bluuebunny/crossref_metadata_2025_split huggingface dataset:
Factor Analysis: Multiple Groups
Authors: Little Todd D. , Slegers David W. 
Published: September 2014

Abstract
The general factor model, when extended to include mean‐level information, is a very powerful tool for cross‐group and longitudinal comparisons. The multiple‐group mean and covariance structures (MACS) approach is particularly useful for making cross‐group (or cross‐time) comparisons because it allows for (a) simultaneous estimation of all parameters in each group (or at each occasion) and (b) direct statistical comparisons of the estimated parameters across the groups (or occasions). Because the means of measured indicators are included explicitly in the analyses, they provide a basis to make a very strong test of the validity of construct comparisons (i.e., measurement equivalence) across groups and across time. Specifically, strong factorial invariance indicates that constructs are fundamentally similar in each group or across time (i.e., comparable) and hypotheses about the nature of possible group‐ or time‐related influences can be meaningfully tested on any of the constructs' basic moments (means, variances, or covariances) across time or across each group whether the groups are defined on the basis of culture, gender, or any other grouping criteria.
Structural Equation Modeling: Checking Substantive Plausibility
Authors: Jaffe Adi , Hershberger Scott L. 
Published: September 2014

Abstract
The process of construct validation involves a series of three steps, namely, concept definition, concept operationalization, and empirical confirmation. These steps lead to specifying and confirming a nomological network for the construct to be validated. Structural equation modeling efficiently confirms the substantive plausibility of the nomological network.
Fuzzy Cluster Analysis
Authors: Manton Kenneth G. , Lowrimore Gene , Yashin Anatoli , Kovtun Mikhail 
Published: September 2014

AbstractUsually in cluster analysis, an object is a member of one and only one cluster, a property described as ‘crisp’ membership. Fuzzy cluster analysis allows an object to have partial membership in more than one cluster. Selecting a good membership function is important to the success of the methods. The Grade of Membership model – which has a long history of usage in other contexts – is proposed as a straightforward way of performing fuzzy cluster analysis. The Grade of Membership model is illustrated by an example involving gene expression data.
Pattern recognition and classification
Authors: Kuncheva Ludmila I. , Whitaker Christopher J. 
Published: September 2014

Abstract

Pattern recognition concerns assigning objects to classes. The objects are described by features (variables or measurements) organized as
p
‐dimensional points in some feature space. A classifier is a formula, an algorithm or a technique that can assign a class label to any given point in the feature space. Pattern recognition comprises supervised learning (predefined class labels) and unsupervised learning (unknown class labels). Supervised learning includes choosing a classifier model, training and testing the classifier using a data set and selecting the relevant features. Unsupervised learning is usually approached by cluster analysis. Multiple classifier systems or classifier ensembles are a recent branch of pattern recognition whereby the outputs of several classifiers (regarded as experts) are combined for improved accuracy.
Procrustes Analysis
Authors: Borg Ingwer 
Published: September 2014

Abstract
Procrustes analysis is concerned with fitting one or more configurations of points to some target configuration. In the simplest case, one configuration is rigidly rotated and/or reflected in space so that it matches a fixed target as closely as possible. A common application is to assess how closely the solution of a factor analysis for one sample corresponds to the solution for another sample or to a hypothesized pattern, respectively. The fitting problem can be generalized in several ways by admitting wider classes of transformations that may indicate empirically meaningful patterns of difference among the configurations.
Projection Pursuit‐A Brief Introduction
Authors: Stuetzle Werner 
Published: September 2014

AbstractProjection pursuit was conceived as a method for finding ‘interesting’ one‐ or two‐dimensional projections of multivariate data revealing unanticipated structure such as clusters, skewness, or presence of outliers. The initial idea of exploring high‐dimensional data using low‐dimensional marginals was later extended into a general paradigm for modeling multivariate data that has been applied to density estimation, regression, and classification.
Structural Equation Modeling and Test Validation
Authors: Zumbo Bruno D. 
Published: September 2014

AbstractThe use of structural equation modeling in validity research is described and demonstrated in the context of an example wherein a researcher is providing construct and predictive validity evidence for inferences made from scores on the Center for Epidemiologic Studies Depression (CES‐D) scale. In this light, current concepts of validity are briefly overviewed and contrasted with those found in many research methods texts. In addition, two special cases of the generalized linear structural equation model, confirmatory factor analysis and multiple indicators multiple causes models for ordinal items, that are particularly well suited for measurement validity research, are introduced.
Misclassification Rates
Authors: Krzanowski Wojtek J. 
Published: September 2014

Abstract
This article surveys the ways in which the error rate incurred by a classifier, that is, the proportion of future incorrect classifications, can be estimated. Theoretically derived rates depend heavily on distributional assumptions; so, in practice, data‐based estimates are generally preferred. Methods based on resubstitution, test‐set estimation, cross‐validation, jackknifing, and bootstrapping are described. The phenomenon of tuning the classifier by using one of these methods to optimize its performance is also explained, and the dangers of overoptimism in assessing error rates of a tuned classifier are highlighted. Interval estimation of error rates is briefly discussed, and an illustrative example is provided.
Structural Equation Modeling: Nontraditional Alternatives
Authors: Rigdon Edward E. 
Published: September 2014

AbstractA variety of techniques exist for modeling structural relations in situations where researchers' goals or data do not fit the demands of conventional Structural Equation Modeling. Researchers whose theory or data do not meet the rigorous standards of conventional Structural Equation Modeling (SEM) may employ Partial Least Squares (PLS), a technique based on principal components rather than common factors. Researchers seeking to find models, rather than testing a prespecified model, might employ Tetrad. Confirmatory Tetrad Analysis (CTA) allows researchers to test structural equation models without estimating model parameters. HyBlock conducts structured exploratory factor analysis, allowing researchers to model structural relations based on observed variables that are factorially complex.
Within Case Designs: Distribution Free Methods
Authors: Lix Lisa M. , Keselman H. J. 
Published: September 2014

AbstractIn within‐case designs, subjects are measured repeatedly over time or across multiple experimental conditions. Univariate and multivariate parametric procedures for testing within‐case effects may lose statistical power under departures from a multivariate normal distribution. Nonparametric procedures based on rank scores or bootstrapping are useful alternatives for testing within‐case effects when the data are skewed or have heavy tails.
Confidence Intervals: Nonparametric
Authors: Garthwaite Paul H. 
Published: September 2014

Abstract

These procedures for forming confidence intervals are attractive because they require weaker assumptions than parametric methods. Several of the procedures exploit the relationship between hypothesis tests and confidence intervals and these require hypotheses to be found that give specified
P
values. Finding the appropriate hypotheses can be computationally demanding, but for some problems there are efficient search techniques.
Rank Based Inference
Authors: Hettmansperger T. P. , McKean J. W. , Sheather S. J. 
Published: September 2014

Abstract
The use of ranks has a long history stretching back to 1945 with the seminal work of Wilcoxon. Early nonparametric rank tests were developed for the basic one‐ and two‐sample designs and then extended to the one‐ and two‐way layouts. These tests are popular because of their nonparametric property along with their good efficiency and robust properties. In this entry, we describe and illustrate how to extend rank‐based methods to the general linear model including regression, analysis of variance, and analysis of covariance. We also describe a coefficient of determination that is useful when assessing the fit of a model to the data.
Nonparametric Item Response Theory Models
Authors: Sijtsma Klaas 
Published: September 2014

Abstract
Nonparametric item response theory serves two purposes. The first is to provide a framework for flexible, exploratory analysis of item scores. Several procedures are available for investigating the dimensionality of test data. Estimated item response functions are checked for monotonicity and other order restrictions. Nonparametric item response models imply ordinal scales for persons and items. Ordinal scales are sufficient for many practical applications in psychology, education, sociology, and so on. The second purpose is to provide a mathematical framework for studying the potentials and the limitations of item response theory. Observable data properties implied by nonparametric item response theory may also be valuable for fitting parametric models, and relationships between item response models may be clarified. Present research in nonparametric IRT involves preference data analysis and Bayesian methods for model fitting.
Pitman Test: Introduction
Authors: Lunneborg Clifford E. 
Published: September 2014

Abstract
The two‐group Pitman Test, proposed by E. J. G. Pitman in 1937, is one of the earliest nonparametric or distribution‐free tests. The test has applications both to random samples drawn independently from two (large) populations, and to the randomization of available cases between two treatments. Although the mechanics of the two applications are identical, the hypotheses tested and the interpretation of those tests differ markedly between the two applications.
Kendall's Tau: Basic
Authors: Kornbrot Diana 
Published: September 2014

Abstract

Kendall's tau, τ, is a correlation measure of association based on ranks of scores rather than raw scores. It is based on the number of swaps needed to put the second variable into exactly the same or exactly the opposite order to the first variable. It is applicable if either or both variables are direct rankings, or only
ordinal
. It is also applicable when both variables are metric but not
normally distributed
, or when the relation between the variables is monotonic, but nonlinear. Methods for calculating τ and procedures for hypothesis testing are provided. Kendall's τ is compared with Spearman's ρ and Pearson's
r
.
MEstimators of Location
Authors: Wilcox Rand R. 
Published: September 2014

AbstractAn approach to developing measures of location is to search for some value, sayc, that is close to the values in a sample, sayX1, …,Xn. If we measure closeness with the sum of squared differences between each of thenobservations andc, this leads to takingcto be the sample mean. But the sample mean can perform poorly in terms of achieving a small standard error when sampling from nonnormal distributions. M‐estimators attempt to correct this problem by replacing squared error with some other measure of closeness. Certain M‐estimators have standard errors that compete well with the sample mean under normality, but they continue to perform well in situations in which the sample mean performs poorly.
Normal Scores & Expected Order Statistics
Authors: Lunneborg Clifford E. 
Published: September 2014

Abstract
Rank tests replace raw scores with their ranks prior to computing a test statistic and its reference distribution. This use of ranks is advocated where the normality of the raw score observations is in doubt. An alternative approach is to replace the raw scores with values that resemble observations from a normal distribution more closely than do the integer‐spaced ranks, while taking the order of the raw scores into account. Permutation tests that are carried out following such a rank‐preserving transformation of the data is called a normal scores test.
Power and Sample Size in Multilevel Linear Models
Authors: B. Snijders Tom A. 
Published: September 2014

Abstract
Sample size determination in multilevel designs requires attention to the fact that statistical power depends on the total sample sizes for each level. It is usually desirable to have as many units as possible at the top level of the multilevel hierarchy. Some formulas are given to obtain insight in the design aspects that are most influential for standard errors and power.
Repeated Measures Analysis of Variance
Authors: Everitt Brian S. 
Published: September 2014

Abstract
Repeated measures data arise when each participant in a study has measurements of a response variable of interest made under several different conditions, on different occasions, and so on. A univariate analysis of variance approach can be used if the covariance structure of the repeated measurements satisfies a condition known as sphericity, otherwise a multivariate analysis of variance approach may be needed.
Analysis of Variance: Cell Means Approach
Authors: Kirk Roger E. , Bekele B. Nebiyou 
Published: September 2014

Abstract
The two forms of the cell means model are described: the unrestricted model and the restricted model. Computational procedures are presented for a completely randomized design, randomized block design, and completely randomized factorial design. Computational procedures also are presented for a completely randomized analysis of covariance (ANCOVA) design. The relative merits of the cell means model and the classical analysis of variance (ANOVA) model approaches to analysis of variance are discussed.
Direct and Indirect Effects
Authors: Muller Dominique , Judd Charles M. 
Published: September 2014

Abstract

A three‐variable model with one independent variable (

X

), one dependent variable (

Y

), and a possible mediator (or suppressor) can be decomposed into three different types of effects. The first one is the indirect effect which is the portion of the relationship between

X

and

Y

that goes through the mediator. The second one is the direct effect which is the portion of the relationship between

X

and

Y

that does not go through the mediator. And, finally, the total effect is the sum of both the direct and the indirect effects.
Probits
Authors: Stefanescu Catalina , Berger Vance W. , Hershberger Scott L. 
Published: September 2014

AbstractThe Probit model is frequently used as a transformation of probabilities from an observed categorical variable's distribution into scale values. These scale values (‘probits’) are derived from the normally distributed, continuous latent variable that is assumed to underlie an observed categorical variable. Probit models are especially useful for modeling censored or truncated variables. Binary, ordinal, and multinominal categorical variables can be modeled by probit transformations.
Confounding in the Analysis of Variance
Authors: Bogartz Richard S. 
Published: September 2014

Abstract
Unintentional and intentional confounding in the analysis of variance is discussed. Some different kinds of unintentional confounding that can occur in between‐subject designs, within‐subject designs, and mixed designs are considered. The usefulness of losing information to conserve resources by intentionally confounding variables gives rise to split‐plot, confounded factorial, and fractional replication designs. An example from infancy research is provided.
Dropouts in Longitudinal Studies: Methods of Analysis
Authors: Little Roderick J. 
Published: September 2014

Abstract
The statistical analysis of repeated‐measures data when some participants drop out prior to the end of the study has been reviewed. Methods considered include complete‐case analysis, where only the cases that are followed to the end of the study, are analyzed; imputation methods that fill in values after drop out, and multiple imputation, a refinement that accounts for imputation uncertainty; and methods that can be applied to the nonrectangular data set that arises from the missing data, including maximum likelihood for linear and nonlinear mixed models. Methods of analysis when the missing data are not missing at random are also reviewed.
Interaction Effects
Authors: Aiken Leona S. , West Stephen G. 
Published: September 2014

Abstract
Interaction effects refer to the effects of particular unique combinations of variables on an outcome that would not be expected from their average effects. When two variables interact, the conditional effect of one variable at a particular value of the other variable depends on the specific value of the other variable. One variable moderates the effect of the other variable. When variables interact, the effects of the two variables in combination are nonadditive; their simultaneous effect is not the sum of their individual effects. Continuous and categorical variables may interact; a variety of patterns of interactions are possible.
Centering in Linear Multilevel Models
Authors: Leeuw Jan 
Published: September 2014

Abstract
This entry considers the effects of centering the predictors in a multilevel regression analysis. It is shown that grand mean centering of first‐level predictors does not change the model or the fit, and merely leads to a different parametrization. Within‐group centering of first‐level predictors does lead to an essentially different model, and not to a simple reexpression of the same model.
Least Squares Estimation
Authors: Geer Sara A. 
Published: September 2014

Abstract

The method of least squares is about estimating parameters by minimizing the squared discrepancies between observed data on the one hand, and their expected values on the other. It is commonly used in the context of a regression model, where one observes pairs of variables (
X
,
Y
), with
X
a covariable and
Y
a response variable. The expectation of the response variable
Y
given the covariable
X
is modeled as a function
f
β
(
X
) depending on parameters β.

We present an explicit expression for the least squares estimator of β in the linear regression model, and also give its covariance matrix. The calculations are illustrated with a numerical example. The F statistic for testing linear hypotheses on β is also given. We conclude with some extensions.
Eta and Eta Squared
Authors: Field Andy P. 
Published: September 2014

Abstract

Eta squared (η
2
) is an elegant and simple way to express an effect size (typically the effect of manipulations across several groups). Put simply, it is the ratio of variability explained by the manipulations (the group means) to the total variability. It is an accurate measure for the sample, but is a biased estimate of the effect in the population.
Residual Plot
Authors: Miles Jeremy 
Published: September 2014

Abstract
In a regression analysis, a number of assumptions about the data must be made and tested. One of the most powerful ways to do this is to produce a range of graphs of the residuals from the regression. Valuable information may be gained from examining a histogram of the residuals, a plot of the residuals against time, and a plot of the residuals against the predicted values from the regression equation.
Slicing Inverse Regression
Authors: Chen Chun‐Houh 
Published: September 2014

AbstractSliced inverse regression (SIR) is a computationally simple and fast method for reducing the dimension of the explanatory variablesxin regression problems. SIR does the following: (a) it determines the dimension of a subspace spanned by the linear combinations ofxthat contains all information needed for describing the relationship betweenxand the output variableY; (b) it assesses the significance of the contribution from each input variable to dimension reduction; (c) it provides a foundation for further exploratory graphical analysis and nonparametric regression. (Color versions of the figures presented in this article can be obtained fromhttp://gap.stat.sinica.edu.tw)
Intrinsic Linearity
Authors: Goldsmith L. Jane , Berger Vance W. 
Published: September 2014

Abstract
In some cases in which a response variable is related to one or more predictor variables through a nonlinear relationship, suitable transformations of the response variable, predictor variables, parameters, or various combinations can lead to a linear model, thereby enabling the use of the powerful and efficient theory of linear models for estimation and prediction. Care must be taken with the use of such transformations to ensure that the resulting linear model has an error term of the appropriate, additive form.
Partial Least Squares‐Background and Applications
Authors: Sampson Paul D. , Bookstein Fred L. 
Published: September 2014

Abstract
Partial Least Squares (PLS), as described in this article, is a method of statistical analysis for characterizing and making inferences about the relationship(s) among two or more causally related blocks of variables in terms of pairs of latent variables. The methods of computation and inference for 2‐block PLS analysis are described and illustrated for an application in behavioral teratology relating a block of 9 subscale scores on the WAIS‐R IQ test measured on 419 subjects to a block of 13 measures of prenatal maternal alcohol consumption.
Nonrandom Samples
Authors: Wainer Howard 
Published: September 2014

Abstract
Drawing causal inferences from observational studies in which the data are not generated from a process of random allocation to treatment yields the often‐likely outcome of substantial nonrandom error. In this essay, we illustrate several examples of the kind and magnitude of such errors that have been made in the past and indicate how, if random assignment to treatment is not possible, we can at least estimate the level of our uncertainty.
Stratification
Authors: Berger Vance W. , Zhang Jialu 
Published: September 2014

Abstract
When a population is composed of several subpopulations and the subpopulations vary considerably on the factors in which we are interested, stratification can reduce the variability of the estimates by dividing the population into relatively homogeneous subgroups, and treating each subgroup separately. This concept can be applied for stratified sampling (sampling from within each stratum) and stratified random allocation of subjects that need not constitute a random sample, stratified or not.
Telephone Surveys
Authors: Driskell Robyn Bateman 
Published: September 2014

Abstract
Telephone survey methodology is often the preferred approach to surveying as it is a valid and reliable means of collecting data. The advantages of telephone surveys include cost efficiency, reduced survey time, and the ability to reach a large, representative sample. With the recent technologies of random‐digit dialing and computer‐assisted telephone‐interviewing, telephone survey methodologies have enhanced and improved. While some limitations exist in telephone surveys, the advantages outweigh the disadvantages, resulting in an efficient and effective method for collecting data.