An investigation of the goodness of fit of the maximum likelihood estimation procedure in factor analysis /

Thesis--Illinois.

Stochastic volatility and the goodness-of-fit of the Heston model

Recently, Drǎgulescu and Yakovenko proposed an analytical formula for computing the probability density function of stock log returns, based on the Heston model, which they tested empirically. Their research design inadvertently favourably biased the fit of the data to the Heston model, thus overstating their empirical results. Furthermore, Drǎgulescu and Yakovenko did not perform any goodness-of-fit statistical tests. This study employs a research design that facilitates statistical tests of the goodness-of-fit of the Heston model to empirical returns. Robustness checks are also performed. In brief, the Heston model outperformed the Gaussian model only at high frequencies and even so does not provide a statistically acceptable fit to the data. The Gaussian model performed (marginally) better at medium and low frequencies, at which points the extra parameters of the Heston model have adverse impacts on the test statistics. © 2005 Taylor & Francis Group Ltd.

An Alternative Goodness-of-fit Test for Normality with Unknown Parameters

Goodness-of-fit tests have been studied by many researchers. Among them, an alternative statistical test for uniformity was proposed by Chen and Ye (2009). The test was used by Xiong (2010) to test normality for the case that both location parameter and scale parameter of the normal distribution are known. The purpose of the present thesis is to extend the result to the case that the parameters are unknown. A table for the critical values of the test statistic is obtained using Monte Carlo simulation. The performance of the proposed test is compared with the Shapiro-Wilk test and the Kolmogorov-Smirnov test. Monte-Carlo simulation results show that proposed test performs better than the Kolmogorov-Smirnov test in many cases. The Shapiro Wilk test is still the most powerful test although in some cases the test proposed in the present research performs better.

The Goodness of Simultaneous Fits in ISIS

In a previous work, we introduced a tool for analyzing multiple datasets simultaneously, which has been implemented into ISIS. This tool was used to fit many spectra of X-ray binaries. However, the large number of degrees of freedom and individual datasets raise an issue about a good measure for a simultaneous fit quality. We present three ways to check the goodness of these fits: we investigate the goodness of each fit in all datasets, we define a combined goodness exploiting the logical structure of a simultaneous fit, and we stack the fit residuals of all datasets to detect weak features. These tools are applied to all RXTE-spectra from GRO 1008−57, revealing calibration features that are not detected significantly in any single spectrum. Stacking the residuals from the best-fit model for the Vela X-1 and XTE J1859+083 data evidences fluorescent emission lines that would have gone undetected otherwise.

On the nature of over-dispersion in motor vehicle crash prediction models

Statistical modeling of traffic crashes has been of interest to researchers for decades. Over the most recent decade many crash models have accounted for extra-variation in crash counts—variation over and above that accounted for by the Poisson density. The extra-variation – or dispersion – is theorized to capture unaccounted for variation in crashes across sites. The majority of studies have assumed fixed dispersion parameters in over-dispersed crash models—tantamount to assuming that unaccounted for variation is proportional to the expected crash count. Miaou and Lord [Miaou, S.P., Lord, D., 2003. Modeling traffic crash-flow relationships for intersections: dispersion parameter, functional form, and Bayes versus empirical Bayes methods. Transport. Res. Rec. 1840, 31–40] challenged the fixed dispersion parameter assumption, and examined various dispersion parameter relationships when modeling urban signalized intersection accidents in Toronto. They suggested that further work is needed to determine the appropriateness of the findings for rural as well as other intersection types, to corroborate their findings, and to explore alternative dispersion functions. This study builds upon the work of Miaou and Lord, with exploration of additional dispersion functions, the use of an independent data set, and presents an opportunity to corroborate their findings. Data from Georgia are used in this study. A Bayesian modeling approach with non-informative priors is adopted, using sampling-based estimation via Markov Chain Monte Carlo (MCMC) and the Gibbs sampler. A total of eight model specifications were developed; four of them employed traffic flows as explanatory factors in mean structure while the remainder of them included geometric factors in addition to major and minor road traffic flows. The models were compared and contrasted using the significance of coefficients, standard deviance, chi-square goodness-of-fit, and deviance information criteria (DIC) statistics. The findings indicate that the modeling of the dispersion parameter, which essentially explains the extra-variance structure, depends greatly on how the mean structure is modeled. In the presence of a well-defined mean function, the extra-variance structure generally becomes insignificant, i.e. the variance structure is a simple function of the mean. It appears that extra-variation is a function of covariates when the mean structure (expected crash count) is poorly specified and suffers from omitted variables. In contrast, when sufficient explanatory variables are used to model the mean (expected crash count), extra-Poisson variation is not significantly related to these variables. If these results are generalizable, they suggest that model specification may be improved by testing extra-variation functions for significance. They also suggest that known influences of expected crash counts are likely to be different than factors that might help to explain unaccounted for variation in crashes across sites

Development of accident prediction models for rural highway intersections

A study was done to develop macrolevel crash prediction models that can be used to understand and identify effective countermeasures for improving signalized highway intersections and multilane stop-controlled highway intersections in rural areas. Poisson and negative binomial regression models were fit to intersection crash data from Georgia, California, and Michigan. To assess the suitability of the models, several goodness-of-fit measures were computed. The statistical models were then used to shed light on the relationships between crash occurrence and traffic and geometric features of the rural signalized intersections. The results revealed that traffic flow variables significantly affected the overall safety performance of the intersections regardless of intersection type and that the geometric features of intersections varied across intersection type and also influenced crash type.

Psychometric analysis of the Brisbane Practice Environment Measure (B-PEM)

Purpose: To undertake rigorous psychometric testing of the newly developed contemporary work environment measure (the Brisbane Practice Environment Measure [B-PEM]) using exploratory factor analysis and confirmatory factor analysis. Methods: Content validity of the 33-item measure was established by a panel of experts. Initial testing involved 195 nursing staff using principal component factor analysis with varimax rotation (orthogonal) and Cronbach's alpha coefficients. Confirmatory factor analysis was conducted using data from a further 983 nursing staff. Results: Principal component factor analysis yielded a four-factor solution with eigenvalues greater than 1 that explained 52.53% of the variance. These factors were then verified using confirmatory factor analysis. Goodness-of-fit indices showed an acceptable fit overall with the full model, explaining 21% to 73% of the variance. Deletion of items took place throughout the evolution of the instrument, resulting in a 26-item, four-factor measure called the Brisbane Practice Environment Measure-Tested. Conclusions: The B-PEM has undergone rigorous psychometric testing, providing evidence of internal consistency and goodness-of-fit indices within acceptable ranges. The measure can be utilised as a subscale or total score reflective of a contemporary nursing work environment. Clinical Relevance: An up-to-date instrument to measure practice environment may be useful for nursing leaders to monitor the workplace and to assist in identifying areas for improvement, facilitating greater job satisfaction and retention.

Validation of the Chinese version of the Problem Areas in Diabetes (PAID-C) scale

OBJECTIVE To examine the psychometric properties of a Chinese version of the Problem Areas In Diabetes (PAID-C) scale. RESEARCH DESIGN AND METHODS The reliability and validity of the PAID-C were evaluated in a convenience sample of 205 outpatients with type 2 diabetes. Confirmatory factor analysis, Bland-Altman analysis, and Spearman's correlations facilitated the psychometric evaluation. RESULTS Confirmatory factor analysis confirmed a one-factor structure of the PAID-C (χ2/df ratio = 1.894, goodness-of-fit index = 0.901, comparative fit index = 0.905, root mean square error of approximation = 0.066). The PAID-C was associated with A1C (rs = 0.15; P < 0.05) and diabetes self-care behaviors in general diet (rs = −0.17; P < 0.05) and exercise (rs = −0.17; P < 0.05). The 4-week test-retest reliability demonstrated satisfactory stability (rs = 0.83; P < 0.01). CONCLUSIONS The PAID-C is a reliable and valid measure to determine diabetes-related emotional distress in Chinese people with type 2 diabetes.

The role of non-factorizability in determining "pseudo-classical" non-separability

This article introduces a “pseudo classical” notion of modelling non-separability. This form of non-separability can be viewed as lying between separability and quantum-like non-separability. Non-separability is formalized in terms of the non-factorizabilty of the underlying joint probability distribution. A decision criterium for determining the non-factorizability of the joint distribution is related to determining the rank of a matrix as well as another approach based on the chi-square-goodness-of-fit test. This pseudo-classical notion of non-separability is discussed in terms of quantum games and concept combinations in human cognition.

Quantum-like non-separability of concept combinations, emergent associates and abduction

Consider the concept combination ‘pet human’. In word association experiments, human subjects produce the associate ‘slave’ in relation to this combination. The striking aspect of this associate is that it is not produced as an associate of ‘pet’, or ‘human’ in isolation. In other words, the associate ‘slave’ seems to be emergent. Such emergent associations sometimes have a creative character and cognitive science is largely silent about how we produce them. Departing from a dimensional model of human conceptual space, this article will explore concept combinations, and will argue that emergent associations are a result of abductive reasoning within conceptual space, that is, below the symbolic level of cognition. A tensor-based approach is used to model concept combinations allowing such combinations to be formalized as interacting quantum systems. Free association norm data is used to motivate the underlying basis of the conceptual space. It is shown by analogy how some concept combinations may behave like quantum-entangled (non-separable) particles. Two methods of analysis were presented for empirically validating the presence of non-separable concept combinations in human cognition. One method is based on quantum theory and another based on comparing a joint (true theoretic) probability distribution with another distribution based on a separability assumption using a chi-square goodness-of-fit test. Although these methods were inconclusive in relation to an empirical study of bi-ambiguous concept combinations, avenues for further refinement of these methods are identified.

Modeling and multiway analysis of chatroom tensors

This work identifies the limitations of n-way data analysis techniques in multidimensional stream data, such as Internet chat room communications data, and establishes a link between data collection and performance of these techniques. Its contributions are twofold. First, it extends data analysis to multiple dimensions by constructing n-way data arrays known as high order tensors. Chat room tensors are generated by a simulator which collects and models actual communication data. The accuracy of the model is determined by the Kolmogorov-Smirnov goodness-of-fit test which compares the simulation data with the observed (real) data. Second, a detailed computational comparison is performed to test several data analysis techniques including svd [1], and multi-way techniques including Tucker1, Tucker3 [2], and Parafac [3].

Collective sampling and analysis of high order tensors for chatroom communications

This work investigates the accuracy and efficiency tradeoffs between centralized and collective (distributed) algorithms for (i) sampling, and (ii) n-way data analysis techniques in multidimensional stream data, such as Internet chatroom communications. Its contributions are threefold. First, we use the Kolmogorov-Smirnov goodness-of-fit test to show that statistical differences between real data obtained by collective sampling in time dimension from multiple servers and that of obtained from a single server are insignificant. Second, we show using the real data that collective data analysis of 3-way data arrays (users x keywords x time) known as high order tensors is more efficient than centralized algorithms with respect to both space and computational cost. Furthermore, we show that this gain is obtained without loss of accuracy. Third, we examine the sensitivity of collective constructions and analysis of high order data tensors to the choice of server selection and sampling window size. We construct 4-way tensors (users x keywords x time x servers) and analyze them to show the impact of server and window size selections on the results.

The first year experience of social work students : developing a “sense of fit” and engagement with the profession : a practice report

Engagement is believed to be critical to a successful first year experience. This paper examines a range of strategies introduced into a first year Social Work and Human Services unit at Queensland University of Technology. The focus of these strategies was to enhance student engagement through building connections with peers, lecturers and the Social Work and Human Services professions. It is argued in this paper that students are more likely to continue with their studies if they are supported in building an emerging identity as both a university student and as a Social Work or Human Services practitioner. A range of strategies was introduced, including restructuring the unit to include an early intensive teaching block; inviting current practitioners to speak with students about the realities of practice; and embedding an academic skills component into the unit. Feedback from students highlighted the success of these strategies in developing their academic skills, building connections and embedding a sense of fit with the profession.

The "caring experience": testing the psychometric properties of the Caring Efficacy Scale

The purpose of the study was to undertake rigorous psychometric testing of the Caring Efficacy Scale in a sample of Registered Nurses. A cross-sectional survey of 2000 registered nurses was undertaken. The Caring Efficacy Scale was utilised to inform the psychometric properties of the selected items of the Caring Efficacy Scale. Cronbach’s Alpha identified reliability of the data. Exploratory Factor Analysis and Confirmatory Factor Analysis were undertaken to validate the factors. Confirmatory factor analysis confirmed the development of two factors; Confidence to Care and Doubts and Concerns. The Caring Efficacy Scale has undergone rigorous psychometric testing, affording evidence of internal consistency and goodness-of-fit indices within satisfactory ranges. The Caring Efficacy Scale is valid for use in an Australian population of registered nurses. The scale can be used as a subscale or total score reflective of self-efficacy in nursing. This scale may assist nursing educators to predict levels of caring efficacy.