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- Creators: Arizona State University
- Genre: Doctoral Dissertation
Description
Designing studies that use latent growth modeling to investigate change over time calls for optimal approaches for conducting power analysis for a priori determination of required sample size. This investigation (1) studied the impacts of variations in specified parameters, design features, and model misspecification in simulation-based power analyses and (2) compared power estimates across three common power analysis techniques: the Monte Carlo method; the Satorra-Saris method; and the method developed by MacCallum, Browne, and Cai (MBC). Choice of sample size, effect size, and slope variance parameters markedly influenced power estimates; however, level-1 error variance and number of repeated measures (3 vs. 6) when study length was held constant had little impact on resulting power. Under some conditions, having a moderate versus small effect size or using a sample size of 800 versus 200 increased power by approximately .40, and a slope variance of 10 versus 20 increased power by up to .24. Decreasing error variance from 100 to 50, however, increased power by no more than .09 and increasing measurement occasions from 3 to 6 increased power by no more than .04. Misspecification in level-1 error structure had little influence on power, whereas misspecifying the form of the growth model as linear rather than quadratic dramatically reduced power for detecting differences in slopes. Additionally, power estimates based on the Monte Carlo and Satorra-Saris techniques never differed by more than .03, even with small sample sizes, whereas power estimates for the MBC technique appeared quite discrepant from the other two techniques. Results suggest the choice between using the Satorra-Saris or Monte Carlo technique in a priori power analyses for slope differences in latent growth models is a matter of preference, although features such as missing data can only be considered within the Monte Carlo approach. Further, researchers conducting power analyses for slope differences in latent growth models should pay greatest attention to estimating slope difference, slope variance, and sample size. Arguments are also made for examining model-implied covariance matrices based on estimated parameters and graphic depictions of slope variance to help ensure parameter estimates are reasonable in a priori power analysis.
ContributorsVan Vleet, Bethany Lucía (Author) / Thompson, Marilyn S. (Thesis advisor) / Green, Samuel B. (Committee member) / Enders, Craig K. (Committee member) / Arizona State University (Publisher)
Created2011
Description
This dissertation consists of two essays. The first measures the degree to which schooling accounts for differences in industry value added per worker. Using a sample of 107 economies and seven industries, the paper considers the patterns in the education levels of various industries and their relative value added per worker. Agriculture has notably less schooling and is less productive than other sectors, while a group of services including financial services, education and health care has higher rates of schooling and higher value added per worker. The essay finds that in the case of these specific industries education is important in explaining sector differences, and the role of education all other industries are less defined. The second essay provides theory to investigate the relationship between agriculture and schooling. During structural transformation, workers shift from the agriculture sector with relatively low schooling to other sectors which have more schooling. This essay explores to what extent changes in the costs of acquiring schooling drive structural transformation using a multi-sector growth model which includes a schooling choice. The model is disciplined using cross country data on sector of employment and schooling constructed from the IPUM International census collection. Counterfactual exercises are used to determine how much structural transformation is accounted for by changes in the cost of acquiring schooling. These changes account for small shares of structural transformation in all economies with a median near zero.
ContributorsSchreck, Paul (Author) / Herrendorf, Berthold (Committee member) / Lagakos, David (Committee member) / Schoellman, Todd (Committee member) / Arizona State University (Publisher)
Created2011
Description
By the von Neumann min-max theorem, a two person zero sum game with finitely many pure strategies has a unique value for each player (summing to zero) and each player has a non-empty set of optimal mixed strategies. If the payoffs are independent, identically distributed (iid) uniform (0,1) random variables, then with probability one, both players have unique optimal mixed strategies utilizing the same number of pure strategies with positive probability (Jonasson 2004). The pure strategies with positive probability in the unique optimal mixed strategies are called saddle squares. In 1957, Goldman evaluated the probability of a saddle point (a 1 by 1 saddle square), which was rediscovered by many authors including Thorp (1979). Thorp gave two proofs of the probability of a saddle point, one using combinatorics and one using a beta integral. In 1965, Falk and Thrall investigated the integrals required for the probabilities of a 2 by 2 saddle square for 2 × n and m × 2 games with iid uniform (0,1) payoffs, but they were not able to evaluate the integrals. This dissertation generalizes Thorp's beta integral proof of Goldman's probability of a saddle point, establishing an integral formula for the probability that a m × n game with iid uniform (0,1) payoffs has a k by k saddle square (k ≤ m,n). Additionally, the probabilities of a 2 by 2 and a 3 by 3 saddle square for a 3 × 3 game with iid uniform(0,1) payoffs are found. For these, the 14 integrals observed by Falk and Thrall are dissected into 38 disjoint domains, and the integrals are evaluated using the basic properties of the dilogarithm function. The final results for the probabilities of a 2 by 2 and a 3 by 3 saddle square in a 3 × 3 game are linear combinations of 1, π2, and ln(2) with rational coefficients.
ContributorsManley, Michael (Author) / Kadell, Kevin W. J. (Thesis advisor) / Kao, Ming-Hung (Committee member) / Lanchier, Nicolas (Committee member) / Lohr, Sharon (Committee member) / Reiser, Mark R. (Committee member) / Arizona State University (Publisher)
Created2011
Description
Mostly, manufacturing tolerance charts are used these days for manufacturing tolerance transfer but these have the limitation of being one dimensional only. Some research has been undertaken for the three dimensional geometric tolerances but it is too theoretical and yet to be ready for operator level usage. In this research, a new three dimensional model for tolerance transfer in manufacturing process planning is presented that is user friendly in the sense that it is built upon the Coordinate Measuring Machine (CMM) readings that are readily available in any decent manufacturing facility. This model can take care of datum reference change between non orthogonal datums (squeezed datums), non-linearly oriented datums (twisted datums) etc. Graph theoretic approach based upon ACIS, C++ and MFC is laid out to facilitate its implementation for automation of the model. A totally new approach to determining dimensions and tolerances for the manufacturing process plan is also presented. Secondly, a new statistical model for the statistical tolerance analysis based upon joint probability distribution of the trivariate normal distributed variables is presented. 4-D probability Maps have been developed in which the probability value of a point in space is represented by the size of the marker and the associated color. Points inside the part map represent the pass percentage for parts manufactured. The effect of refinement with form and orientation tolerance is highlighted by calculating the change in pass percentage with the pass percentage for size tolerance only. Delaunay triangulation and ray tracing algorithms have been used to automate the process of identifying the points inside and outside the part map. Proof of concept software has been implemented to demonstrate this model and to determine pass percentages for various cases. The model is further extended to assemblies by employing convolution algorithms on two trivariate statistical distributions to arrive at the statistical distribution of the assembly. Map generated by using Minkowski Sum techniques on the individual part maps is superimposed on the probability point cloud resulting from convolution. Delaunay triangulation and ray tracing algorithms are employed to determine the assembleability percentages for the assembly.
ContributorsKhan, M Nadeem Shafi (Author) / Phelan, Patrick E (Thesis advisor) / Montgomery, Douglas C. (Committee member) / Farin, Gerald (Committee member) / Roberts, Chell (Committee member) / Henderson, Mark (Committee member) / Arizona State University (Publisher)
Created2011
Description
The current study was a benefit cost analysis that examined mental and behavioral health and prescription drug service use data of 347 participants (212 youth and 135 caregivers) from a bereavement intervention, the Family Bereavement Program (FBP).The preliminary goals of the current study were to compare the FBP intervention and the Literature Control (LC) groups at the six year follow-up on: (a) number of participants using mental/behavioral health services and prescription drugs, (b) the frequency of use of mental/behavioral health services and prescription drugs, and (c) the costs of mental/behavioral health services and prescription drugs. The final, and primary goal, was to (d) calculate the benefits of the FBP by analyzing the monetary difference between the LC and FBP groups in terms of cost of services used and then by applying those benefits to the cost of the intervention. Data representing participating youths' and caregivers' mental health service use and prescription drug use at the sixth year post-intervention were collected, as were the costs of those services. Results indicated that fewer FBP participants used services and prescription drugs than the Literature Control (LC) participants, but FBP participants, particularly the youth, used some low intensity services more frequently whereas the LC youth used more intensive and costly services more frequently. Consequently, service costs were greater for participants in the LC group than for participants in the FBP group. The benefit cost ratio revealed that the FBP, as delivered, saved society between $.15 and $.27 in mental and behavioral health costs for every dollar spent on the intervention. Implications of these findings and directions for future research are discussed.
ContributorsPorter, Michèle M (Author) / Hanish, Laura D. (Thesis advisor) / Sandler, Irwin N. (Committee member) / Wolchik, Sharlene A (Committee member) / Johnson, William G. (Committee member) / Arizona State University (Publisher)
Created2011
Description
It is common in the analysis of data to provide a goodness-of-fit test to assess the performance of a model. In the analysis of contingency tables, goodness-of-fit statistics are frequently employed when modeling social science, educational or psychological data where the interest is often directed at investigating the association among multi-categorical variables. Pearson's chi-squared statistic is well-known in goodness-of-fit testing, but it is sometimes considered to produce an omnibus test as it gives little guidance to the source of poor fit once the null hypothesis is rejected. However, its components can provide powerful directional tests. In this dissertation, orthogonal components are used to develop goodness-of-fit tests for models fit to the counts obtained from the cross-classification of multi-category dependent variables. Ordinal categories are assumed. Orthogonal components defined on marginals are obtained when analyzing multi-dimensional contingency tables through the use of the QR decomposition. A subset of these orthogonal components can be used to construct limited-information tests that allow one to identify the source of lack-of-fit and provide an increase in power compared to Pearson's test. These tests can address the adverse effects presented when data are sparse. The tests rely on the set of first- and second-order marginals jointly, the set of second-order marginals only, and the random forest method, a popular algorithm for modeling large complex data sets. The performance of these tests is compared to the likelihood ratio test as well as to tests based on orthogonal polynomial components. The derived goodness-of-fit tests are evaluated with studies for detecting two- and three-way associations that are not accounted for by a categorical variable factor model with a single latent variable. In addition the tests are used to investigate the case when the model misspecification involves parameter constraints for large and sparse contingency tables. The methodology proposed here is applied to data from the 38th round of the State Survey conducted by the Institute for Public Policy and Michigan State University Social Research (2005) . The results illustrate the use of the proposed techniques in the context of a sparse data set.
ContributorsMilovanovic, Jelena (Author) / Young, Dennis (Thesis advisor) / Reiser, Mark R. (Thesis advisor) / Wilson, Jeffrey (Committee member) / Eubank, Randall (Committee member) / Yang, Yan (Committee member) / Arizona State University (Publisher)
Created2011
Description
Although the issue of factorial invariance has received increasing attention in the literature, the focus is typically on differences in factor structure across groups that are directly observed, such as those denoted by sex or ethnicity. While establishing factorial invariance across observed groups is a requisite step in making meaningful cross-group comparisons, failure to attend to possible sources of latent class heterogeneity in the form of class-based differences in factor structure has the potential to compromise conclusions with respect to observed groups and may result in misguided attempts at instrument development and theory refinement. The present studies examined the sensitivity of two widely used confirmatory factor analytic model fit indices, the chi-square test of model fit and RMSEA, to latent class differences in factor structure. Two primary questions were addressed. The first of these concerned the impact of latent class differences in factor loadings with respect to model fit in a single sample reflecting a mixture of classes. The second question concerned the impact of latent class differences in configural structure on tests of factorial invariance across observed groups. The results suggest that both indices are highly insensitive to class-based differences in factor loadings. Across sample size conditions, models with medium (0.2) sized loading differences were rejected by the chi-square test of model fit at rates just slightly higher than the nominal .05 rate of rejection that would be expected under a true null hypothesis. While rates of rejection increased somewhat when the magnitude of loading difference increased, even the largest sample size with equal class representation and the most extreme violations of loading invariance only had rejection rates of approximately 60%. RMSEA was also insensitive to class-based differences in factor loadings, with mean values across conditions suggesting a degree of fit that would generally be regarded as exceptionally good in practice. In contrast, both indices were sensitive to class-based differences in configural structure in the context of a multiple group analysis in which each observed group was a mixture of classes. However, preliminary evidence suggests that this sensitivity may contingent on the form of the cross-group model misspecification.
ContributorsBlackwell, Kimberly Carol (Author) / Millsap, Roger E (Thesis advisor) / Aiken, Leona S. (Committee member) / Enders, Craig K. (Committee member) / Mackinnon, David P (Committee member) / Arizona State University (Publisher)
Created2011
Description
Many longitudinal studies, especially in clinical trials, suffer from missing data issues. Most estimation procedures assume that the missing values are ignorable or missing at random (MAR). However, this assumption leads to unrealistic simplification and is implausible for many cases. For example, an investigator is examining the effect of treatment on depression. Subjects are scheduled with doctors on a regular basis and asked questions about recent emotional situations. Patients who are experiencing severe depression are more likely to miss an appointment and leave the data missing for that particular visit. Data that are not missing at random may produce bias in results if the missing mechanism is not taken into account. In other words, the missing mechanism is related to the unobserved responses. Data are said to be non-ignorable missing if the probabilities of missingness depend on quantities that might not be included in the model. Classical pattern-mixture models for non-ignorable missing values are widely used for longitudinal data analysis because they do not require explicit specification of the missing mechanism, with the data stratified according to a variety of missing patterns and a model specified for each stratum. However, this usually results in under-identifiability, because of the need to estimate many stratum-specific parameters even though the eventual interest is usually on the marginal parameters. Pattern mixture models have the drawback that a large sample is usually required. In this thesis, two studies are presented. The first study is motivated by an open problem from pattern mixture models. Simulation studies from this part show that information in the missing data indicators can be well summarized by a simple continuous latent structure, indicating that a large number of missing data patterns may be accounted by a simple latent factor. Simulation findings that are obtained in the first study lead to a novel model, a continuous latent factor model (CLFM). The second study develops CLFM which is utilized for modeling the joint distribution of missing values and longitudinal outcomes. The proposed CLFM model is feasible even for small sample size applications. The detailed estimation theory, including estimating techniques from both frequentist and Bayesian perspectives is presented. Model performance and evaluation are studied through designed simulations and three applications. Simulation and application settings change from correctly-specified missing data mechanism to mis-specified mechanism and include different sample sizes from longitudinal studies. Among three applications, an AIDS study includes non-ignorable missing values; the Peabody Picture Vocabulary Test data have no indication on missing data mechanism and it will be applied to a sensitivity analysis; the Growth of Language and Early Literacy Skills in Preschoolers with Developmental Speech and Language Impairment study, however, has full complete data and will be used to conduct a robust analysis. The CLFM model is shown to provide more precise estimators, specifically on intercept and slope related parameters, compared with Roy's latent class model and the classic linear mixed model. This advantage will be more obvious when a small sample size is the case, where Roy's model experiences challenges on estimation convergence. The proposed CLFM model is also robust when missing data are ignorable as demonstrated through a study on Growth of Language and Early Literacy Skills in Preschoolers.
ContributorsZhang, Jun (Author) / Reiser, Mark R. (Thesis advisor) / Barber, Jarrett (Thesis advisor) / Kao, Ming-Hung (Committee member) / Wilson, Jeffrey (Committee member) / St Louis, Robert D. (Committee member) / Arizona State University (Publisher)
Created2013
Description
The use of bias indicators in psychological measurement has been contentious, with some researchers questioning whether they actually suppress or moderate the ability of substantive psychological indictors to discriminate (McGrath, Mitchell, Kim, & Hough, 2010). Bias indicators on the MMPI-2-RF (F-r, Fs, FBS-r, K-r, and L-r) were tested for suppression or moderation of the ability of the RC1 and NUC scales to discriminate between Epileptic Seizures (ES) and Non-epileptic Seizures (NES, a conversion disorder that is often misdiagnosed as ES). RC1 and NUC had previously been found to be the best scales on the MMPI-2-RF to differentiate between ES and NES, with optimal cut scores occurring at a cut score of 65 for RC1 (classification rate of 68%) and 85 for NUC (classification rate of 64%; Locke et al., 2010). The MMPI-2-RF was completed by 429 inpatients on the Epilepsy Monitoring Unit (EMU) at the Scottsdale Mayo Clinic Hospital, all of whom had confirmed diagnoses of ES or NES. Moderated logistic regression was used to test for moderation and logistic regression was used to test for suppression. Classification rates of RC1 and NUC were calculated at different bias level indicators to evaluate clinical utility for diagnosticians. No moderation was found. Suppression was found for F-r, Fs, K-r, and L-r with RC1, and for all variables with NUC. For F-r and Fs, the optimal RC1 and NUC cut scores increased at higher levels of bias, but tended to decrease at higher levels of K-r, L-r, and FBS-r. K-r provided the greatest suppression for RC1, as well as the greatest increases in classification rates at optimal cut scores, given different levels of bias. It was concluded that, consistent with expectations, taking account of bias indicator suppression on the MMPI-2-RF can improve discrimination of ES and NES. At higher levels of negative impression management, higher cut scores on substantive scales are needed to attain optimal discrimination, whereas at higher levels of positive impression management and FBS-r, lower cut scores are needed. Using these new cut scores resulted in modest improvements in accuracy in discrimination. These findings are consistent with prior research in showing the efficacy of bias indicators, and extend the findings to a psycho-medical context.
ContributorsWershba, Rebecca E (Author) / Lanyon, Richard I (Thesis advisor) / Barrera, Manuel (Committee member) / Karoly, Paul (Committee member) / Millsap, Roger E (Committee member) / Arizona State University (Publisher)
Created2013
Description
Estimating cointegrating relationships requires specific techniques. Canonical correlations are used to determine the rank and space of the cointegrating matrix. The vectors used to transform the data into canonical variables have an eigenvector representation, and the associated canonical correlations have an eigenvalue representation. The number of cointegrating relations is chosen based upon a theoretical difference in the convergence rates of the eignevalues. The number of cointegrating relations is consistently estimated using a threshold function which places a lower bound on the eigenvalues associated with cointegrating relations and an upper bound on the eigenvalues on the eigenvalues not associated with cointegrating relations. The proposed estimator performs better with a large number of cross-sectional observations and moderate time series length.
ContributorsNowak, Adam (Author) / Ahn, Seung C (Thesis advisor) / Liu, Crocker (Committee member) / Kallberg, Jarl (Committee member) / Arizona State University (Publisher)
Created2012