bluuebunny/crossref_metadata_2025_split huggingface dataset:
Three Dimensional (3
D
) Scatterplots
Authors: Wright Daniel B. , Williams Siân E. 
Published: September 2014

Abstract
A three‐dimensional scatterplot displays the relationship between three continuous variables at once. The data are represented as a cloud of points within the three‐dimensional space formed by the three axes of the plot. Such plots can be difficult to interpret and other methods of representing the third variable are generally more effective.
Graphical Presentation of Longitudinal Data
Authors: Wainer Howard , Spence Ian 
Published: September 2014

AbstractThere are some ideas that are so ubiquitous that we cannot imagine the world without them: language and numbers come to mind as immediate examples. Data‐based graphics provide a third example. The graphical representation and communication of data is such a simple and clear process that it is no easier to think of a world before graphs than a world before arithmetic. Yet, graphs were invented and, moreover, invented relatively recently. The very first plots were graphs of longitudinal data. In this essay, we will trace some of the development of graphs for the display of longitudinal data.
Trellis Graphics
Authors: Everitt Brian S. 
Published: September 2014

Abstract

In trellis graphics two or more variables are plotted for (conditioned on) different values or categories of a given variable (or variables). Component graphs for each level of the selected variable are arranged in a single display in order to make comparisons. Many different types of plot lend themselves to this treatment, including
scatterplots
and
three‐dimensional scatterplots
. Trellis graphics are helpful help in understanding both the structure of the data and how well proposed models for the data actually fit.
Mid‐

P

Values
Authors: Berger Vance W. 
Published: September 2014

Abstract

Generally, hypothesis testing is conducted by way of a comparison of the value of a test statistic that summarizes the extent to which the data deviate from the null hypothesis with a reference distribution. The
P
value is the tail area of reference distribution relative to the value of the test statistic. Often, the reference distribution will be discrete, and when it is, the test will be conservative, as only certain
P
values can be attained. This conservatism will result in a loss of power. One approach to dealing with this is the mid‐
P
value, which essentially credits back half of the lost power.
Robust Testing Procedures
Authors: Wilcox Rand R. 
Published: September 2014

AbstractRobust testing procedures are hypothesis testing techniques that are relatively insensitive to violations of assumptions such as normality and homoscedasticity. Major advances on how to study and develop robust testing techniques have appeared during the last forty years. The result has been a deeper understanding of why conventional ANOVA and regression methods can be unsatisfactory, plus a collection of new methods that have practical value.
A Priori v Post Hoc Testing
Authors: Berger Vance W. 
Published: September 2014

Abstract
In many situations, statistical analyses are given more credibility when they are planned prospectively, that is, in advance of the collection of the data. Such prespecified analyses cannot be said to have been suggested by the data, as post hoc analyses would be. A simple measure to prevent the difficult interpretation that can arise from post hoc analyses is to simply avoid them. This approach may be overly conservative, however, as the need may arise to test a hypothesis that the data suggested, and use the same data to test it. Several approaches exist for doing so, although not all of them have been cast as tests of post hoc analyses. In the analysis of variance framework, Fisher's least significant difference (LSD) and Scheffe's method can both be viewed as a means of performing post hoc linear comparisons, although they may not always be explicitly referred to as post hoc analyses. The Smirnov test may be viewed as a method to allow for the data to select the cut point of an ordinal outcome measure. Certain adaptive tests for ordinal data may be viewed as taking the Smirnov test to the next level, and allowing for the optimal combination of cut points, based on the data. The information‐preserving composite end point is a method to allow for data‐dependent outcome measure selection.
Event History Analysis ‐ Models
Authors: Vermunt Jeroen K. , Moors Guy 
Published: September 2014

AbstractThe purpose of event history analysis is to explain why certain individuals are at a higher risk of experiencing the event(s) of interest than others. This can be accomplished by using special types of methods which are usually referred to as hazard models. Two special features of hazard models are that they can deal with censored observations and with covariates that change their values during the observation period.
Classical Test Models
Authors: Muñiz José 
Published: September 2014

Abstract
The term ‘Classical Test Theory’ covers an entire set of psychometric models and procedures whose main objective is to solve the psychometric problems arising in the measurement of variables in the social sciences. Classical test theory permits us to estimate the psychometric properties of the tests, questionnaires, and scales used in social science measurement, guaranteeing that measurements are made with the appropriate scientific and technical rigor. The first work in this area appeared at the beginning of the twentieth century, and by the 1960s, the core of the classical approach was well established. The classical model assumes that a person's empirical score in a test is made up of two additive components, the true score corresponding to the assessed person in that test, and a certain measurement error. From this simple model, and with the addition of some assumptions and the definition of parallel tests, we obtain the principal classical formulas that allow the estimation of the psychometric properties of tests, such as reliability and validity.
Test Bias Detection
Authors: Beller Michal 
Published: September 2014

AbstractMuch of the criticism of psychological tests is derived from the observation that certain groups differ extensively in test performance. However, much of the polemic concerning the issues of test bias rests on two main areas of confusion: (a) differences in test performance among groups are often regarded, in and of themselves, as an indication of test bias, ignoring performance on the external criterion that the test is designed to predict. Often, groups that perform poorly on tests also tend to perform poorly on measures of the criterion. Furthermore, analysis of the relationship between tests and criteria often reveals similar regression lines for the various groups; and (b) the issue of test bias is often confused with the possibility of bias in the content of some individual items included in a test. Group differences in test performance are attributed to the content of specific items, and rather than eliminating problematic items in a systematic way (i.e., checking all items for differential performance), this confusion has, in some cases, led to suggestions of a wholesale rejection of reliable and valid test batteries.
Item Response Theory (IRT) Models for Dichotomous Data
Authors: Hambleton Ronald K. , Zhao Yue 
Published: September 2014

AbstractThis entry provides an introduction to the topic of item response theory. Shortcomings of classical test models are considered first. Second, current item response models for the analysis of dichotomously scored item response data are introduced. Estimation of model parameters, assessment of model fit, and available software, are described next. Finally, applications of item response theory IRT models to test development, item bias, equating, and computer‐adaptive testing are briefly described.
Item Response Theory: Cognitive Models
Authors: Hendrickson Amy B. , Mislevy Robert J. 
Published: September 2014

Abstract
Advances in cognitively based assessments have increased the need for inferences that can address complex task performance and instructionally useful information. These assessments integrate empirically based models of student learning and cognition with methods for designing tasks and observing student performance, with procedures for interpreting the meaning of those observations. Several psychometric models have been introduced to handle claims cast in such information‐processing terms, explicitly modeling performance in terms of theory‐based predictions of performance. Cognitively based item response theory (IRT) models incorporate features of items that influence persons' responses, and relate these features to response probabilities. Examples of IRT models that incorporate cognitively motivated structures are presented, including the Linear Logistic Test Model, multidimensional cognitive IRT models, and latent class models.
Computer‐Adaptive Testing
Authors: Luecht Richard M. 
Published: September 2014

AbstractThis entry presents an overview of computer‐adaptive testing (CAT). The basic CAT algorithm is introduced, followed by a discussion of item response theory (IRT) test information functions and their role in adaptive testing. Issues such as test efficiency and security risks under CAT are also discussed. The entry concludes with a description of four promising CAT variants, including CAT shadow tests, a‐stratified CAT, testlet‐based CAT, and computer‐adaptive multistage testing.
Latent Transition Models
Authors: Pol Frank , Langeheine Rolf 
Published: September 2014

Abstract
Flows between states for discrete periods of time can be described with a Markov chain, a process without memory. More realistic for social science data is a heterogeneous mixture of Markov chains, of movers and stayers. Alternatively, or in conjunction with heterogeneity in the tendency to change, one can take measurement unreliability into account, using latent or indirectly measured Markov models. The basic model variants are explained with data examples. References to overview papers are given.
Optimal Scaling
Authors: Takane Yoshio 
Published: September 2014

Abstract
A data matrix typically represents some kind of relationship between row and column entities. The relationship represented by the data may be described by a model presumed to have generated the data. Observed data, on the other hand, may be measured on one of a variety of scale levels: nominal, ordinal, interval, or ratio. In such cases, we may attempt to do two things simultaneously: (a) we transform the data by a transformation appropriate for the scale level, and (b) we fit a model to the transformed data to account for the data. This process of simultaneous data transformations and data representations is called optimal scaling. In this article, we briefly discuss some of the key features of optimal scaling.
Cross‐Lagged Panel Design
Authors: Kenny David A. 
Published: September 2014

Abstract
The minimal cross‐lagged panel design is two variables measured at two times. Multiple regression analyses, in which the time two measures are regressed on the time one measures, have become the standard method of analyzing the design. Currently, methods to rule out third‐variable causation are little used. Several analysts have argued that two waves are insufficient to obtain much information about how processes unfold over time.
Multivariate Normality Test in Practice
Authors: Keselman H. J. 
Published: September 2014

AbstractMost classical multivariate procedures (e.g., multivariate analysis of variance, multivariate measures of effect size, classification procedures, maximum likelihood factor analysis) require that the data follow a multivariate normal density function. Behavioral science researchers risk committing many more Type I errors, quantifying inaccurately the magnitude of effect sizes, missing treatment effects, establishing inaccurate confidence intervals, and so on by failing to consider whether their data conform to multivariate normality. This paper discusses a number of options for assessing and dealing with nonnormal multivariate data including: (a) testing for univariate normality among thepmeasures, (b) transforming the data to achieve normality, (c) univariate normal probability plots, (d) multivariate measures of skewness and kurtosis, (e) computing squared distance statistics to locate outlying values, and (f) adopting robust estimators with robust test statistics to circumvent the biasing effects of nonnormality.
Independent Pathway Model
Authors: Rijsdijk Frühling 
Published: September 2014

Abstract

While traditional multivariate statistical methods, can describe correlational patterns of a set of variables (e.g., psychiatric symptoms or problem behaviors in children), they cannot provide insight into why certain symptoms or behaviors tend to co‐occur in a population. This can be achieved using methods of
multivariate genetic analysis
. In multivariate genetic models 2 main classes can be distinguished, which differ in the way the common factors are assumed to influence the different observed variables. The way unique factors influence the observed variables is the same in both classes. The first class of models is referred to as
common pathway models
or psychometric models. Common genetic and environmental factors influence all observed variables via a single psychometric factor, or underlying latent liability. The second class of models is referred to as independent pathway or biometric models. The common genetic and environmental factors influence the observed variables directly, without an intermediate higher order factor. As a result, the common genetic and environmental do not necessarily cause similar groupings. This means that different clusters of variables can be identified for shared genetic and environmental effects. For this reason biometric models can yield different results compared to higher order phenotypic factor models, which implicitly assume identical groupings for genetic and environmental effects.
Covariance Matrices: Testing Equality of
Authors: Krzanowski Wojtek J. 
Published: September 2014

Abstract
Parametric multivariate inferential techniques make distributional assumptions about the data, and a common assumption in multisample problems is that dispersion matrices are equal in all the populations from which the samples have come. There is therefore need for a hypothesis test that can check on the adequacy of this assumption. In this article, we provide an appropriate test statistic, give its approximate (large sample) null distribution, illustrate its use on a small data set, and provide some cautionary comments about interpretation.
Mahalanobis Distance
Authors: Huberty Carl J. 
Published: September 2014

Abstract

The Mahalanobis distance is a generalization of the distance concept to
p
‐dimensional correlated data. The measure uses an appropriate covariance matrix to take account of differences in variable variances and correlations between variables. It is frequently employed in multivariate statistical methods, for example, in multivariate analysis of variance, discriminant analysis, and cluster analysis.
Minimum Spanning Tree
Authors: Michailidis George 
Published: September 2014

AbstractA minimum spanning tree (MST) connects all the vertices of a weighted graph by existing edges whose total weight is minimum. It has been the object of intensive study due to its importance in combinatorial optimization. In this paper, we discuss the formulation of the MST problem, present some of the most commonly used algorithms for its construction, and discuss several of its applications in statistics, probability, and data analysis.
Psychophysical Scaling
Authors: Irtel Hans 
Published: September 2014

Abstract
Psychophysical scaling investigates methods for mapping physical stimulus properties into sensation scales. The two major types of subject tasks used are either based on discriminability of rather similar stimulus intensities, or on direct judgments about perceived differences of clearly distinct stimuli. Classical discrimination scaling tries to find a stimulus transformation such that equally discriminable stimuli are mapped onto constant differences on the sensation scale. Direct scaling methods include operations on the set of stimuli that represent certain numerical ratios of perceived stimulus intensity, or require the subject to actually assign these numerical ratios to given pairs of stimuli. In many cases, the power law is an acceptable description of the empirical data.
Scaling of Preferential Choice
Authors: Böckenholt Ulf 
Published: September 2014

Abstract
Scaling models for preferential choice data serve the dual purpose to summarize choice data and to facilitate the forecasting of choices by decision makers facing possibly new or different variants of the choice options. The summary representation obtained by scaling methods can provide useful information for identifying both option characteristics that influence choice and systematic sources of individual differences in the evaluation of these option characteristics. Many scaling models are based on Thurstone's random‐utility approach and allow the analysis of different types of both revealed and stated choice data.
Path Analysis and Path Diagrams
Authors: Boker Steven M. , McArdle John J. 
Published: September 2014

Abstract
Path analysis refers to the calculation of moment structures within and between variables, for example, covariances or correlations, implied by a set of simultaneous linear regression equations – one type of structural equation model. Path diagrams of structural equation models offer a graphical representation with exact one‐to‐one mapping to the simultaneous linear regression equations. Path analysis allows one to decompose the covariance between two variables in a structural equation model into additive components, thus helping to understand how the interrelationships between many variables in a model predict the covariance between two selected variables. By performing path analysis calculations on all variables and pairs of variables in a model, one may calculate the expected moment structure implied by that model. Path analysis preceded and led to the development of modern structural equation modeling methods of parameter estimation.
Random Forests
Authors: Cutler Adele 
Published: September 2014

Abstract
Random forests are collections of trees that give accurate predictions for regression, classification, and clustering problems. They handle missing values, can be used for continuous and/or categorical input variables, and allow class weighting to adjust for unequal sampling schemes. Random forests do not overfit the data so they can be used for problems in which the number of input variables is much larger than the number of observations. Random forests provide measures of variable importance and proximities that can be used to interpret the data.
Robust Statistics for Multivariate Methods
Authors: Victoria‐Feser Maria‐Pia 
Published: September 2014

AbstractRobust statistics deals with slightly misspecified models. When the data have not been generated exactly from the assumed models, robust procedures are by definition not (or very little) influenced by these model deviations. This is, in general, not the case with classical procedures such as least squares, maximum likelihood, and so on. Numerous multivariate models are based on the multivariate normal distribution, for which a relatively large number of robust procedures have been proposed. Most of the robust estimators are based on weighted means and covariances, and the weights are decreasing functions of the Mahalanobis distances. For nonnormal multivariate models, weights are more difficult to define, and more research is needed to develop robust procedures in these cases.
Factor Score Estimation
Authors: Hershberger Scott L. 
Published: September 2014

AbstractFactors scores are measures of principal components or common factors. Under the principal components model, the factor scores are uniquely determined; under the common factor model, they are not. In the latter situation, the factor scores are indeterminate, potentially having an infinite number of solution sets, and thus their true values can only be estimated. Three methods of factor score estimation are discussed: (a) regression, (b) Bartlett's method, and (c) Anderson and Rubin's method. Although the properties and values of the factor score estimates produced by the three methods differ, the estimates are in general highly correlated.
Two‐Way Factorial: Distribution‐Free Methods
Authors: Toothaker Larry E. 
Published: September 2014

AbstractNonparametric and resampling approaches for the two‐way factorial design include permutation tests, bootstrap tests, the rank transform, aligned ranks tests, tests on trimmed means, and a rank‐based ANOVA method that allows heteroscedastic variances, one known as the BDM method, or combinations of these such as bootstrap tests on trimmed means. Research shows the BDM method, parametric tests on trimmed means, and bootstrap tests on trimmed means to be the most promising methods in terms of α‐control and power.
Kernel Smoothing
Authors: Hazelton Martin L. 
Published: September 2014

AbstractKernel smoothing is a nonparametric technique for exposing structure or trend in data. It can be applied in a wide variety of settings, including the problems of density estimation and nonparametric regression on which we focus attention. In each case, the performance of kernel methods is highly dependent on the choice of bandwidth, a parameter that controls the amount of smoothing applied to the data.
Runs Test: Examples
Authors: Lunneborg Clifford E. 
Published: September 2014

Abstract
The Wald–Wolfowitz runs test dates from 1940, making it one of the earliest nonparametric tests. It provides a test of a common distribution for two independent random samples. However, the test has low power relative to such alternatives as the Kolmogorov–Smirnov or Cramér–von Mises two‐sample tests and has declined in popularity.
Kolmogorov–Smirnov Test: Overview
Authors: Berger Vance W. , Zhou YanYan 
Published: September 2014

Abstract
While often confused, the Kolmogorov–Smirnov test and the Smirnov test are actually distinct. Specifically, the Kolmogorov–Smirnov test is used to test the goodness of fit of a given set of data to a theoretical distribution, making this a one‐sample test. In contrast, the Smirnov test is a two‐sample test, used to determine if two samples appear to follow the same distribution. The intuition behind the two tests is the same, however, in that both compare cumulative distribution functions, either two empirical cumulative distribution functions for the two‐sample Smirnov test, or one empirical cumulative distribution function and one known cumulative distribution function for the one‐sample Kolmogorov–Smirnov test.
Multiple Comparison Tests: Nonparametric and Resampling Approaches
Authors: Keselman H. J. , Wilcox Rand R. 
Published: September 2014

Abstract
Resampling‐based multiple comparison procedures attempt to circumvent the deleterious effects of nonnormality and/or variance heterogeneity by utilizing empirical rather than theoretical sampling distributions of test statistics. In particular, the original observed data are randomly resampled in order to build an empirical sampling distribution for the test statistic, and the observed test statistic can then be compared to quantiles in this empirical distribution to determine statistical significance or to compute confidence intervals. We present resampling test statistics that can be used to test pairwise and complex contrasts among treatment group trimmed means. Trimmed means are used to circumvent problems due to nonnormality. Moreover, the test statistic is designed to deal with variance heterogeneity. Combining robust estimators (trimmed means) with a heteroscedastic test statistic (e.g., Welch's (1938) two‐sample test) and applying a bootstrap method results in test statistics that should be robust to the combined effects of nonnormality and variance heterogeneity.