Probing three-way interactions in moderated multiple regression:Development and application of a slope difference test

Researchers often use 3-way interactions in moderated multiple regression analysis to test the joint effect of 3 independent variables on a dependent variable. However, further probing of significant interaction terms varies considerably and is sometimes error prone. The authors developed a significance test for slope differences in 3-way interactions and illustrate its importance for testing psychological hypotheses. Monte Carlo simulations revealed that sample size, magnitude of the slope difference, and data reliability affected test power. Application of the test to published data yielded detection of some slope differences that were undetected by alternative probing techniques and led to changes of results and conclusions. The authors conclude by discussing the test's applicability for psychological research. Copyright 2006 by the American Psychological Association.

Statnote 16: fitting a regression line to data

Fitting a linear regression to data provides much more information about the relationship between two variables than a simple correlation test. A goodness of fit test of the line should always be carried out. Hence, ‘r squared’ estimates the strength of the relationship between Y and X, ANOVA whether a statistically significant line is present, and the ‘t’ test whether the slope of the line is significantly different from zero. In addition, it is important to check whether the data fit the assumptions for regression analysis and, if not, whether a transformation of the Y and/or X variables is necessary.

Data methods in optometry. Part 6: fitting a regression line to data

1. Fitting a linear regression to data provides much more information about the relationship between two variables than a simple correlation test. A goodness of fit test of the line should always be carried out. Hence, r squared estimates the strength of the relationship between Y and X, ANOVA whether a statistically significant line is present, and the ‘t’ test whether the slope of the line is significantly different from zero. 2. Always check whether the data collected fit the assumptions for regression analysis and, if not, whether a transformation of the Y and/or X variables is necessary. 3. If the regression line is to be used for prediction, it is important to determine whether the prediction involves an individual y value or a mean. Care should be taken if predictions are made close to the extremities of the data and are subject to considerable error if x falls beyond the range of the data. Multiple predictions require correction of the P values. 3. If several individual regression lines have been calculated from a number of similar sets of data, consider whether they should be combined to form a single regression line. 4. If the data exhibit a degree of curvature, then fitting a higher-order polynomial curve may provide a better fit than a straight line. In this case, a test of whether the data depart significantly from a linear regression should be carried out.

Factors determining disease duration in Alzheimer's disease:a postmortem study of 103 cases using the Kaplan-Meier estimator and Cox regression

Factors associated with duration of dementia in a consecutive series of 103 Alzheimer's disease (AD) cases were studied using the Kaplan-Meier estimator and Cox regression analysis (proportional hazard model). Mean disease duration was 7.1 years (range: 6 weeks-30 years, standard deviation = 5.18); 25% of cases died within four years, 50% within 6.9 years, and 75% within 10 years. Familial AD cases (FAD) had a longer duration than sporadic cases (SAD), especially cases linked to presenilin (PSEN) genes. No significant differences in duration were associated with age, sex, or apolipoprotein E (Apo E) genotype. Duration was reduced in cases with arterial hypertension. Cox regression analysis suggested longer duration was associated with an earlier disease onset and increased senile plaque (SP) and neurofibrillary tangle (NFT) pathology in the orbital gyrus (OrG), CA1 sector of the hippocampus, and nucleus basalis of Meynert (NBM). The data suggest shorter disease duration in SAD and in cases with hypertensive comorbidity. In addition, degree of neuropathology did not influence survival, but spread of SP/NFT pathology into the frontal lobe, hippocampus, and basal forebrain was associated with longer disease duration. © 2014 R. A. Armstrong.

A survey based analysis of IT adoption and 3PLs' performance

Purpose: In today's competitive scenario, effective supply chain management is increasingly dependent on third-party logistics (3PL) companies' capabilities and performance. The dissemination of information technology (IT) has contributed to change the supply chain role of 3PL companies and IT is considered an important element influencing the performance of modern logistics companies. Therefore, the purpose of this paper is to explore the relationship between IT and 3PLs' performance, assuming that logistics capabilities play a mediating role in this relationship. Design/methodology/approach: Empirical evidence based on a questionnaire survey conducted on a sample of logistics service companies operating in the Italian market was used to test a conceptual resource-based view (RBV) framework linking IT adoption, logistics capabilities and firm performance. Factor analysis and ordinary least square (OLS) regression analysis have been used to test hypotheses. The focus of the paper is multidisciplinary in nature; management of information systems, strategy, logistics and supply chain management approaches have been combined in the analysis. Findings: The results indicate strong relationships among data gathering technologies, transactional capabilities and firm performance, in terms of both efficiency and effectiveness. Moreover, a positive correlation between enterprise information technologies and 3PL financial performance has been found. Originality/value: The paper successfully uses the concept of logistics capabilities as mediating factor between IT adoption and firm performance. Objective measures have been proposed for IT adoption and logistics capabilities. Direct and indirect relationships among variables have been successfully tested. © Emerald Group Publishing Limited.

Analysis of Spatial-temporal Dynamics in the System of Economic Security of Different Subjects of Economic Management

The importance to solve the problem of spatial-temporal dynamics analysis in the system of economic security of different subjects of economic management is substantiated. Various methods and approaches for carrying out analysis of spatial-temporal dynamics in the system of economic security are considered. The basis of the generalized analysis of spatial-temporal dynamics in economic systems is offered.

Correlating liposomal adjuvant characteristics to in-vivo cell-mediated immunity using a novel Mycobacterium tuberculosis fusion protein:a multivariate analysis study

Objective In this study, we have used a chemometrics-based method to correlate key liposomal adjuvant attributes with in-vivo immune responses based on multivariate analysis. Methods The liposomal adjuvant composed of the cationic lipid dimethyldioctadecylammonium bromide (DDA) and trehalose 6,6-dibehenate (TDB) was modified with 1,2-distearoyl-sn-glycero-3-phosphocholine at a range of mol% ratios, and the main liposomal characteristics (liposome size and zeta potential) was measured along with their immunological performance as an adjuvant for the novel, postexposure fusion tuberculosis vaccine, Ag85B-ESAT-6-Rv2660c (H56 vaccine). Partial least square regression analysis was applied to correlate and cluster liposomal adjuvants particle characteristics with in-vivo derived immunological performances (IgG, IgG1, IgG2b, spleen proliferation, IL-2, IL-5, IL-6, IL-10, IFN-γ). Key findings While a range of factors varied in the formulations, decreasing the 1,2-distearoyl-sn-glycero-3-phosphocholine content (and subsequent zeta potential) together built the strongest variables in the model. Enhanced DDA and TDB content (and subsequent zeta potential) stimulated a response skewed towards a cell mediated immunity, with the model identifying correlations with IFN-γ, IL-2 and IL-6. Conclusion This study demonstrates the application of chemometrics-based correlations and clustering, which can inform liposomal adjuvant design.

Dimension Reduction of the Explanatory Variables in Multiple Linear Regression

2002 Mathematics Subject Classification: 62J05, 62G35.

Fiscal and organizational determinants of transportation outcomes: A quantitative and qualitative analysis of sustainability factors

Federal transportation legislation in effect since 1991 was examined to determine outcomes in two areas: (1) The effect of organizational and fiscal structures on the implementation of multimodal transportation infrastructure, and (2) The effect of multimodal transportation infrastructure on sustainability. Triangulation of methods was employed through qualitative analysis (including key informant interviews, focus groups and case studies), as well as quantitative analysis (including one-sample t-tests, regression analysis and factor analysis). ^ Four hypotheses were directly tested: (1) Regions with consolidated government structures will build more multimodal transportation miles: The results of the qualitative analysis do not lend support while the results of the quantitative findings support this hypothesis, possibly due to differences in the definitions of agencies/jurisdictions between the two methods. (2) Regions in which more locally dedicated or flexed funding is applied to the transportation system will build a greater number of multimodal transportation miles: Both quantitative and qualitative research clearly support this hypothesis. (3) Cooperation and coordination, or, conversely, competition will determine the number of multimodal transportation miles: Participants tended to agree that cooperation, coordination and leadership are imperative to achieving transportation goals and objectives, including targeted multimodal miles, but also stressed the importance of political and financial elements in determining what ultimately will be funded and implemented. (4) The modal outcomes of transportation systems will affect the overall health of a region in terms of sustainability/quality of life indicators: Both the qualitative and the quantitative analyses provide evidence that they do. ^ This study finds that federal legislation has had an effect on the modal outcomes of transportation infrastructure and that there are links between these modal outcomes and the sustainability of a region. It is recommended that agencies further consider consolidation and strengthen cooperation efforts and that fiscal regulations are modified to reflect the problems cited in qualitative analysis. Limitations of this legislation especially include the inability to measure sustainability; several measures are recommended. ^

Estimation of average annual daily traffic (AADT) using geographically weighted regression (GWR) method and geographic information system (GIS)

Annual average daily traffic (AADT) is important information for many transportation planning, design, operation, and maintenance activities, as well as for the allocation of highway funds. Many studies have attempted AADT estimation using factor approach, regression analysis, time series, and artificial neural networks. However, these methods are unable to account for spatially variable influence of independent variables on the dependent variable even though it is well known that to many transportation problems, including AADT estimation, spatial context is important. ^ In this study, applications of geographically weighted regression (GWR) methods to estimating AADT were investigated. The GWR based methods considered the influence of correlations among the variables over space and the spatially non-stationarity of the variables. A GWR model allows different relationships between the dependent and independent variables to exist at different points in space. In other words, model parameters vary from location to location and the locally linear regression parameters at a point are affected more by observations near that point than observations further away. ^ The study area was Broward County, Florida. Broward County lies on the Atlantic coast between Palm Beach and Miami-Dade counties. In this study, a total of 67 variables were considered as potential AADT predictors, and six variables (lanes, speed, regional accessibility, direct access, density of roadway length, and density of seasonal household) were selected to develop the models. ^ To investigate the predictive powers of various AADT predictors over the space, the statistics including local r-square, local parameter estimates, and local errors were examined and mapped. The local variations in relationships among parameters were investigated, measured, and mapped to assess the usefulness of GWR methods. ^ The results indicated that the GWR models were able to better explain the variation in the data and to predict AADT with smaller errors than the ordinary linear regression models for the same dataset. Additionally, GWR was able to model the spatial non-stationarity in the data, i.e., the spatially varying relationship between AADT and predictors, which cannot be modeled in ordinary linear regression. ^

Fiscal decentralization and development: An analysis of city governments in Argentina and Mexico, 1980--2010

This dissertation examines local governments' efforts to promote economic development in Latin America. The research uses a mixed method to explore how cities make decisions to innovate, develop, and finance economic development programs. First, this study provides a comparative analysis of decentralization policies in Argentina and Mexico as a means to gain a better understanding of the degree of autonomy exercised by local governments. Then, it analyzes three local governments each within the province of Santa Fe, Argentina and the State of Guanajuato, Mexico. The principal hypothesis of this dissertation is that if local governments collect more own-source tax revenue, they are more likely to promote economic development and thus, in turn, promote growth for their region. ^ By examining six cities, three of which are in Santa Fe—Rosario, Santa Fe (capital) and Rafaela—and three in Guanajuato—Leon, Guanajuato (capital) and San Miguel de Allende, this dissertation provides a better understanding of public finances and tax collection efforts of local governments in Latin America. Specific attention is paid to each city's budget authority to raise new revenue and efforts to promote economic development. The research also includes a large statistical dataset of Mexico's 2,454 municipalities and a regression analysis that evaluates local tax efforts on economic growth, controlling for population, territorial size, and the professional development. In order to generalize these results, the research tests these discoveries by using statistical data gathered from a survey administered to Latin American municipal officials. ^ The dissertation demonstrates that cities, which experience greater fiscal autonomy measured by the collection of more own-source revenue, are better able to stimulate effective economic development programs, and ultimately, create jobs within their communities. The results are bolstered by a large number of interviews, which were conducted with over 100 finance specialists, municipal presidents, and local authorities. The dissertation also includes an in-depth literature review on fiscal federalism, decentralization, debt financing and local development. It concludes with a discussion of the findings of the study and applications for the practice of public administration.^

Comparison of Some Improved Estimators for Linear Regression Model under Different Conditions

Multiple linear regression model plays a key role in statistical inference and it has extensive applications in business, environmental, physical and social sciences. Multicollinearity has been a considerable problem in multiple regression analysis. When the regressor variables are multicollinear, it becomes difficult to make precise statistical inferences about the regression coefficients. There are some statistical methods that can be used, which are discussed in this thesis are ridge regression, Liu, two parameter biased and LASSO estimators. Firstly, an analytical comparison on the basis of risk was made among ridge, Liu and LASSO estimators under orthonormal regression model. I found that LASSO dominates least squares, ridge and Liu estimators over a significant portion of the parameter space for large dimension. Secondly, a simulation study was conducted to compare performance of ridge, Liu and two parameter biased estimator by their mean squared error criterion. I found that two parameter biased estimator performs better than its corresponding ridge regression estimator. Overall, Liu estimator performs better than both ridge and two parameter biased estimator.

The mosses of Terra Nova National Park, Eastern Newfoundland, a bryofloristic analysis and interpretation

The known moss flora of Terra Nova National Park, eastern Newfoundland, comp~ises 210 species. Eighty-two percent of the moss species occurring in Terra Nova are widespread or widespread-sporadic in Newfoundland. Other Newfoundland distributional elements present in the Terra Nova moss flora are the northwestern, southern, southeastern, and disjunct elements, but four of the mosses occurring in Terra Nova appear to belong to a previously unrecognized northeastern element of the Newfoundland flora. The majority (70.9%) of Terra Nova's mosses are of boreal affinity and are widely distributed in the North American coniferous forest belt. An additional 10.5 percent of the Terra Nova mosses are cosmopolitan while 9.5 percent are temperate and 4.8 percent are arctic-montane species. The remaining 4.3 percent of the mosses are of montane affinity, and disjunct between eastern and western North America. In Terra Nova, temperate species at their northern limit are concentrated in balsam fir stands, while arctic-montane species are restricted to exposed cliffs, scree slopes, and coastal exposures. Montane species are largely confined to exposed or freshwater habitats. Inability to tolerate high summer temperatures limits the distributions of both arctic-montane and montane species. In Terra Nova, species of differing phytogeographic affinities co-occur on cliffs and scree slopes. The microhabitat relationships of five selected species from such habitats were evaluated by Discriminant Functions Analysis and Multiple Regression Analysis. The five mosses have distinct and different microhabitats on cliffs and scree slopes in Terra Nova, and abundance of all but one is associated with variation in at least one microhabitat variable. Micro-distribution of Grimmia torquata, an arctic-montane species at its southern limit, appears to be deterJ]lined by sensitivity to high summer temperatures. Both southern mosses at their northern limit (Aulacomnium androgynum, Isothecium myosuroides) appear to be limited by water availability and, possibly, by low winter temperatures. The two species whose distributions extend both north and south or the study area (Encalypta procera, Eurhynchium pulchellum) show no clear relationship with microclimate. Dispersal factors have played a significant role in the development of the Terra Nova moss flora. Compared to the most likely colonizing source (i .e. the rest of the island of Newfoundland), species with small diaspores have colonized the study area to a proportionately much greater extent than have species with large diaspores. Hierarchical log-linear analysis indicates that this is so for all affinity groups present in Terra Nova. The apparent dispersal effects emphasize the comparatively recent glaciation of the area, and may also have been enhanced by anthropogenic influences. The restriction of some species to specific habitats, or to narrowly defined microhabitats, appears to strengthen selection for easily dispersed taxa.

Biological factors affecting sea survival of Atlantic salmon Salmo salar L., in Western Arm Brook and an analysis of selection by the commercial fishery of nearby St. Barbe Bay, Newfoundland

The problems faced by scientists in charge of managing Atlantic salmon (Salmo salar) stocks are : i) how to maintain spawning runs consisting of repeat spawners and large multi-sea-winter (MSW) adults in the face of selective homewater and distant commercial fisheries and , ii) how to more accurately predict returns of adults. Using data from scales collected from maiden Atlantic salmon grilse from two locations on the Northern Peninsula of Newfoundland, St. Barbe Bay and Western Arm Brook, their length at smolting was back calculated. These data were then used to examine whether the St. Barbe commercial fishery is selective for salmon of particular smolt age and/or size. Analysis indicated that come commercial fishery selected larger, but not necessarily older adults that those escaping to Western Arm Brook over the period of this study, 1978-1987. It was determined that less than average size smolts survived better than above average size smolts. Slection for repeat spawners, large MSW salmon, and larger grilse has meant reductions in the proportions of these adults in the spawning runs on Western Arm Brook. This may impact the Western Arm Brook salmon stock by increasing the population instability. Sea survival was significantly correlated with selection by the commercial fishery. Characteristics of adults in Western Arm Brook during the period of study (1978-1987) did not help in explaining yearly variation in sea survival. The characteristics of smolts, however, when subjected to multiple regression analysis explained 57.2 percent of the yearly variation in sea survival.

Discrete choice experiment response rates : A meta-analysis

Funding: Verity Watson acknowledges financial support from the Chief Scientist Office of the Scottish Government Health and Social Care Directorates. The funders had no role in the study design; in the collection, analysis and interpretation of data; in the writing of the report; and in the decision to submit the article for publication. Acknowledgements: We thank Marjon van der Pol, Mandy Ryan and Rainer Schulz for helpful comments and suggestions throughout the project. We also thank Karen Gerard and Tim Bolt for comparing the results of our systematic review with a similar systematic review they are conducting at the same time. We would like to thank Douglas Olley for excellent research assistance.