Thesis (Ph. D.)--University of Texas at Austin, 2002. / Vita. Includes bibliographical references. Available also from UMI Company.

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Multiple-indicators multiple-causes (MIMIC) modeling is often employed for measurement invariance testing under the structural equation modeling framework. This Monte Carlo study explored the behaviors of MIMIC as a measurement invariance testing method in different research situations. First, the performance of MIMIC under the factor loading noninvariance conditions was investigated through model fit evaluations and likelihood ratio tests. This study demonstrated that the violation of factor loading invariance was not detected by any of the typically reported model fit indices. Consistently, the likelihood ratio tests for MIMIC models exhibited poor performance in identifying noninvariance in factor loadings. That is, MIMIC was insensitive to the presence of factor loading noninvariance, which implies that factor loading invariance should be examined through other measurement invariance testing techniques. To control Type I error inflation in detecting the noninvariance of intercepts or thresholds, this simulation study with both continuous and categorical variables employed the likelihood ratio test with two critical value adjustment strategies, Oort adjustment and Bonferroni correction. The simulation results showed that the likelihood ratio test with Oort adjustment not only controlled Type I error rates below the basal Type I error rates but also maintained high power across study conditions. However, it was observed that power to detect the noninvariant variables slightly attenuated with multiple (i.e., two) noninvariant variables in a model. Given that the modification index is the chi-square difference after relaxing one parameter for estimation, this study investigated modification indices under four research scenarios based on a combination of the cutoffs of modification indices and the procedures of model modification: (a) the noniterative method (i.e., modification indices at the initial stage of model modification) using the conventional critical value, (b) the noniterative method using the Oort adjusted critical value, (c) the iterative procedure of model modification using the conventional critical value, and (d) the iterative procedure using the Oort adjustment. The iterative model search procedure using modification indices showed high performance in detecting noninvariant variables even without critical value adjustment, which indicates that iterative model search specification does not require critical value adjustment in identifying the noninvariance correctly. On the other hand, when the noniterative procedure was used, the Oort adjustment yielded adequate results.

abstract: To make meaningful comparisons on a construct of interest across groups or over time, measurement invariance needs to exist for at least a subset of the observed variables that define the construct. Often, chi-square difference tests are used to test for measurement invariance. However, these statistics are affected by sample size such that larger sample sizes are associated with a greater prevalence of significant tests. Thus, using other measures of non-invariance to aid in the decision process would be beneficial. For this dissertation project, I proposed four new effect size measures of measurement non-invariance and analyzed a Monte Carlo simulation study to evaluate their properties and behavior in addition to the properties and behavior of an already existing effect size measure of non-invariance. The effect size measures were evaluated based on bias, variability, and consistency. Additionally, the factors that affected the value of the effect size measures were analyzed. All studied effect sizes were consistent, but three were biased under certain conditions. Further work is needed to establish benchmarks for the unbiased effect sizes. / Dissertation/Thesis / Doctoral Dissertation Psychology 2019

The purpose of the present study was to examine the invariance of the factor structure and item response model parameter estimates obtained from a set of 27 items selected from the 2002 and 2003 forms of Your First College Year (YFCY). The first major research question of the present study was: How similar/invariant are the factor structures obtained from two datasets (i.e., identical items, different people)? The first research question was addressed in two parts: (1) Exploring factor structures using the YFCY02 dataset; and (2) Assessing factorial invariance using the YFCY02 and YFCY03 datasets. After using exploratory and confirmatory and factor analysis for ordered data, a four-factor model using 20 items was selected based on acceptable model fit for the YFCY02 and YFCY03 datasets. The four factors (constructs) obtained from the final model were: Overall Satisfaction, Social Agency, Social Self Concept, and Academic Skills. To assess factorial invariance, partial and full factorial invariance were examined. The four-factor model fit both datasets equally well, meeting the criteria for partial and full measurement invariance. The second major research question of the present study was: How similar/invariant are person and item parameter estimates obtained from two different datasets (i.e., identical items, different people) for the homogenous graded response model (Samejima, 1969) and the partial credit model (Masters, 1982)? To evaluate measurement invariance using IRT methods, the item discrimination and item difficulty parameters obtained from the GRM need to be equivalent across datasets. The YFCY02 and YFCY03 GRM item discrimination parameters (slope) correlation was 0.828. The YFCY02 and YFCY03 GRM item difficulty parameters (location) correlation was 0.716. The correlations and scatter plots indicated that the item discrimination parameter estimates were more invariant than the item difficulty parameter estimates across the YFCY02 and YFCY03 datasets.

A system of nonrelativistic charged particles and radiation is canonically quantized in the Coulomb gauge and Maxwell's equations in quantum electrodynamics are derived. By requiring form invariance of the Schrodinger equation under a space and time dependent unitary transformation, operator gauge transformations on the quantized electromagnetic potentials and state vectors are introduced. These gauge transformed potentials have the same form as gauge transformations in non-Abelian gauge field theories. A gauge-invariant method for solving the time-dependent Schrodinger equation in quantum electrodynamics is given. Maxwell's equations are written in a form which holds in all gauges and which has formal similarity to the equations of motion of non-Abelian gauge fields. A gauge-invariant derivation of conservation of energy in quantum electrodynamics is given. An operator gauge transformation is made to the multipolar gauge in which the potentials are expressed in terms of the electromagnetic fields. The multipolar Hamiltonian is shown to be the minimally coupled Hamiltonian with the electromagnetic potentials in the multipolar gauge. The model of a charged harmonic oscillator in a single-mode electromagnetic field is considered as an example. The gauge-invariant procedure for solving the time-dependent Schrodinger equation is used to obtain the gauge-invariant probabilities that the oscillator is in an energy eigenstate For comparison, the conventional approach is also used to solve the harmonic oscillator problem and is shown to give gauge-dependent amplitudes.

This thesis presents the search for the supersymmetric partner of the top quark in p s Æ 13 TeV proton-proton collisions at the LHC using data collected by the ATLAS detector in 2015 and 2016. Results were interpreted considering natural supersymmetric extensions of the Standard Model in R-parity conserving decays. Events characterised by four or more jets and missing transverse momentum in the final states were selected. The performance of the tracking algorithms used by the ATLAS online trigger were studied. Optimisation studies of the search regions to increase the sensitivity to supersymmetric signals were performed and data-driven techniques to estimate StandardModel backgrounds were employed. The agreement between data and background predictionswas extensively checked and the extrapolations frombackgroundenriched regions to signal-enriched regions were validated. The analysis yielded no significant excess therefore exclusion limits on various models were set.

The purpose of this study was to investigate population invariance of the true-score linking functions with respect to the ability subgroups (i.e., average-achieving students, low-achieving students, and students with learning disabilities). The mean/mean linking functions for five alternate forms of a curriculum-based math problem solving measure were based on the Rasch model. Most studies of curriculum-based measurement have reported only the reliability and validity of alternate forms of measures. This is necessary but insufficient for establishing alternate forms of curriculum-based measures. It is also necessary to establish equivalency of the forms. The present study was based on data from a previous study that developed equivalent forms of curriculum-based measures using Item Response Theory. The participants in the present study were 1,861 seventh- and eighth-grade students. Equatability indices were used to evaluate population invariance of the Rasch mean/mean linking functions over the ability subgroups. Results indicated that the Rasch mean/mean linking functions were population invariant for the ability subgroups across the five alternate forms. The differences between the linking functions computed on the ability subgroups and the linking function on the whole group were negligible for the five forms. Several implications and recommendations for future studies on population invariance of the linking functions with alternate forms of curriculum-based measures were discussed.

abstract: In the past, it has been assumed that measurement and predictive invariance are consistent so that if one form of invariance holds the other form should also hold. However, some studies have proven that both forms of invariance only hold under certain conditions such as factorial invariance and invariance in the common factor variances. The present research examined Type I errors and the statistical power of a method that detects violations to the factorial invariant model in the presence of group differences in regression intercepts, under different sample sizes and different number of predictors (one or two). Data were simulated under two models: in model A only differences in the factor means were allowed, while model B violated invariance. A factorial invariant model was fitted to the data. Type I errors were defined as the proportion of samples in which the hypothesis of invariance was incorrectly rejected, and statistical power was defined as the proportion of samples in which the hypothesis of factorial invariance was correctly rejected. In the case of one predictor, the results show that the chi-square statistic has low power to detect violations to the model. Unexpected and systematic results were obtained regarding the negative unique variance in the predictor. It is proposed that negative unique variance in the predictor can be used as indication of measurement bias instead of the chi-square fit statistic with sample sizes of 500 or more. The results of the two predictor case show larger power. In both cases Type I errors were as expected. The implications of the results and some suggestions for increasing the power of the method are provided. / Dissertation/Thesis / M.A. Psychology 2010