Structural equation and factor analyses for several populations and longitudinal data

This dissertation considers the use of latent variable modeling in multi-population studies and longitudinal studies. Possibly correlated populations and unbalanced longitudinal data are considered. For non-normal samples, practical statistical procedures are developed using the existing computer packages designed for normally distributed observations and independent populations or occasions. Model formulations and parameterizations are found, so that the results from the statistical analysis make sense, and so that the analysis produces correct inferences for parameters and model fit. The dissertation consists of three papers;In the first paper, a general latent variable model with mean and covariance structures is considered for multi-population studies. A model formulation that allows meaningful interpretation is suggested. The parameters are estimated by the maximum normal likelihood estimation method. The asymptotic properties of the estimates are derived under assumptions covering most types of non-normal data. It is shown that the limiting distribution of the estimators for the important parameters is common for normal and non-normal data, and for independent and correlated populations. A simulation study is also presented;In the second paper, the analysis using the model with augmented-moment structure is discussed. A certain part of the limiting covariance matrix of the proposed estimator is common under four different sets of assumptions. Thus, the correct standard errors can be computed under an incorrect but simpler set of assumptions. A simulation study compares the finite-sample and asymptotic standard errors;The third paper proposes a new method for analyzing unbalanced longitudinal data using factor analysis. Difficulties and disadvantages of the full-likelihood method and time series modeling approach are explained. The proposed method uses a reduced form of the likelihood, does not assume restrictive time series structure, and can be readily implemented. The new method is shown to produce valid and useful asymptotic results for models with non-normal factors and errors and without any specified correlation structure over time. The efficiency loss of the method relative to the full-likelihood method, when the latter can be carried out, is shown to be negligible

A hybrid modular approach for dynamic fault tree analysis

YesOver the years, several approaches have been developed for the quantitative analysis of dynamic fault trees (DFTs). These approaches have strong theoretical and mathematical foundations; however, they appear to suffer from the state-space explosion and high computational requirements, compromising their efficacy. Modularisation techniques have been developed to address these issues by identifying and quantifying static and dynamic modules of the fault tree separately by using binary decision diagrams and Markov models. Although these approaches appear effective in reducing computational effort and avoiding state-space explosion, the reliance of the Markov chain on exponentially distributed data of system components can limit their widespread industrial applications. In this paper, we propose a hybrid modularisation scheme where independent sub-trees of a DFT are identified and quantified in a hierarchical order. A hybrid framework with the combination of algebraic solution, Petri Nets, and Monte Carlo simulation is used to increase the efficiency of the solution. The proposed approach uses the advantages of each existing approach in the right place (independent module). We have experimented the proposed approach on five independent hypothetical and industrial examples in which the experiments show the capabilities of the proposed approach facing repeated basic events and non-exponential failure distributions. The proposed approach could provide an approximate solution to DFTs without unacceptable loss of accuracy. Moreover, the use of modularised or hierarchical Petri nets makes this approach more generally applicable by allowing quantitative evaluation of DFTs with a wide range of failure rate distributions for basic events of the tree.This work was supported in part by the Dependability Engineering Innovation for Cyber Physical Systems (CPS) (DEIS) H2020 Project under Grant 732242, and in part by the LIVEBIO: Light-weight Verification for Synthetic Biology Project under Grant EPSRC EP/R043787/1

Structural equation and factor analyses for several populations and longitudinal data

This dissertation considers the use of latent variable modeling in multi-population studies and longitudinal studies. Possibly correlated populations and unbalanced longitudinal data are considered. For non-normal samples, practical statistical procedures are developed using the existing computer packages designed for normally distributed observations and independent populations or occasions. Model formulations and parameterizations are found, so that the results from the statistical analysis make sense, and so that the analysis produces correct inferences for parameters and model fit. The dissertation consists of three papers;In the first paper, a general latent variable model with mean and covariance structures is considered for multi-population studies. A model formulation that allows meaningful interpretation is suggested. The parameters are estimated by the maximum normal likelihood estimation method. The asymptotic properties of the estimates are derived under assumptions covering most types of non-normal data. It is shown that the limiting distribution of the estimators for the important parameters is common for normal and non-normal data, and for independent and correlated populations. A simulation study is also presented;In the second paper, the analysis using the model with augmented-moment structure is discussed. A certain part of the limiting covariance matrix of the proposed estimator is common under four different sets of assumptions. Thus, the correct standard errors can be computed under an incorrect but simpler set of assumptions. A simulation study compares the finite-sample and asymptotic standard errors;The third paper proposes a new method for analyzing unbalanced longitudinal data using factor analysis. Difficulties and disadvantages of the full-likelihood method and time series modeling approach are explained. The proposed method uses a reduced form of the likelihood, does not assume restrictive time series structure, and can be readily implemented. The new method is shown to produce valid and useful asymptotic results for models with non-normal factors and errors and without any specified correlation structure over time. The efficiency loss of the method relative to the full-likelihood method, when the latter can be carried out, is shown to be negligible.</p

Inference for structural equation modelling on dependent populations

Latent variable modelling is used widely in applications to economics, social and behavioural sciences. Since the normality-based model fitting procedures are simple and broadly available, and since such procedures are often applied to non-normal data or non-random samples, it is important to investigate the appropriateness of such practice and to suggest simple remedies. This paper addresses these issues for the analysis of multiple populations. For a very general class of latent variable models, a particular parameterisation is used for meaningful and interpretable analysis of several populations. It turns out that under this parameterisation the large sample statistical inferences based on the assumption of normal and independent populations are valid for virtually any non-normal and dependent populations. This result is also valid when some latent variables are treated as fixed instead of random, or when a group of individuals is measured over several time points longitudinally.structural equation modelling; latent variables; LISREL; fixed variables; non-normal factors; asymptotic robustness; multi-sample methods; dependent populations; panel data; longitudinal data; inference.

Theory and methodology for dynamic panel data: tested by simulations based on financial data

A new method is introduced for panel-data models. Asymptotic robustness is used for a multivariate model with latent variables for a family of estimators. It is shown numerically that in comparison to standard methods we obtain: 1) better predictions in out-of-sample occasions; 2) smaller asymptotic standard errors (a.s.e.s); 3) more accurate a.s.e.s; 4) very small bias. Our methodology handles dynamic models with lag-independent variables, individual and time effects, time heteroscedasticity, non-normality, non-stationarity, fixed variables, non-linear and variant-over-time coefficients, and unbalanced data, by using restrictions on the parameters and the multi-sample technique (m.s.t.). Also, a novel formula for the duplication matrix is provided and a solution for a matrix equation is given.longitudinal data, repeated measures, duplication matrix, maximum likelihood estimator, MLE, generalised method of moments, GMM, MD estimators, dynamic panel data, simulation, financial data, dynamic modelling,

A DECOMPOSITION OF THE PEARSON'S CORRELATION COEFFICIENT: PARALLEL-LINE DETECTION

We decompose the Pearson correlation coefficient into two components. We recommend the first component for detecting linear relationships and the second for recognizing patterns of two parallel lines, providing robust versions to outliers. The significance of the Pearson coefficient without significant components indicates a fit of three parallel lines. Thus, we reveal the unknown aspect of the Pearson coefficient that identifies a two- or three-group association other than a group, producing Type I or III[1] errors. Finally, we apply the proposed coefficients with permutation tests to simulated and real data. The proposed coefficients identify two- or three-parallel line correlations or weaker but significant relationships not recognized by the Pearson coefficient. In testing correlation hypotheses with normal data, the proposed methodology minimizes the total error resulting from the Person coefficient by 4%.</p

Technical efficiency of economic systems of EU-15 countries based on energy consumption

c Technical efficiency index of EU-15 countries is determined through the DEA method. c Level of the TE index is determined from the energy mix used in each country. c TE level depends on the maximization level of GDP without waste of energy resources. c Capacity of an economy to produce more GDP for a given energy input is determined. c TE differentiation before and after the integration of nuclear energy is performed. a r t i c l e i n f o t r a c t In the present study, Data Envelopment Analysis is used to determine the Technical Efficiency index of EU-15 countries from 1980 to 2008, using cross-country comparison. Technical Efficiency index represents the capacity of an economy to produce a higher level of Gross Domestic Product for a given level of total energy input. The level of the Technical Efficiency index is determined from the energy mix (fossil fuels, non-fossil fuels, nuclear energy) of each country and depends on the maximization level of the production of the Gross Domestic Product of the economic system, without waste of energy resources. The current study is applied in the case of the EU15 countries. Its scope is to highlight the differentiations of country classifications before and after the integration of nuclear energy in the energy mix of each country. The main result is that the integration of nuclear energy as an additional input in the energy mixture affects negatively the Technical Efficiency of countries. Also, when an economy achieves a decrease of the energy consumption produced from fossil fuels, and a better exploitation of renewable energy sources, clearly improves its capacity to produce more output with the given levels of inputs