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Quadratic growth curves of 2nd degree polynomial are widely used in longitudinal studies. For a 2nd degree polynomial, the vertex represents the location of the curve in the XY plane. For a quadratic growth curve, we propose an approximate confidence region as well as the confidence interval for x and

Quadratic growth curves of 2nd degree polynomial are widely used in longitudinal studies. For a 2nd degree polynomial, the vertex represents the location of the curve in the XY plane. For a quadratic growth curve, we propose an approximate confidence region as well as the confidence interval for x and y-coordinates of the vertex using two methods, the gradient method and the delta method. Under some models, an indirect test on the location of the curve can be based on the intercept and slope parameters, but in other models, a direct test on the vertex is required. We present a quadratic-form statistic for a test of the null hypothesis that there is no shift in the location of the vertex in a linear mixed model. The statistic has an asymptotic chi-squared distribution. For 2nd degree polynomials of two independent samples, we present an approximate confidence region for the difference of vertices of two quadratic growth curves using the modified gradient method and delta method. Another chi-square test statistic is derived for a direct test on the vertex and is compared to an F test statistic for the indirect test. Power functions are derived for both the indirect F test and the direct chi-square test. We calculate the theoretical power and present a simulation study to investigate the power of the tests. We also present a simulation study to assess the influence of sample size, measurement occasions and nature of the random effects. The test statistics will be applied to the Tell Efficacy longitudinal study, in which sound identification scores and language protocol scores for children are modeled as quadratic growth curves for two independent groups, TELL and control curriculum. The interpretation of shift in the location of the vertices is also presented.

ContributorsYu, Wanchunzi (Author) / Reiser, Mark R. (Thesis advisor) / Barber, Jarrett (Committee member) / Kao, Ming-Hung (Committee member) / St Louis, Robert D (Committee member) / Wilson, Jeffrey (Committee member) / Arizona State University (Publisher)
Created2015
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Description

We attempted to apply a novel approach to stock market predictions. The Logistic Regression machine learning algorithm (Joseph Berkson) was applied to analyze news article headlines as represented by a bag-of-words (tri-gram and single-gram) representation in an attempt to predict the trends of stock prices based on the Dow Jones

We attempted to apply a novel approach to stock market predictions. The Logistic Regression machine learning algorithm (Joseph Berkson) was applied to analyze news article headlines as represented by a bag-of-words (tri-gram and single-gram) representation in an attempt to predict the trends of stock prices based on the Dow Jones Industrial Average. The results showed that a tri-gram bag led to a 49% trend accuracy, a 1% increase when compared to the single-gram representation’s accuracy of 48%.

ContributorsBarolli, Adeiron (Author) / Jimenez Arista, Laura (Thesis director) / Wilson, Jeffrey (Committee member) / School of Life Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05