest pore width considered. The maximum volumetric loading decreases with a decrease in the wt% of the functional groups and with an increase in the pore width.

A new model developed for the entire bathtub-shaped hazard rate curve has been evaluated as to its usefulness as a method of reliability estimation. The model is of the form: F(t) = 1 - exp - (ϴ1tL + ϴ2t + ϴ3tM) where "L" and "M" were assumed known. The estimate of reliability obtained from the new model was compared with the traditional restricted sample estimate for four different time intervals and was found to have less bias and variance for all time points. The was a monte carlo study and the data generated showed that the new model has much potential as a method for estimating reliability. (51 pages)

Objetivo. Comparar, teórica e empiricamente, dois estimadores do coeficiente de correlação intraclasse momento-produto de Pearson para pares repetidos Pi. O primeiro é o estimador \"natural\", obtido mediante a correlação momento-produto de Pearson para membros de uma mesma classe (rI) e o segundo, obtido como função de componentes de variância (icc). Métodos. Comparação teórica e empírica dos parâmetros e estimadores. A comparação teórica envolve duas definições do coeficiente de correlação intraclasse PI como medida de confiabilidade (*), para o caso de duas réplicas, assim como uma apresentação da técnica de análise de variância e a definição e interpretação dos estimadores ri e icc. A comparação empírica é realizada mediante um estudo de simulação Monte Carlo com a geração de pares de valores correlacionados segundo o coeficiente de correlação intraclasse, momento-produto de Pearson para pares repetidos. Os pares de valores são distribuídos segundo uma distribuição Normal bivariada, com valores do tamanho da amostra e da correlação intraclasse previamente fixados em: n= 15, 30 e 45 e pI = {O; 0,15; 0,30; 0,45; 0,60; 0,75; 0,9}. Resultados. Comparando-se o vício e o erro quadrático médio dos estimadores, bem como as amplitudes dos intervalos de confiança, tem-se como resultado que o vício de icc foi sempre menor que o vício de rI, mesmo ocorrendo com o erro quadrático médio. Conclusões. O icc é um estimador melhor, principalmente para n pequeno (por exemplo 15). Para valores maiores de n (30 ou mais), os estimadores produzem resultados iguais até a segunda casa decimal. / Objective. This thesis presents and compares, theoretically and empirically, two estimators of the intraclass correlation coefficient pI, defined as Pearson\'s pairwise intraclass correlation coefficient. The first is the \"natural\" estimator, obtained by Pearson\'s moment-product correlation for members of one class (rI) while the second was obtained as a function of components of variance (icc). Methods. Theoretical and empirical comparison of the parameters and estimators are performed. The theoretical comparison involves two definitions of the intrac1ass correlation coefficient pI as a measure of reliability (*) for two repeated measurements in the same class and the presentation of the technique of analysis of variance, as well as for the definition and interpretation of the estimators ri and icc. The empirical comparison was carried out by means of a Monte Carlo simulation study of pairs of correlated values according Pearson\'s pairwise correlation. The pairs of values follow a normal bivariate distribution, with correlation values and sample size previously fixed: n= 15, 30 e 45 and Pl = . Results. Bias and mean square error for the estimators were compared as well as the range of the intervals of confidence. The comparison shows that the bias of icc is always smaller than of rI This also applies to the mean square error. Conclusions. The icc is a better estimator, especially for n less than or equal to 15. For larger samples sízes (n 30 or more), the estimators produce results that are equal to the second decimal place. (*) Fórmula

Objetivo. Comparar, teórica e empiricamente, dois estimadores do coeficiente de correlação intraclasse momento-produto de Pearson para pares repetidos Pi. O primeiro é o estimador \"natural\", obtido mediante a correlação momento-produto de Pearson para membros de uma mesma classe (rI) e o segundo, obtido como função de componentes de variância (icc). Métodos. Comparação teórica e empírica dos parâmetros e estimadores. A comparação teórica envolve duas definições do coeficiente de correlação intraclasse PI como medida de confiabilidade (*), para o caso de duas réplicas, assim como uma apresentação da técnica de análise de variância e a definição e interpretação dos estimadores ri e icc. A comparação empírica é realizada mediante um estudo de simulação Monte Carlo com a geração de pares de valores correlacionados segundo o coeficiente de correlação intraclasse, momento-produto de Pearson para pares repetidos. Os pares de valores são distribuídos segundo uma distribuição Normal bivariada, com valores do tamanho da amostra e da correlação intraclasse previamente fixados em: n= 15, 30 e 45 e pI = {O; 0,15; 0,30; 0,45; 0,60; 0,75; 0,9}. Resultados. Comparando-se o vício e o erro quadrático médio dos estimadores, bem como as amplitudes dos intervalos de confiança, tem-se como resultado que o vício de icc foi sempre menor que o vício de rI, mesmo ocorrendo com o erro quadrático médio. Conclusões. O icc é um estimador melhor, principalmente para n pequeno (por exemplo 15). Para valores maiores de n (30 ou mais), os estimadores produzem resultados iguais até a segunda casa decimal. / Objective. This thesis presents and compares, theoretically and empirically, two estimators of the intraclass correlation coefficient pI, defined as Pearson\'s pairwise intraclass correlation coefficient. The first is the \"natural\" estimator, obtained by Pearson\'s moment-product correlation for members of one class (rI) while the second was obtained as a function of components of variance (icc). Methods. Theoretical and empirical comparison of the parameters and estimators are performed. The theoretical comparison involves two definitions of the intrac1ass correlation coefficient pI as a measure of reliability (*) for two repeated measurements in the same class and the presentation of the technique of analysis of variance, as well as for the definition and interpretation of the estimators ri and icc. The empirical comparison was carried out by means of a Monte Carlo simulation study of pairs of correlated values according Pearson\'s pairwise correlation. The pairs of values follow a normal bivariate distribution, with correlation values and sample size previously fixed: n= 15, 30 e 45 and Pl = . Results. Bias and mean square error for the estimators were compared as well as the range of the intervals of confidence. The comparison shows that the bias of icc is always smaller than of rI This also applies to the mean square error. Conclusions. The icc is a better estimator, especially for n less than or equal to 15. For larger samples sízes (n 30 or more), the estimators produce results that are equal to the second decimal place. (*) Fórmula

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Traditional latent class analysis (LCA) considers entropy R2 as the only measure of effect size. However, entropy may not always be reliable, a low boundary is not agreed upon, and good separation is limited to values of greater than .80. As applications of LCA grow in popularity, it is imperative to use additional sources to quantify LCA classification accuracy. Greater classification accuracy helps to ensure that the profile of the latent classes reflect the profile of the true underlying subgroups. This Monte Carlo study compared the quantification of classification accuracy and confidence intervals of three effect sizes, entropy R2, I-index, and Cohen’s d. Study conditions included total sample size, number of dichotomous indicators, latent class membership probabilities (γ), conditional item-response probabilities (ρ), variance ratio, sample size ratio, and distribution types for a 2-class model. Overall, entropy R2 and I-index showed the best accuracy and standard error, along with the smallest confidence interval widths. Results showed that I-index only performed well for a few cases.

The unique problems encountered when analyzing weather data sets - that is, measurements taken while conducting a meteorological experiment- have forced statisticians to reconsider the conventional analysis methods and investigate permutation test procedures. The problems encountered when analyzing weather data sets are simulated for a Monte Carlo study, and the results of the parametric and permutation t-tests are compared with regard to significance level, power, and the average coilfidence interval length. Seven population distributions are considered - three are variations of the normal distribution, and the others the gamma, the lognormal, the rectangular and empirical distributions. The normal distribution contaminated with zero measurements is also simulated. In those simulated situations in which the variances are unequal, the permutation test procedure was performed using other test statistics, namely the Scheffe, Welch and Behrens-Fisher test statistics. / Mathematical Sciences / M. Sc. (Statistics)

Crystallographically solids with well defined crystal structures are normally assumed to be highly ordered. However, it is not uncommon to find considerable degree of disorder amongst many of these crystalline substances. Disorder among crystalline substances often arise from the rotational motion which leads to the well known class of plastic crystalline substances. Typically, globular molecules such as methane, carbon tetrachloride or adamantane exhibit plastic crystalline phase with significant amount of orientational disorder. In many other substances, disorder arises from torsional motion as in the case of biphenyl, p- or o-terphenyls, stilbene or azobenzenes. In case of molecules with flexible segment, such as alkanes or surfactants, motion of the terminal methyl group or terminal ethyl group is responsible for the observed disorder. Chapter 1 discusses various aspects of disorder in crystals. A new pressure induced solid phase of biphenyl is reported at room temperature. Isothermal-isobaric ensemble variable shape simulation cell Monte Carlo calculations are reported on biphenyl at 300K as a function of pressure between 0-4 GPa. The potential proposed by Williams for inter-molecular and Benkert-Heine-Simmons(BHS) for intramolecular interactions have been employed. Different properties indicating changes in the crystal structure, molecular structure, distributions of inter- and intra-molecular energy are reported as a function of pressure. With increase in pressure beyond 0.8 GPa, the dihedral angle distribution undergoes a change from a bimodal to an unimodal distribution. The changes in IR and Raman spectra across the transition computed from ab initio calculations are in agreement with the experimental measurements. It is shown that at pressures larger than 0.8 GPa, competition between inter-molecular interactions with intra-molecular terms v/z., conjugation energy and the ortho-ortho repulsion favors a planar biphenyl due to better packing and consequently a predominant inter-molecular term. The exact value of the transition pressure will depend on the accuracy of the inter- and intra-molecular potentials employed here. p-terphenyl has been modeled at 300K and atmospheric pressure with different potential models. Modified Fihppini parameters for mtermolecular interactions and BHS potential for inter-ring torsion predict the structure of p-terphenyl reasonably well. Pressure variation calculations are carried out with this combination of inter- and intra-molecular potential. The structure as a function of pressure upto 5 GPa has been compared with experimental structure provided by Puschnig et al. The transformation of functional form of the potential energy curve (associated with the inter-ring flipping) from W-shaped to [/-shaped form as a function of pressure has been observed. This is in excellent agreement with previous studies of polyphenyls including biphenyl and p-hexaphenyl. The complete planarization of molecules occurs when the pressure range is 1.0 GPa-1.5 GPa. Molecular simulation of solid stilbene in the isothermal-isobaric ensemble with variable shape simulation are reported. Structure has been characterized by means of lattice parameters and radial distribution functions. Simulations show existence of pedal-like motion at higher temperatures in agreement with the recent X-ray diffraction measurements by Ogawa and co-workers and several others previously. Difference in energy between the major and minor conformers, barrier to conformational change at both the crystallographic sites have been calculated. Temperature dependence of the equilibrium constant between the two conformers as well as the rate of conversion between the con-formers at the two sites have been calculated. These are in agreement with the recent analysis by Harada and Ogawa of non-equilibrium states obtained by rapid cooling of stilbene. Volume and total intermolecular energy suggest existence of two transitions in agreement with previous Raman phonon spectroscopic and calorimetric studies. They seem to be associated with change from order to disorder at the two sites. Ab initio calculations coupled with simulations suggest that the disorder accounts for only a small part of the observed shortening in ethylene bond ength. A Monte Carlo simulation with variable shape simulation cell has been carried out on stilbene. The study attempts to investigate the disorder at various pressures upto 4 GPa. It is seen that the population of minor conformers at sites 1 and 2 decrease with increase in pressure. Population of minor conformers at site 2 decreases to zero by 1.5 GPa. In contrast, the population of minor conformers at site 1 remains finite for the runs reported here. It is seen that the population of minor conformers at site 1 is higher than at site 2 at room temperature which is to be expected on the basis of the activation energies. Associated changes in the unit cell as well as molecular conformation are discussed. Isothermal-isobaric ensemble Monte Carlo simulation of adamantane has been earned out with variable shape simulation cell. Low temperature crystalline phase and the room temperature plastic crystalline phases have been studied employing the Williams potential. We show that at room temperature, the plastic crystalline phase transforms to the crystalline phase on increase in pressure. Further, we show that this is the same phase as the low temperature ordered tetragonal phase of adamantane. The high pressure ordered phase appears to be characterized by a slightly larger shift of the first peak towards lower value of r in C-C, C-H and H-H rdfs as compared to the low temperature tetragonal phase. Co-existence curve between the crystalline and plastic crystalline phase has been obtained approximately upto a pressure of 4 GPa. We investigate the equation of state, variation of lattice parameters and the distortion of molecular geometry of low temperature phase of adamantane upto 26 GPa pressure. A rigid and a flexible model of adamantane have been studied using variable shape simulation within the isothermal-isobaric ensemble. Including six low frequency modes obtained from density functional theory carried out on a single-molecule has incorporated the flexibility. These calculations used Becke 3-parameter method and Lee-Yang-Parr electron correlation functional with 6-31G(d) basis set. The simulated equation of state and variation of c/a ratio as a function of pressure are compared with the experimental results. The results are in good agreement with high pressure experiments. Nature of distortion in molecular geometry obtained from the calculation are also in good agreement with the experiment.

The unique problems encountered when analyzing weather data sets - that is, measurements taken while conducting a meteorological experiment- have forced statisticians to reconsider the conventional analysis methods and investigate permutation test procedures. The problems encountered when analyzing weather data sets are simulated for a Monte Carlo study, and the results of the parametric and permutation t-tests are compared with regard to significance level, power, and the average coilfidence interval length. Seven population distributions are considered - three are variations of the normal distribution, and the others the gamma, the lognormal, the rectangular and empirical distributions. The normal distribution contaminated with zero measurements is also simulated. In those simulated situations in which the variances are unequal, the permutation test procedure was performed using other test statistics, namely the Scheffe, Welch and Behrens-Fisher test statistics. / Mathematical Sciences / M. Sc. (Statistics)