bluuebunny/crossref_metadata_2025 huggingface dataset:
History of the Control Group
Authors: Dehue Trudy
Published: September 2014

In contemporary behavioral and social research, scientific experimentation means comparing experimental groups to control groups and establishing the statistical significance of the resulting averages. Yet, this design is of a rather recent date. From the early nineteenth century, scientific experimentation with human beings has been a much debated topic. The rule of comparing groups, however, did not appear in methodological manuals until the second decade of the twentieth century. This article presents a history of the control group. It first discusses nineteenth‐century methodological views on human science experimentation, and explains why the notion of the control group could not be conceived at the time. Next, it describes and explains the introduction of control groups in the course of the twentieth century. By analyzing the nineteenth‐century values that excluded group comparison, it aims to identify the twentieth‐century principles endorsing it.
Graphical Methods Pre‐20th Century
Authors: Smith Laurence D.
Published: September 2014

Despite their utility for analyzing and presenting data, the use of graphs in science is a relatively late development and their emergence through history has been uneven and contested. Modern statistical graphics date largely to the pioneering work of William Playfair in the late eighteenth century. The gradual spread of graphical methods in the early nineteenth century was slowed by various antigraph prejudices, but eventually culminated in their enthusiastic reception during the second half of that century. During the Golden Age of graphics, graphs were used extensively in fields ranging from demography to laboratory physiology. Hailed as the universal language of science, graphs underwent a proliferation of novel formats, and they figured crucially in a number of scientific discoveries. The behavioral scientists of that period – including many of psychology's founding figures – made sophisticated applications of graphical methods, but such methods would be eclipsed by the rise of inferential statistics in the behavioral sciences after 1900.
History of Surveys of Sexual Behaviour
Authors: Everitt Brian S.
Published: September 2014

According to psychiatrist Anthony Storr, sexual intercourse is one of the most natural and certainly the most rewarding and the most life‐enhancing of all human experiences'. Few of us would argue with that, but although sex plays a vital part in our lives, it has for long periods been associated with guilt and shame, rather than enjoyment. Perhaps this explains why it is only in the last hundred years or so that psychologists, biologists, and others have tried to discover the truth about human sexual behavior in a scientific and objective manner. One of the main tools used in such investigations has been the sample survey, and this paper presents a brief (and therefore necessarily incomplete) history of surveys about sex.
J
onckheere–Terpstra Test
Authors: Lunneborg Clifford E.
Published: September 2014

For the one‐way design, the Jonckheere‐Terpstra procedure tests the null hypothesis of no difference in response magnitude across treatments against an ordered alternative, that response magnitude increases over a pre‐specified ordering of the
treatments. Where the treatment levels can be ordered according to expected response magnitude (e.g., drug dosages, stimulus intensities, and hours of practice), the Jonckheere–Terpstra test (1954) employs a more coherent, directional alternative hypothesis, that is, the response magnitude does not decrease for any treatment level increase and actually increases for one or more treatment level increases.
Confidence Intervals
Authors: Dracup Chris
Published: September 2014

In estimating a population parameter from sample data, it is more informative to provide a range of ‘plausible’ parameter values rather than a one‐point estimate. A 95% confidence interval contains those values of the population parameter that would not be rejected at the 0.05 significance level by a statistical test applied to the sample data. In the long run, such intervals should provide 95% ‘coverage,’ with 95% of them including their true population value (assuming the data meet any distribution assumptions). Topics covered include the construction of confidence intervals for means, proportions, and mean differences; the effects of discrete and nonsymmetrical sampling distributions; central and noncentral intervals; bootstrapped intervals and the Bayesian approach.
Sphericity Test
Authors: Keselman H. J.
Published: September 2014

Classical test statistics, such as the usual
F
test, for the analysis of repeated measures or longitudinal treatment effects, will provide accurate assessments (i.e., correct Type I error probabilities) of null hypotheses when their assumptions of independence, normality, and homogeneity hold. Homogeneity in this context is referred to as sphericity or circularity. This paper enumerates the validity assumptions for simple‐order and higher‐order repeated measures designs, as well as discussing why for many behavioral science applications sphericity will not be satisfied, and concludes by noting procedures that researchers can adopt to circumvent the biasing effects of nonsphericity.
Power
Authors: Howell David C.
Published: September 2014

The power of a test refers to the probability with which that test will reject the null hypothesis in those situations in which it is false. This article focuses on the variables that influence power and discusses the different conceptions of power.A prioripower is computed before the experiment is conducted and is critical to selecting an appropriate sample size. Retrospective power is calculated on the basis of the completed study. This article outlines a number of concerns with retrospective power. Compromise power is based on the relative seriousness of Type I and Type II errors, and should be considered seriously for exploratory research. Finally, the article discusses the importance of considering confidence intervals on effect sizes, in addition to power.
Binomial Confidence Interval
Authors: Lunneborg Clifford E.
Published: September 2014

The binomial parameterp, the proportion of successes in a population, has as its point estimator the proportion of successes observed in a random sample from that population,p* = s/n. A confidence interval for the binomial parameter broadens that point estimate out, reflecting the uncertainty associated with the limited size of the sample.
Catalogue of Parametric Tests
Authors: Clark‐Carter David
Published: September 2014

Parametric tests derive their probability from probability distributions such as the normal distribution and thetdistributions. They make more assumptions about the nature of the population from which samples have been drawn than their nonparametric equivalents. However, when the assumptions of a parametric test are met, the test will have more statistical power than a nonparametric equivalent.
Sample Size and Power Calculation
Authors: Murphy Kevin R.
Published: September 2014

The precision with which sample statistics estimate population parameters is strongly influenced by the number of observations. Statistical power analysis provides a method of determining the sample sizes needed to control for errors in hypothesis testing. Power is largest when the effects being studied are large and the sample is large.
T
ype
I
,
T
ype
II
and
T
ype
III
Sums of Squares
Authors: Hershberger Scott L.
Published: September 2014

Whenever factorial designs have equal cell frequencies, the factors are orthogonal. Although orthogonal factors are not required, orthogonal factors permit a unique decomposition of the variance in the dependent variable. If cell frequencies vary, or there are empty cells, the factors are nonorthogonal: The variance decomposition of the dependent variable differs depending on which of Type I, II, III, or IV sums of squares is used for the analysis.
Sensitivity Analysis in Observational Studies
Authors: Rosenbaum Paul R.
Published: September 2014

In an observational study, subjects are not randomly assigned to treatment or control, as they would be in a controlled clinical trial. As a consequence, differing outcomes in treated and control groups may not reflect effects of the treatment, but rather some way the groups were not comparable prior to treatment, that is, some hidden bias. A sensitivity analysis appraises how the conclusions of a study might be altered by hidden biases of various magnitudes.
Additivity Tests
Authors: Karabatsos George
Published: September 2014

Additive linear models are ubiquitous in applied areas of behavioral statistics, and so it is often important to test whether data fit the assumption of additivity. In a test of additivity, the null hypothesis is that a dependent variable is an additive, noninteractive function of two (or more) independent variables, while the alternative hypothesis of nonadditivity is characterized by one or more interactions between the independent variables. It is possible to test for additivity in the context of Analysis of Variance (ANOVA), while the theory of Additive Conjoint Measurement provides a more general basis for testing additivity.
Directed Alternatives in Testing
Authors: Cohen Arthur
Published: September 2014

Consider a hypothesis‐testing problem concerned with a one‐dimensional parameter θ. In testing a null hypothesis
H
 : θ = θ

o

, a two‐sided alternative is
K
 : θ ≠ θ

o

. A one‐sided alternative is
K
 : θ > θ

o

. This latter alternative is appropriate when it is reasonably certain that θ cannot be less then θ

o

. The advantage of posing a one‐sided alternative is that the appropriate one‐sided test is much more powerful than the corresponding two‐sided test. The idea of one‐sided and two‐sided alternatives extends to the case of testing a
k
‐dimensional parameter
θ
. If the null hypothesis is
H
 : 
θ
 = 
θ
o
, then the analogue to the two‐sided alternative is
K
 : 
θ
 ≠ 
θ
o
. This latter alternative is said to be unrestricted or not directed. An example of the analogue to the one‐sided alternative is
K
 : θ

i

 ≥ θ

io

, for
i
 = 1, …,
k
, with strict inequality for at least one index
i
. Here
θ
 = (θ
1
, …θ

k

). Such an alternative is called a
directed alternative
.

We introduce the notion of directed alternatives for multidimensional parameters. Among the special cases treated are the simple order alternative in which parameters are nondecreasing, the tree order alternative in which case one mean parameter is assumed to be less than or equal to each of the other mean parameters, and the stochastic order alternative in which one multinomial distribution is more concentrated at higher categories than another distribution. We indicate appropriate tests for these directed alternatives.
Simple V Composite Tests
Authors: Macdonald Ranald R.
Published: September 2014

If a null hypothesis takes the form θ = 
c
, where c is a constant and θ is the only unknown parameter in the supposed chance probability distribution, then this hypothesis is called a simple hypothesis. Where the chance distribution has more than one unknown parameter, the null hypothesis is said to be composite. Often, but not always, composite hypotheses are phrased in terms of several parameters. Examples include θ
1
 = 
c
1
, θ
2
 = 
c
2
, …θ

k

 = 
c

k

or θ
1
 = θ
2
 = θ
3
 = ⋯ = θ

k

. Where this is the case, the overall null hypothesis can be split into separate testable component hypotheses and this raises multiple testing issues.
C
ochran's
C
Test
Authors: Mair Patrick , Eye Alexander
Published: September 2014

Cochran's C test is used to test the assumption of variance homogeneity of the residuals in the analysis of variance. The test statistic is a ratio that relates the largest empirical variance of a particular treatment to the sum of the variances of the remaining treatments. The theoretical distribution with the corresponding critical values can be specified.
Test Dimensionality: Assessment of
Authors: Gessaroli Marc E. , Champlain Andre F.
Published: September 2014

The ability to properly assess the dimensionality of a set of item responses is essential in psychometrics. Many popular psychometric methods using item response theory (IRT) such as item calibration and test equating assume that there is a single latent trait underlying the responses. As well, the popularity of multidimensional models has increased. Furthermore, test dimensionality is directly linked to the structural aspect of the construct validity of a test. History has shown some confusion in the definition of dimensionality and in the methods to assess it. Recent literature relates both the definition of dimensionality and its methods of assessment to the concepts of local independence and essential independence. This entry provides an overview of these definitions and of the more current methods of dimensionality assessment.
Computer‐Based Test Designs
Authors: Zenisky April L.
Published: September 2014

Among the decisions to be made in implementing a computer‐based test, the choice of test design is one of the most important. A test design is the manner by which individual items are selected for presentation to examinees during administration. The importance of evaluating test design options is critical because it not only concerns test administration but also basic activities in the test development process and the quality and precision of scores to be obtained for a specified testing purpose. Essentially, conceptualizing the test design options for computerized testing first hinges on the property of being adaptive or not, and then there are varied approaches within each of those two groupings. The purpose of this entry is to provide an overview of selected test designs, adaptive and otherwise, while highlighting certain measurement advantages and concerns associated with each.
Computer‐based Testing
Authors: Davey Tim
Published: September 2014

Most broadly defined, computer‐based tests (CBTs) include not just tests administered on computers or workstations but also exams delivered via telephones, PDAs, and other electronic devices. There have been three main reasons for test developers to move beyond conventional paper and pencil administration. The first is to change the nature of what is being measured. The second is to improve measurement precision or efficiency. The third is to make test administration more convenient for examinees, test sponsors, or both. This entry details some of the advantages of CBTs relative to conventional paper and pencil tests, and describes some of the methods used for test administration and scoring.
Conditional Standard Errors of Measurement
Authors: Tong Ye , Kolen Michael J.
Published: September 2014

Errors of measurement for test scores generally are viewed as random and unpredictable. Conditional standard errors of measurement (SEMs) index the amount of error in the measurement process and are required to be reported for tests. Methods of estimating conditional SEMs, based on both classical test theory and generalizability theory, are described in this entry. These methods are based on differing assumptions, but the conditional SEMs estimates obtained from these methods are commonly highly related for educational achievement tests.

Conditional SEMs vary by score level. Conditional SEMs typically have high values for extreme scores and have low values for middle scores on the raw score scale. However, a nonlinear transformation of the raw scores to scale scores can lead to conditional SEMs that have other patterns across score levels.
Attitude Scaling
Authors: Johnson Matthew S. , Junker Brian W.
Published: September 2014

Attitude scaling is the process of locating
J
attitude statements or items and/or
N
individuals on a latent continuum or scale. There are numerous methods available for the scaling of attitudes. The earliest methods, developed by L. L. Thurstone, R. Likert, and L. Guttman required two stages: One stage to locate the items on the scale and a second stage to locate the respondents. Other early work on the scaling of attitudes by C. H. Coombs allowed for the simultaneous estimation of both items and respondents, but the assumptions proved too restrictive for most real examples. Modern attitude scaling techniques use item response theory models, both monotone and unfolding, to perform attitude scaling.
Criterion‐Referenced Assessment
Authors: Hambleton Ronald K. , Li Shuhong
Published: September 2014

This entry provides an introduction to criterion‐referenced testing and approaches for resolving several technical problems. Several of the important differences between norm‐referenced testing and criterion‐referenced testing will be introduced first. Next, the challenge of setting performance standards on criterion‐referenced tests and several of the methods will be discussed. Finally, approaches for estimating decision consistency and decision accuracy from single and double test administrations are described.
Differential Item Functioning
Authors: Rogers H. Jane
Published: September 2014

Differential item functioning (DIF) occurs when individuals at the same level on the trait(s) or construct(s) being assessed but from different subpopulations have unequal probabilities of attaining a given score on the item. Methods for investigating DIF have been developed for both dichotomously and polytomously scored items. These methods may be classified by whether they condition on an unobserved or observed variable. Item response theory, logistic regression, Mantel–Haenszel, and SIBTEST procedures for dichotomously scored responses and their extensions to polytomous responses are currently the most widely used methods for detecting DIF.
Item Bias Detection: Classical Approaches
Authors: Mellenbergh Gideon J.
Published: September 2014

Under the assumptions of Classical Test Theory (CTT), a person's observed test score is an estimate of his (her) true test score. Therefore, CTT‐based methods to detect differentially functioning items use the test score to equate members of different groups. An item is considered to be differentially functioning between two groups when item responses differ between members of the two groups at the same test score. Five methods for the detection of differentially functioning dichotomous item responses and their generalization to ordinal‐polytomous item responses are discussed.
Log‐linear
R
asch Models for Stability and Change
Authors: Meiser Thorsten
Published: September 2014

This entry presents Rasch models for the analysis of longitudinal data and log‐linear representations of Rasch models to test specific hypotheses about change. The use of log‐linear Rasch models is illustrated by an empirical example concerning the development of arithmetic competence in elementary school. The final section discusses model extensions for the analysis of polytomous items, multidimensional latent constructs, and several latent subpopulations in longitudinal research.
Test Construction: Automated
Authors: Veldkamp Bernard P.
Published: September 2014

Optimal test construction deals with automated assembly of tests for educational and psychological measurement. Items are selected from an item bank to meet a predefined set of test specifications. Several models for optimal test construction are presented, and two algorithms for optimal test assembly are discussed. A number of current issues are mentioned.
Classical Test Score Equating
Authors: Kolen Michael J. , Tong Ye
Published: September 2014

Test equating procedures are statistical score adjustment procedures that are used when alternate forms of educational and psychological tests are constructed to a common set of content and statistical specifications. Alternate forms enhance the security of tests and allow for examinees to be tested more than one time with a different set of test questions. Even though efforts are made by test developers for the alternate forms to be equivalent, such forms differ somewhat in difficulty. A data collection design is necessary for conducting equating. Equating also involves application of statistical methodology. Traditional equating methods equate score distributions. In this entry, equating designs and traditional equating methods are described. Error in equating is considered. Selected practical issues are also discussed.
Item Exposure
Authors: Robin Frederic
Published: September 2014

Often necessary in practice, the reuse of items over administrations is a threat to the validity of test scores. This entry briefly describes the nature of that threat and shows how item exposure can be used as a means for continuously evaluating, managing and monitoring it. This entry also outlines major strategies and methodologies for controlling item exposure within levels that testing programs can find acceptable.
Maximum Likelihood Item Response Theory Estimation
Authors: Rupp André A.
Published: September 2014

An overview and short didactic for three common estimation techniques for parameters in item response theory models are described: (a) joint maximum likelihood, (b) conditional maximum likelihood, and (c) marginal maximum likelihood. Specifically, likelihood equations fundamental to all three estimation approaches are presented first and joint as well as conditional maximum likelihood estimation are briefly described next. The main part of the entry focuses on an extended description of marginal maximum likelihood estimation and illustrates, in a step‐by‐step fashion, how it makes use of the EM algorithm and a fully Bayesian estimation framework to estimate item parameters. A brief description of how person parameters are subsequently estimated follows. Finally, a few words on alternative estimation approaches are offered.
Item Bias Detection: Modern Approaches
Authors: Mellenbergh Gideon J.
Published: September 2014

A general definition of differential item functioning (DIF) is presented. The definition is specified for DIF between two groups and a test (questionnaire) that measures one latent trait. Methods for DIF detection are described for dichotomous, ordinal‐polytomous, and continuous item responses under unidimensional item response theory (IRT) models.
Facet Theory
Authors: Borg Ingwer
Published: September 2014

Facet theory (FT) is a methodology for designing and analyzing observations. A facet classifies objects of interest in one particular way. Several facets can be linked in a mapping sentence to yield schemes for the construction of multifaceted observations. Such designs also serve to predict certain structures for its data. To check these structures, FT has developed particular data analytic methods such as multidimensional scalogram analysis (MSA) or partial order structuple analysis with coordinates (POSAC), or suggests to use main‐stream techniques such as multidimensional scaling (MDS) in particular ways.
T
au‐Equivalent and Congeneric Measurements
Authors: F. Ten Berge Jos M.
Published: September 2014

To evaluate the reliability of a test, one needs a parallel test. When parallel tests are absent, one option is to rely on hypotheses such as that the test parts are essentially tau‐equivalent or congeneric, having only one factor in factor analysis. Such hypotheses are unrealistic, except that a test may be congeneric when there are only three test parts; in that case, however, it is impossible to decide what the number of factors really is. A preferable option is to use lower bounds to reliability, such as coefficient alpha. The Jackson & Agunwamba greatest lower bound (glb) is better than alpha but has a sampling bias problem. Bias correction methods are still under study. Nevertheless, when compared to reliability estimates derived from the hypothesis of congeneric tests, the glb is already to be preferred, because these estimates behave very similarly to glb, and display the same sampling bias but do not rely on the hypothesis of a congeneric test
Hierarchical Item Response Theory Modeling
Authors: Bolt Daniel , Kim Jee‐Seon
Published: September 2014

The synthesis of hierarchical modeling with item response theory (IRT) has led to psychometric models for item response datasets that possess hierarchical structure. In this entry, an overview is provided of hierarchical IRT methodology and its usefulness as a general framework both for traditional IRT models and new extensions. Models for both random person and random item effects are discussed.
Rasch Models for Ordered Response Categories
Authors: Andrich David
Published: September 2014

This article explains the latent response structure and process compatible with the Rasch model (RM) for ordered response categories in standard formats. It considers the rationale for the RM but is not concerned with details of parameter estimation and tests of fit. There are a number of software packages that implement the Rasch model at an advanced level.
Item Response Theory Models for Polytomous Response Data
Authors: Keller Lisa A.
Published: September 2014

Many measurement tools are constructed of items that can be scored in several categories. For example, essay items, or other constructed response items, or personality and attitude inventories composed of Likert‐type items. Several item response models have been developed to deal with items of this type. The models are extensions of the dichotomous items presented in this volume. The five models discussed are the Graded Response Model, the Rating Scale Model, the Partial Credit Model, the Generalized Partial Credit Model, and the Nominal Response Model. Descriptions of the models are provided, along with graphical representations, and descriptions of how to interpret the parameters. The entry concludes with a list of articles that have applied these models in different contexts.
Item Response Theory Models for Rating Scale Data
Authors: Engelhard George
Published: September 2014

The purpose of this entry is to provide a brief description of several IRT models that can be used to analyze rating scale data. Rating scale data are defined as responses scored in two or more ordered categories. Rating scale data represent the most common formats for collecting information from examinees or raters. The basic idea that motivates the use of IRT models for rating scale data is that the scoring ofm + 1 ordered categories with ordered integers (0, 1, …,m) using the assumption that there are equal intervals between the categories may not be justified. IRT models provide a framework to explicitly examine this assumption, and parameterize the categories without this assumption. The specific IRT models that are described in this entry are direct models (Partial Credit Model, Generalized Partial Credit, and Rating Scale Model) and indirect models (Graded Response Model and Modified Graded Response Model). Graphical procedures are used to illustrate various aspects of these IRT models.
Test Construction
Authors: Gierl Mark J.
Published: September 2014

Item response theory (IRT) provides a method to determine the amount of psychometric information each item (i.e., item information function) and combination of items (i.e., test information function) provides in the estimation of an examinee's ability. In a 1977 paper, Lord described a basic four‐step procedure for using these functions to construct a test using calibrate items from a bank. Lord's procedure requires specifying a target function, selecting items from the bank to fill this target, adding the item information functions together during the selection process, and continuing until the test information function approximates the target function. Some key issues related to specifying the target function and selecting items are presented and discussed. More recent developments in test construction using item and test information functions are also described.
Person Misfit
Authors: Meijer Rob R.
Published: September 2014

Methods are discussed that can be used to investigate the fit of an item score pattern to a test model. Person‐fit statistics that are formulated in the context of item response theory(IRT) take a prominent place in the literature. Also, methods formulated outside the IRT context, and methods investigating particular types of response behavior are discussed. Finally, the usefulness of person‐fit statistics to solve practical measurement problems is considered.
Setting Performance Standards ‐ Issues, Methods
Authors: Plake Barbara S.
Published: September 2014

Setting performance standards has been a controversial topic over the years. In this entry, several examinee‐based and test‐based methods for setting performance standards on educational tests are introduced.
Incompleteness of Probability Models
Authors: Macdonald Ranald R.
Published: September 2014

Probabilities are unable to incorporate all the uncertainty that there is about anything that happens in the world because the world has to be packaged by someone before a probability model can apply. As a result, all probabilities and inferences from them are subjective and open to challenge.
Parsimony/Occham's Razor
Authors: Mulaik Stanley A.
Published: September 2014

In modeling data, parsimony is the fewness of model parameters estimated relative to the number of data points fit by the model. The more parsimonious a model, the more degrees of freedom by which the model can fail to fit the data, thus making the model more potentially disconfirmable and more strongly supported when the model fits.
Hierarchical Linear Models
Authors: Ployhart Robert E.
Published: September 2014

This chapter provides a brief and relatively nontechnical introduction to hierarchical linear models. The purpose of such models is first explained in graphical terms. This is followed by a description of the model and then an empirical example. Numerous primary sources are provided for readers to learn the more technical details.
Battery Reduction
Authors: Massaro Joseph M.
Published: September 2014

Battery reduction is used to select a subset of
m
variables from an original set of
n
variables (
m
 < 
n
) that reproduce a large proportion of the variance in the original set of
n
variables. There are a number of procedures for performing battery reduction analysis. A popular method involves performing a principal components analysis first to select
m
components, which account for the salient variance in the original data. Gram–Schmidt orthogonal rotations are then performed to determine the
m
variables that account for the largest proportion of variance. The procedure is illustrated and reference made to a SAS macro for performing the analysis.
Covariance Structure Models
Authors: Thum Y. M.
Published: September 2014

As originally formulated by Bock and by Bock and Bargmann, covariance structure analysis is a statistical method for the structural analysis of the sample variance–covariance matrix of respondent scores on a test battery aimed at validating the constructs making up the battery. A generalization of the mixed‐effects model, we examine some of its applications beyond tests and testing. We provide revised results for the data analyzed by Wiley, Schmidt, and Bramble. We note its formal equivalence with a confirmatory factor analysis with known factor loading and note some of its connections to other statistical models for multivariate outcomes.
Number of Clusters
Authors: Wishart David
Published: September 2014

Various tests for the best number of clusters in a data set are reviewed, following an exhaustive validation exercise using artificial data sets with hierarchical agglomerative clustering methods. The chapter concludes with a discussion about whether it is appropriate to apply statistical tests or to evaluate a classification at several levels of usability.
Overlapping Clusters
Authors: Leese Morven
Published: September 2014

The ability to identify overlapping clusters in a cluster analysis is important in subject areas such as market research and social network research. A number of methods are available, most of which require special software. Some allow only limited overlap whereas others are more flexible, but the latter entail balancing the complexity of the model against goodness of fit.
Second Order Factor Analysis: Confirmatory
Authors: Tisak John , Tisak Marie S.
Published: September 2014

Confirmatory second‐order factor analysis may be conceptualized as a further factor analyzing of the results of an initial factor analysis of some observed variables. Specifically, the initial or first‐order factor means, variances, and covariances are re‐analyzed into more general or abstracted variables. For pedagogical reasons, this approached is initially developed via a first and second‐order multivariate multiple regression analysis using measured or observed variables. Next by analogy, the approach is extended to latent variates or unobserved factors. Throughout an illustration is presented using Thurstone's Primary Mental Abilities, Horn and Cattell's Fluid and Crystallized Intelligences, and Spearmen's General Intelligence.
C
holesky Decomposition
Authors: Cherny Stacey S.
Published: September 2014

The Cholesky decomposition is probably the most commonly used model in behavior genetic analysis. Referring to it as a model, however, is somewhat misleading, since it is, in fact, primarily a method for estimating a covariance structure under the constraint that the estimated covariance matrix is positive semidefinite. The specific parameter estimates of the decomposition are of less interest than the expected covariance matrix it implies.
Structural Equation Modeling: Software
Authors: Rigdon Edward E.
Published: September 2014

The first widely distributed special‐purpose software for estimating structural equation models appeared more than twenty years ago. Today, researchers can choose from a variety of packages that differ markedly in terms of their intellectual heritage, interface, statistical sophistication, flexibility, integration with other statistical packages, and price. Despite numerous advances, there is still substantial room for improvement.
Structural Equation Modeling: Overview
Authors: Schumacker Randall E.
Published: September 2014

Structural equation modeling (SEM) software programs analyze theoretical models using a sample variance–covariance matrix, although a correlation matrix with means and standard deviations for the observed variables can be input because these values can be used to create a variance–covariance matrix. A LISREL‐SIMPLIS program is given below to illustrate how the theoretical model and sample data are included in a SEM program.
Three‐Mode Component and Scaling Methods
Authors: Kroonenberg Pieter M.
Published: September 2014

In this entry, the basic principles and rationale for three‐mode analysis of three‐way data are introduced. The wealth of the three‐mode world is sketched, and the power of its methods is illustrated with a three‐mode component analysis analyzing how children cope in several school‐related situations and an individual differences scaling analysis of the perception of pain.
Unidimensional Scaling
Authors: Leeuw Jan
Published: September 2014

We discuss the one‐dimensional special case of multidimensional scaling and the various algorithms that have been proposed to solve the corresponding computational problem. We concentrate on least squares unidimensional scaling and on the combinatorial nature of finding the best scaling. Examples from paired comparison analysis and genetic location analysis are discussed.
Correspondence Analysis
Authors: Greenacre Michael
Published: September 2014

Correspondence analysis is a method of multivariate analysis applicable to categorical data. In its simple form it is used to visualize the relationship between two categorical variables, but can be extended to multiple correspondence analysis to visualize the relationship among several variables. These methods are explained from a correlational and geometric viewpoint and are illustrated by cross‐national survey data on sexual attitudes.
Factor Analysis: Multitrait–Multimethod
Authors: Wothke Werner
Published: September 2014

Confirmatory factor analysis is the preferred multivariate model for describing multitrait–multimethod matrices. Trait‐only factor analysis assumes that all common variation is due to shared traits. An expanded trait‐method factor model allows for additional variation due to shared methods. Experience shows that the trait‐only model fits few empirical matrices but that the more general trait‐method model is usually plagued by estimation problems. Reasons for the model failure are referenced.
Data Mining
Authors: Hand David J.
Published: September 2014

Data mining is the discovery of structures and patterns in large data sets. There are two aspects to data mining: model building and pattern detection. Model building in data mining is very similar to statistical modeling, although new problems do arise because of the large sizes of the data sets and the fact that data mining is secondary data analysis. Pattern detection seeks anomalies or small local structures in data, with the vast mass of the data being irrelevant. Although some subdisciplines of statistics have examined special cases of this problem, the bulk of the work on pattern detection to date has been computational, with an emphasis on algorithms.
Multivariate Genetic Analysis
Authors: Gillespie Nathan A. , Martin Nicholas G.
Published: September 2014

The goal of multivariate genetic analysis is to estimate the causes of genetic and environmental covariation between phenotypes. As with univariate modeling, when data from genetically informative relatives such as twins are available, the genetic and environmental components of covariation can be separated by a technique which is analogous to factor analysis (Martin & Eaves,). This is achieved by making use of the additional information in the cross‐correlations between relatives for different traits (or same traits measured at different times) and can allow researches to estimate the extent to which genetic and environmental influences are shared in common by several traits or are trait specific. The various forms of multivariate analyses covered in this section include the Cholesky decomposition, common and independent genetic pathway models, and genetic simplex modeling. This section will give the reader an appreciation for the flexibility of SEM approaches to address more complicated questions beyond simpler univariate decompositions.
Structural Equation Modeling: Latent Growth Curve Analysis
Authors: Willett John B. , Bub Kristen L.
Published: September 2014

In this chapter, we use an example of panel data on the longitudinal development of reading in children to introduce the latent growth curve analysis. Latent growth modeling originates in a simple mapping of the standard multilevel model for change onto the general model available for covariance structure analysis (CSA). Here, we illustrate how the latent growth modeling approach can be enacted by using the CSA Y‐measurement model to contain the level‐1 individual growth model and the CSA structural model to contain the level‐2 model for interindividual differences in change. Because this mapping is possible, all fixed and random parameters in the multilevel model for change can be estimated by fitting the corresponding CSA model to data using standard structural equation modeling software (such as LISREL). Latent growth curve analysis is important because it capitalizes on the intrinsic flexibility of the general CSA model to test interesting and complex hypotheses about change, many of which are either more difficult or impossible to test using standard multilevel modeling approaches.
Additive Constant Problem
Authors: Trosset Michael W.
Published: September 2014

The additive constant problem arises in multidimensional scaling (MDS), a collection of techniques for visualizing dissimilarity data. Certain experiments result in dissimilarities that are most naturally modeled as distances from which an unknown constant has been subtracted. The additive constant problem is the problem of estimating this unknown constant.
Two‐mode Clustering
Authors: Mechelen Iven Van , Bock Hans‐Hermann , Boeck Paul
Published: September 2014

Two‐mode clustering methods provide a simultaneous clustering of the rows and columns of a rectangular data matrix. By the simultaneity of the methods they may reveal the value, interaction or dependence information as implied by the data.
Factor Analysis of Personality Measures
Authors: Chaplin William F.
Published: September 2014

Factor analysis refers to a broad array of statistical models and techniques that have the general goal of describing underlying patterns in relational data. A common application of factor analysis is to items that assess personality, with the goal of identifying the major dimensions of human personality. These dimensions may be viewed as descriptive or causal depending upon the views of the investigator, and different numbers and types of dimensions have been proposed. Subjective decisions about the items to include in the analysis, the method of factor identification (principle components or principle factors), the number of factors, the rotation of the factors, and the interpretation of the factors all contribute to the diversity of the results obtained with different factor analyses. The goal of factor analysis is generally to simplify the complex structure of human personality, not to fully model that complexity. Thus, recent results from the application of confirmatory factor analysis to personality data that indicate that established factor models do not adequately model all the covariation among personality measures are neither surprising nor particularly relevant.
Cluster Analysis: Overview
Authors: Manton Kenneth G. , Lowrimore Gene , Yashin Anatoli , Kovtun Mikhail
Published: September 2014

This article discusses analysis techniques for clustering objects into hopefully meaningful sets. Hierarchical methods are presented for clustering both variables and cases. Examples are presented for variations on the methods. A nonhierarchical method, k‐means, is discussed for continuous data. Finally, an example comparing the results of k‐means clustering to an ad hoc method using principal components analysis is given.
Factor Analysis: Multiple Groups
Authors: Little Todd D. , Slegers David W.
Published: September 2014

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

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

Usually 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.
Independent Components Analysis
Authors: Stone James V.
Published: September 2014

Independent component analysis (ICA) extracts statistically independent variables from a set of measured variables, where each measured variable is affected by a number of underlying physical causes. Extracting such variables is desirable because independent variables are usually generated by different physical processes. Thus, by extracting independent variables, ICA can effectively extract the underlying physical causes for a given set of measured variables.
Pattern recognition and classification
Authors: Kuncheva Ludmila I. , Whitaker Christopher J.
Published: September 2014

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

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

Projection 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

The 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.