Using Amos graphics to enhance the understanding and communication of multiple regression

Support for the saying “a picture is worth a 1000 words’ has been consistently found within statistics education. Graphical images are effective in promoting understanding and communication of statistical concepts and results to a variety of audiences. The computer software package, AMOS, was developed for the analysis of structural equation models (SEM) and has a user-friendly graphical interface. However, courses in SEM are generally found only at the postgraduate level. This paper argues that the graphical interface of AMOS has the potential to enhance conceptual understanding and communication of results in undergraduate statistical courses. More specifically, approaches to the teaching and communication of results of multiple regression models when using SPSS and AMOS will be examined and compared.

GIS-integrated mathematical modeling of social phenomena at macro- and micro- levels—a multivariate geographically-weighted regression model for identifying locations vulnerable to hosting terrorist safe-houses: France as case study

Adaptability and invisibility are hallmarks of modern terrorism, and keeping pace with its dynamic nature presents a serious challenge for societies throughout the world. Innovations in computer science have incorporated applied mathematics to develop a wide array of predictive models to support the variety of approaches to counterterrorism. Predictive models are usually designed to forecast the location of attacks. Although this may protect individual structures or locations, it does not reduce the threat—it merely changes the target. While predictive models dedicated to events or social relationships receive much attention where the mathematical and social science communities intersect, models dedicated to terrorist locations such as safe-houses (rather than their targets or training sites) are rare and possibly nonexistent. At the time of this research, there were no publically available models designed to predict locations where violent extremists are likely to reside. This research uses France as a case study to present a complex systems model that incorporates multiple quantitative, qualitative and geospatial variables that differ in terms of scale, weight, and type. Though many of these variables are recognized by specialists in security studies, there remains controversy with respect to their relative importance, degree of interaction, and interdependence. Additionally, some of the variables proposed in this research are not generally recognized as drivers, yet they warrant examination based on their potential role within a complex system. This research tested multiple regression models and determined that geographically-weighted regression analysis produced the most accurate result to accommodate non-stationary coefficient behavior, demonstrating that geographic variables are critical to understanding and predicting the phenomenon of terrorism. This dissertation presents a flexible prototypical model that can be refined and applied to other regions to inform stakeholders such as policy-makers and law enforcement in their efforts to improve national security and enhance quality-of-life.

Structural brain connectivity and cognitive ability differences: A multivariate distance matrix regression analysis

Neuroimaging research involves analyses of huge amounts of biological data that might or might not be related with cognition. This relationship is usually approached using univariate methods, and, therefore, correction methods are mandatory for reducing false positives. Nevertheless, the probability of false negatives is also increased. Multivariate frameworks have been proposed for helping to alleviate this balance. Here we apply multivariate distance matrix regression for the simultaneous analysis of biological and cognitive data, namely, structural connections among 82 brain regions and several latent factors estimating cognitive performance. We tested whether cognitive differences predict distances among individuals regarding their connectivity pattern. Beginning with 3,321 connections among regions, the 36 edges better predicted by the individuals' cognitive scores were selected. Cognitive scores were related to connectivity distances in both the full (3,321) and reduced (36) connectivity patterns. The selected edges connect regions distributed across the entire brain and the network defined by these edges supports high-order cognitive processes such as (a) (fluid) executive control, (b) (crystallized) recognition, learning, and language processing, and (c) visuospatial processing. This multivariate study suggests that one widespread, but limited number, of regions in the human brain, supports high-level cognitive ability differences. Hum Brain Mapp, 2016. © 2016 Wiley Periodicals, Inc.

Meaning in life in earlier and later older-adulthood : confirmatory factor analysis and correlates of the meaning in life questionnaire

OBJECTIVE: To validate the Meaning in Life Questionnaire (MLQ) in earlier and later older-adulthood, and examine its correlates. METHOD: Participants in earlier (n = 341, M age = 68.5) and later older-adulthood (n = 341, M age = 78.6) completed the MLQ and other measures. Confirmatory multigroup analysis, correlations, and regression models were conducted. RESULTS: A two-factor (presence and search), eight-item model of the MLQ had a good fit and was age-invariant. Presence and search for meaning were largely unrelated. Meaning was associated with life satisfaction, well-being across a range of domains, and psychological resources. Searching for meaning correlated negatively with these variables, but to a lesser degree in later older-adulthood. DISCUSSION: The MLQ is valid in older-adulthood. Meaning in life is psychologically adaptive in older-adulthood. Searching for meaning appears less important, especially in later older-adulthood. Findings are discussed in the context of aging and psychosocial development.

Does inter-jurisdictional competition engender a “race to the bottom”? A meta-regression analysis

A growing literature documents the existence of strategic political reactions to publicexpenditure between rival jurisdictions. These interactions can potentially createa downward expenditure spiral (“race to the bottom”) or a rising expenditure spiral(“race to the top”). However, in the course of identifying the existence of such interactions and ascertaining their underlying triggers, the empirical evidence has produced markedly heterogeneous findings. Most of this heterogeneity can be traced back to study design and institutional differences. This article contributes to the literature by applying meta-regression analysis to quantify the magnitude of strategic inter-jurisdictional expenditure interactions, controlling for study, and institutional characteristics. We find several robust results beyond confirming that jurisdictions do engage in strategic expenditure interactions, namely that strategic interactions: (i) are weakening over time, (ii) are stronger among municipalities than among higher levels of government, and (iii) appear to be more influenced from tax competition than yardstick competition, with capital controls and fiscal decentralization shaping the magnitude of fiscal interactions.

Wine prices and quality eatings: a meta-regression analysis

This article examines the empirical support for the hypothesized hedonic theoretical relation between the price of wine and its quality. The examination considers over 180 hedonic wine price models developed over 20 years, covering many countries. The research identifies that the relation between the price of wine and its sensory quality rating is a moderate partial correlation of +0.30. This correlation exists despite the lack of information held by consumers about a wine’s quality and the inconsistency of expert tasters when evaluating wines. The results identify a moderate price-quality correlation, which suggests the existence of strategic buying opportunities for better informed consumers. Strategic price setting possibilities may also exist for wine producers given the incomplete quality information held by consumers. The results from the meta-regression analysis point to the absence of any publication bias, and attribute the observed asymmetry in estimates to study heterogeneity. The analysis suggests the observed heterogeneity is explained by the importance of a wine’s reputation, the use of the 100-point quality rating scale, the analysis of a single wine variety/style, and the employed functional form. The most important implication from the analysis is the relative importance of a wine’s reputation over its sensory quality, inferring that producers need to sustain the sensory quality of a wine over time to extract appropriate returns. The reputation of the wine producer is found not to influence the strength of the price quality relationship. This finding does not contradict the importance of wine producer reputation in directly influencing prices.

Neither fixed nor random: weighted least squares meta-regression

Our study revisits and challenges two core conventional meta-regression estimators: the prevalent use of‘mixed-effects’ or random-effects meta-regression analysis and the correction of standard errors that defines fixed-effects meta-regression analysis (FE-MRA). We show how and explain why an unrestricted weighted least squares MRA (WLS-MRA) estimator is superior to conventional random-effects (or mixed-effects) meta-regression when there is publication (or small-sample) bias that is as good as FE-MRA in all cases and better than fixed effects in most practical applications. Simulations and statistical theory show that WLS-MRA provides satisfactory estimates of meta-regression coefficients that are practically equivalent to mixed effects or random effects when there is no publication bias. When there is publication selection bias, WLS-MRA always has smaller bias than mixed effects or random effects. In practical applications, an unrestricted WLS meta-regression is likely to give practically equivalent or superior estimates to fixed-effects, random-effects, and mixed-effects meta-regression approaches. However, random-effects meta-regression remains viable and perhaps somewhat preferable if selection for statistical significance (publication bias) can be ruled out and when random, additive normal heterogeneity is known to directly affect the ‘true’ regression coefficient.

Process capability analysis in non normal linear regression profiles

When the distribution of a process characterized by a profile is non normal, process capability analysis using normal assumption often leads to erroneous interpretations of the process performance. Profile monitoring is a relatively new set of techniques in quality control that is used in situations where the state of product or process is represented by a function of two or more quality characteristics. Such profiles can be modeled using linear or nonlinear regression models. In some applications, it is assumed that the quality characteristics follow a normal distribution; however, in certain applications this assumption may fail to hold and may yield misleading results. In this article, we consider process capability analysis of non normal linear profiles. We investigate and compare five methods to estimate non normal process capability index (PCI) in profiles. In three of the methods, an estimation of the cumulative distribution function (cdf) of the process is required to analyze process capability in profiles. In order to estimate cdf of the process, we use a Burr XII distribution as well as empirical distributions. However, the resulted PCI with estimating cdf of the process is sometimes far from its true value. So, here we apply artificial neural network with supervised learning which allows the estimation of PCIs in profiles without the need to estimate cdf of the process. Box-Cox transformation technique is also developed to deal with non normal situations. Finally, a comparison study is performed through the simulation of Gamma, Weibull, Lognormal, Beta and student-t data.

A fast malware feature selection approach using a hybrid of multi-linear and stepwise binary logistic regression

Malware replicates itself and produces offspring with the same characteristics but different signatures by using code obfuscation techniques. Current generation anti-virus engines employ a signature-template type detection approach where malware can easily evade existing signatures in the database. This reduces the capability of current anti-virus engines in detecting malware. In this paper, we propose a stepwise binary logistic regression-based dimensionality reduction techniques for malware detection using application program interface (API) call statistics. Finding the most significant malware feature using traditional wrapper-based approaches takes an exponential complexity of the dimension (m) of the dataset with a brute-force search strategies and order of (m-1) complexity with a backward elimination filter heuristics. The novelty of the proposed approach is that it finds the worst case computational complexity which is less than order of (m-1). The proposed approach uses multi-linear regression and the p-value of each individual API feature for selection of the most uncorrelated and significant features in order to reduce the dimensionality of the large malware data and to ensure the absence of multi-collinearity. The stepwise logistic regression approach is then employed to test the significance of the individual malware feature based on their corresponding Wald statistic and to construct the binary decision the model. When the selected most significant APIs are used in a decision rule generation systems, this approach not only reduces the tree size but also improves classification performance. Exhaustive experiments on a large malware data set show that the proposed approach clearly exceeds the existing standard decision rule, support vector machine-based template approach with complete data and provides a better statistical fitness.

Applying Least Absolute Shrinkage Selection Operator and Akaike Information Criterion Analysis to Find the Best Multiple Linear Regression Models between Climate Indices and Components of Cow’s Milk

This study focuses on multiple linear regression models relating six climate indices (temperature humidity THI, environmental stress ESI, equivalent temperature index ETI, heat load HLI, modified HLI (HLI new), and respiratory rate predictor RRP) with three main components of cow’s milk (yield, fat, and protein) for cows in Iran. The least absolute shrinkage selection operator (LASSO) and the Akaike information criterion (AIC) techniques are applied to select the best model for milk predictands with the smallest number of climate predictors. Uncertainty estimation is employed by applying bootstrapping through resampling. Cross validation is used to avoid over-fitting. Climatic parameters are calculated from the NASA-MERRA global atmospheric reanalysis. Milk data for the months from April to September, 2002 to 2010 are used. The best linear regression models are found in spring between milk yield as the predictand and THI, ESI, ETI, HLI, and RRP as predictors with p-value < 0.001 and R2 (0.50, 0.49) respectively. In summer, milk yield with independent variables of THI, ETI, and ESI show the highest relation (p-value < 0.001) with R2 (0.69). For fat and protein the results are only marginal. This method is suggested for the impact studies of climate variability/change on agriculture and food science fields when short-time series or data with large uncertainty are available.

The Drivers of Wage Inequality Across Europe: A Recentered Influence Function Regression Approach

This study analyzes the impact of individual characteristics as well as occupation and industry on male wage inequality in nine European countries. Unlike previous studies, we consider regression models for five inequality measures and employ the recentered influence function regression method proposed by Firpo et al. (2009) to test directly the influence of covariates on inequality. We conclude that there is heterogeneity in the effects of covariates on inequality across countries and throughout wage distribution. Heterogeneity among countries is more evident in education and experience whereas occupation and industry characteristics as well as holding a supervisory position reveal more similar effects. Our results are compatible with the skill biased technological change, rapid rise in the integration of trade and financial markets as well as explanations related to the increase of the remunerative package of top executives.

Obtaining environmental favourability functions from logistic regression

Logistic regression is a statistical tool widely used for predicting species’ potential distributions starting from presence/absence data and a set of independent variables. However, logistic regression equations compute probability values based not only on the values of the predictor variables but also on the relative proportion of presences and absences in the dataset, which does not adequately describe the environmental favourability for or against species presence. A few strategies have been used to circumvent this, but they usually imply an alteration of the original data or the discarding of potentially valuable information. We propose a way to obtain from logistic regression an environmental favourability function whose results are not affected by an uneven proportion of presences and absences. We tested the method on the distribution of virtual species in an imaginary territory. The favourability models yielded similar values regardless of the variation in the presence/absence ratio. We also illustrate with the example of the Pyrenean desman’s (Galemys pyrenaicus) distribution in Spain. The favourability model yielded more realistic potential distribution maps than the logistic regression model. Favourability values can be regarded as the degree of membership of the fuzzy set of sites whose environmental conditions are favourable to the species, which enables applying the rules of fuzzy logic to distribution modelling. They also allow for direct comparisons between models for species with different presence/absence ratios in the study area. This makes themmore useful to estimate the conservation value of areas, to design ecological corridors, or to select appropriate areas for species reintroductions.