bluuebunny/crossref_metadata_2025 huggingface dataset:
THE ISOPODIC AND EQUIPOTENT PRINCIPLES FOR COMPARING FACTOR SCORES ACROSS DIFFERENT POPULATIONS
Authors: Cattell Raymond B.
Published: August 2011

The need to compare factor score estimates across groups differing in age and culture, for example, can be met whenever some variables, factored in all the groups to be compared, are identical.

Within the ordinary factor analytic procedures, an equipotent method is described, which throws scores from different groups into a combined standard score distribution, and operates on the scores of each group with its own factor estimation weights, but with the matrices for all the groups brought to equipotency.

A more satisfactory isopodic procedure is also proposed, using covariance factoring, after first reducing artificial metric differences among variables by ‘universe standardizing’ conversions. But a more radical attainment of the isopodic goat is reached if the mean standardized covariance matrix is applied to the raw score deviations of members of all groups, brought into a combined distribution on each variable.
A MODEL FOR ASSESSING MULTIPLE‐CHOICE TEST PERFORMANCE
Authors: Dalrymple‐Alford E. C.
Published: August 2011

A model is developed for the case where a subject is presented with N alternatives from which he has to choose the single correct one. It is assumed that the subject randomly selects an alternative from a subset consisting of from 1 to N of the alternatives presented. For a given set of alternatives the size, i, of this choice set will depend on the subject's knowledge, which consequently may be measured by some suitable function of i, or, alternatively, of (N — i). Two measures are considered, which require a modification of the usual test procedure, so that subjects are allowed repeated attempts until the correct alternative is selected. The model is shown to be successful in predicting performance in the n‐alternative case from N‐altentative performance (N > n).
FACTORIAL INVARIANCE OF ABILITY MEASURES IN GROUPS DIFFERING IN INTELLIGENCE AND SOCIOECONOMIC STATUS
Authors: McGaw Barry , Jöreskog Karl G.
Published: August 2011

Scores on 12 aptitude and achievement tests for 11,743 subjects, subdivided into four groups according to intelligence and socioeconomic status, were used. A technique, developed by Jöreskog, for simultaneously factor analysing data from several populations was used to determine whether there was factorial invariance over the four groups. A model, in which the same factor pattern (matrix of factor loadings) is assumed to hold for the four groups, was fitted to the data. Goodness‐of‐fit indices suggested that the model fitted satisfactorily. Differences in the factor dispersion matrices and mean factor scores for the subpopulations are then examined and discussed.
OBLIQUE ROTATION TO A PARTIALLY SPECIFIED TARGET
Authors: Browne M. W.
Published: August 2011

This paper presents an iterative procedure for rotating a factor matrix obliquely to a least‐squares fit to a target matrix which need not be fully specified.
THE FAIR BETTING GAME AS AN ADMISSIBLE PROCEDURE FOR ASSESSMENT OF SUBJECTIVE PROBABILITIES
Authors: Vlek Charles A. J.
Published: August 2011

The fair betting game between two players requires one player to propose the proportional distribution of the total stake over two sides of a bet on the outcome of an uncertain binary event. The other player then chooses his most preferred side of the bet. When the first player has no reason to suppose that his relevant degrees of belief differ from his opponent's, the former's best strategy is to propose such a bet that its two sides have equal subjectively expected utility, or SEU, from which subjective probabilities can be directly inferred, if utilities are known or assumed linear in money. The mathematical properties of this game and their possible effectiveness in bringing about honest probability assessments are examined. Under specified conditions the game amounts to an admissible procedure for probability assessment, characterized by a peaked maximum SEU for optimal estimation. Two variants, the complete and simplified versions, of the game are discussed and their properties compared. The effects of uncertainty about one's true subjective probability, under a rational as well as under a partially irrational strategy, are briefly investigated. Two possible applications of the method to the assessment of continuous probability distributions are suggested.
CONDITIONAL INFERENCE FOR MULTIPLE‐CHOICE QUESTIONNAIRES
Authors: Andersen Erling B.
Published: August 2011

Since most of the literature on the extension of Rasch's (1961) model to multiple‐ choice questionnaires is only available in Danish, this paper gives a short introduction to the model. The main body of the paper, however, is concerned with the conditional maximum‐likelihood estimation of the item parameters. The theory is applied to data from a questionnaire used to measure job satisfaction in Danish factories. Finally, the problem of reducing the dimensionality of the parameters is discussed.
A FACTOR MODEL FOR ANALYSING CHANGE
Authors: Corballis M. C.
Published: August 2011

This paper develops a model for factor analysing scores on n tests administered to N persons on p separate occasions. It allows factor scores and factor loadings to vary, but assumes the factors to be mutually orthogonal within, as well as between, all occasions. These assumptions are generally sufficient to specify unique rotations on each separate occasion. A worked example is given.
THE OTHER TAIL
Authors: Wainer Howard
Published: August 2011

It is argued that significantly small values of the F and chi‐square statistic should not be ignored because they often indicate invalid error estimates. Two algorithms for computing the probability of a particular F are presented to facilitate decisions on when a small value may be suspect.
APPLICATION OF THE THEORY OF COMBINATORIAL CHANCE TO THE ESTIMATION OF SIGNIFICANCE OF CLUSTERING IN FREE RECALL
Authors: Kelly Mavis E.
Published: August 2011

Using the theory of combinatorial chance it is shown that the probability of occurrence of any cluster outcome may be expressed as the ratio between the number of combinations which give rise to that particular outcome and the total number of combinations possible given relevant list parameters, these being the number of categories employed in recall and the number of elements recalled per category. The probability measure thus derived is compared with previously developed measures in terms of their effectiveness as measures of the degree to which observed clustering scores depart from chance.
LIMITATIONS ON THE USE OF THE MULTIPLE LINEAR REGRESSION MODEL
Authors: MAXWELL A. E.
Published: August 2011

This paper discusses briefly the classic multiple linear regression model and indicates the principal ways in which its assumptions are inadequately met when it is used as a model for prediction purposes in the social sciences. It also considers the damping effects of errors of measurement and of selective sampling on estimates of partial regression and multiple correlation coefficients and describes techniques whereby these effects may in part be overcome.
PREDICTIVE VALIDITY OF A LINEAR REGRESSION EQUATION
Authors: Browne M. W.
Published: August 2011

The squared correlation coefficient, w2, between an empirically chosen linear function of predictors, B̂0 + B̂′x, and a criterion, y, is employed as a measure of predictive precision. This coefficient is defined over the entire population but is conditional on B̂. Assuming a multinormal distribution for x and y, approximations for the expected value and variance of w2 are derived. If too many predictors are employed, precision of prediction can decrease. This is illustrated by means of an example of a sequence of values of ℰ (w2). A function of the sample squared multiple correlation coefficient, r2, is proposed as an estimator of w2. Results of Monte Carlo experiments are employed to give an impression of the precision of the estimates of w2, and the accuracy of the approximations for ℰ (w2) and var (w2).
AN EMPIRICAL STUDY OF JONCKHEERE'S NON‐PARAMETRIC TEST OF ORDERED ALTERNATIVES
Authors: Nelson Peter L. , Toothaker Larry E.
Published: August 2011

The non‐parametric Jonckheere procedure for testing ordered alternatives in the κ‐sample case is described. The empirical Type I error rate and power are estimated for small samples under several conditions, including sampling from either uniform, normal or exponential populations with unequal variances. A large sample approximation is also studied. The estimated Type I error rate is generally within sampling bounds for the exact test; the large sample approximation is quite adequate when alpha is 0.05 or greater. Power values appear to be not only a function of location differences but also of population kurtosis. Unequal variances and unequal sample sizes have some effect on both the probability of a Type I error and the power for the specific situations studied.
A COMPARISON OF THE DIRECT OBLIMIN AND PRIMARY PARSIMONY METHODS OF OBLIQUE ROTATION
Authors: Crawford Charles
Published: August 2011

The Crawford‐Ferguson family of rotation criteria is extended to the oblique primary factor case. This method of rotation is referred to as the primary parsimony criterion, and it is conceptually and empirically compared with the direct oblimin method. Results of this study indicate that the advantages of the primary parsimony criterion are as follows: (a) the rationale for this approach is well understood; (b) it is a natural extension of the orthomax criterion for orthogonal rotation; (c) it has parameters for altering the properties of the solution; and (d) it does not allow collapse of the factor space. Considering all special cases, its results are superior to those obtained with the direct oblimin criterion.
A correction and proof of a theorem by Duncan Luce
Authors: Laming Donald
Published: August 2011

An amended statement and a correct proof is given of a theorem stated by Luce in connection with a choice model for choice‐reaction times.
The attenuation paradox and the distribution of ability
Authors: Nicewander W. Alan , Price James M. , Mendoza Jorge L. , Henderson Diana
Published: August 2011

The attenuation paradox refers to the increase in test validity that accompanies increasing test reliability up to a point beyond which validity decreases with further increases in reliability. It is shown that, for perfectly discriminating items, this phenomenon can occur regardless of the distribution of underlying ability. A numerical example is also given for a class of non‐perfectly discriminating items and a rectangular distribution of ability.
A comparison of the efficiencies of the c‐sample normal scores and the Kruskal‐Wallis tests in the case of grouped data
Authors: Padmanabhan A. R.
Published: August 2011

The problems of using the Kruskal‐Wallis (KW) test and two equivalent forms of the normal scores (NS) test in analysing data arising from a continuous distribution are discussed for the cases where the data have been rounded to the nearest integer and first decimal place respectively. When the distribution function G is normal, the NS test is asymptotically slightly more efficient than the KW test, whereas when G is double exponential, Cauchy or logistic, the KW test is somewhat more efficient. Even when G is exponential or rectangular, the NS test is only slightly more efficient than the KW test. This is quite surprising by comparison with the continuous case where the NS test is infinitely more efficient than the KW test. Nor do these conclusions need modification for the cases where the populations differ both in location and in scale and where the differences among the location parameters and among the scale parameters tend to zero as the sample sizes tend to infinity, provided G is normal, double exponential, Cauchy or logistic. When homogeneity of variances obtains, the results follow from those of Conover (1973), but with heterogeneous variances his techniques have to be modified as in Goldsmith & Padmanabhan (1976). The limitations of these results and problems for further investigation are explained.
Robustness?
Authors: Bradley James V.
Published: August 2011

The actual behaviour of the probability of a Type I error under assumption violation is quite complex, depending upon a wide variety of interacting factors. Yet allegations of robustness tend to ignore its highly particularistic nature and neglect to mention important qualifying conditions. The result is often a vast overgeneralization which nevertheless is difficult to refute since a standard quantitative definition of what constitutes robustness does not exist. Yet under any halfway reasonable quantitative definition, many of the most prevalent claims of robustness would be demonstrably false. Therefore robustness is a highly questionable concept.
A method for the investigation of irrelevant response set in ordered metric and original questionnaires
Authors: Phillips J. P. N.
Published: August 2011

A statistical method is described for the analysis of response sot in ordinal questionnaires (in which a sequence of statements is presented to the patient, who is asked to say to each whether he feels ‘better or worse than it says on the card’) and ordered metric questionnaires (in which a sequence of pairs of statements is presented, and the patient is asked to say whether the ‘Top’ or the ‘Bottom’ statement better describes how he feels). In the first case, sequential dependency in the sequence of ‘hotter’ and ‘worse’ responses can be tested by means of the Wald‐Wolfowitz runs test. In the second, there are three types of response set to be tested: bias, or preference for ‘Top’ or for ‘Bottom’ responses irrespective of content; sequential dependency in the sequence of implied Health and Illness responses; and sequential dependency in the sequence of ‘Top’ and ‘Bottom’ responses. Significance tests for indices of each are given: the indices themselves are in general correlated (and a large sample method of taking account of the correlations is given), but it is described how to arrange the questionnaire so as to make them as uncorrected as possible. A suite of computer programs for preparation of questionnaire material and scoring and analysis of responses is reported. Possible generalizations of the method are mentioned.
Analysis of repeated measurements
Authors: Rogan Joanne C. , Keselman H. J. , Mendoza Jorge L.
Published: August 2011

Recent literature demonstrates that uniformity of population variances and covariances is a sufficient but not a necessary requirement for valid F ratios in repeated measures designs; the tests will be valid if the loss restrictive condition of circularity is satisfied. The circularity assumptions of various repeated measures designs are presented and the empirical literature is reviewed and interpreted in light of these assumptions. An empirical investigation is then presented which compares numerous data analytic strategies when circularity assumptions have been violated, Results indicate that adjusted univariate and multivariate tests are comparable with respect to Type I error control and power. Furthermore, it is shown that by formulating planned comparisons researchers can by pass all or some circularity constraints.
A Monte Carlo study of local identifiability and degrees of freedom in the asymptotic likelihood ratio test
Authors: McDonald Roderick P. , Krane William R.
Published: August 2011

In applications to restricted factor analysis, it is shown that the determination of local identifiability and degrees of freedom in the asymptotic likelihood ratio test, from the eigenvalues of certain matrices, is not unambiguous in all cases. Some results are given that serve to indicate appropriate reparameterizations of unidentified problems.
The prediction of prison riots
Authors: Smith J. Q.
Published: August 2011

Zeeman et al. (1976) proposed a model of the escalation of disorder in a prison and the subsequent riot. The theoretical foundation of this model was an analogy with Lorentz's (1963) study of the behaviour of a cornered and threatened dog and was couched in terms of catastrophe theory (Isnard & Zeeman, 1975). The escalation to a riot in Gartree in 1972 illustrated the uses of their model.

Since 1975 there have been two more riots, one in Hull in 1976 and one in Gartree in 1978. In the light of these riots Zeeman's model is reformulated using a utility or pay‐off approach. By adjusting his model in this way we found a more efficient method of monitoring disturbances. The changes in the monitored variables over the time preceding each of these three riots are discussed and conclusions drawn from the new model.
On the empirical equivalence of regression components and common factors
Authors: Steiger James H.
Published: August 2011

Schönemann & Steiger (1976, Theorem 5) proved that the common factor model fits a given set of observed variables if and only if a restricted regression component model fits the same variables. In the present paper a number of results, relating factor score estimates and the class of all sets of ‘factor‐equivalent’ regression components, are presented. These results clarify and extend a result given by McDonald (1977).
Unified analysis of variance by ranks
Authors: Meddis Ray
Published: August 2011

Many ‘distribution‐free’ statistical tests using very different computational procedures can be viewed as special cases of two general tests based on the principle of analysis of variance by ranks. The first test, due to Bernard & Van Elteren (1953), is a general test for any differences among the samples. The second test evaluates trends and contrasts between the samples. The two general procedures embrace popular tests by Friedman, Kruskal, Cochran, Spearman, Wilcoxon, Mann & Whitney, Dixon & Mood, Page and Marascuilo & McSweeney as well as chi‐square tests for contingency tables whose dependent variable is in the form of dichotomous or rankable categories. The system can be used to generate convenient computational formulac for a range of new designs, to express popular procedures in a unified notation, as a teaching aid to illustrate the relationships among tests and as the basis for a simple computer program to analyse data from any design within the system.
Choice by features: An extension of Luce's choice model to account for similarities
Authors: Strauss David
Published: August 2011

The standard counter‐examples to Luce's choice axioms involve similarities between some of the choice alternatives. If one regards choice as a random utility process then the similarities can be interpreted as correlation between the utility variables; the counter‐examples are then simply explained. A class of multivariate double exponential distributions is discussed which modifies Luce's probability formula to allow for similarities. The choice by features model proposed here defines one way in which several features, or similarity groupings, may be combined. An important special case of the model is an extension of Luce's to account for similarities; this model can be parameterized in a natural way, and it is then possible to estimate and test hypotheses about the parameters of interest.
A note on the asymptotic relative efficiency of the Wilcoxon rank‐sum test relative to the independent means t test under mixtures of two normal distributions
Authors: Blair R. Clifford , Higgins J. J.
Published: August 2011

Bradley (1977) has shown that the mixed normal family of distributions is an important population model in many behavioural science research contexts. Researchers engaged in studies of the type discussed by Bradley (1977) might well wonder about the relative appropriateness of various statistical techniques that might be employed in data analyses. For example, in the case of a two‐sample test for shift, should one use the parametric t test or some non‐parametric counterpart such as Wilcoxon's rank‐sum test?

The primary purpose of this paper is to examine some of the characteristics of the asymptotic relative efficiency (ARE) of the Wilcoxon rank‐sum test relative to the independent means t test under various mixtures of two normal distributions. Pursuant to this goal, the equation for finding the ARE of the two tests under various mixtures of two distributions is developed, the equation is applied to various example situations, and certain limiting values of the equation are noted. As a result, it is concluded that the Wilcoxon statistic tends to have large ARE advantages over the t test in research contexts similar to those considered by Bradley (1977). It is concluded, therefore, that the Wilcoxon test is the more appropriate statistic for the research situations considered.
Tree structures for proximity data
Authors: Colonius H. , Schulze H. H.
Published: August 2011

Previous work on representing proximity data by tree structures is reviewed. The authors then present two paradigms for data collection and develop appropriate measurement structures for non‐numerical data. Two theorems on representing these data by rooted or unrooted trees are given and their relationship to the more conventional representation by a dissimilarity index is discussed.
Bayesian methods for calibration of examiners
Authors: Paul S. R.
Published: August 2011

In large public examinations many examiners are required to mark the scripts. These examiners are to be calibrated by requiring them all to mark a sample of common scripts. Paul (1979) used an additive model and a linear relationship model to describe the examiners' behaviour in marking the scripts, and gave estimates of the parameters from a sampling theoretic approach. In this paper Bayesian estimates of the parameters of the models are given. Real examination data and simulated data are analysed and the conclusion of Paul (1979) that there is very little to choose between the models is confirmed. It seems that the additive model is adequate.
Correlation coefficients from 2 × 2 tables and from biserial data
Authors: Chambers R. G.
Published: August 2011

Various measures of correlation between two quantities x and y are discussed, and it is shown that the phi coefficient is a logically unacceptable measure except perhaps when both x and y are purely qualitative two‐valued attributes.

For biserial data, a new measure of correlation is proposed which is free from the shortcomings of the biserial coefficient and the point biserial coefficient.
The exact distribution of an index of agreement between partitions
Authors: Verhelst N. D. , Koppen M. G. M. , Van Essen E. P.
Published: August 2011

Given two partitions of the same set, an index of agreement between the two partitions is given by the number of pairs of elements appearing together in an equivalence class in both partitions. In this paper the exact permutational probability distribution of this index is derived, i.e. the probability distribution of the index conditional upon the cardinality of the equivalence classes in both partitions.
A comparison of some methodologies for the factor analysis of non‐normal Likert variables
Authors: Muthén Bengt , Kaplan David
Published: August 2011

This paper considers the problem of applying factor analysis to non‐normal categorical variables. A Monte Carlo study is conducted where five prototypical cases of non‐normal variables are generated. Two normal theory estimators, ML and GLS, are compared to Browne's (1982) ADF estimator. A categorical variable methodology (CVM) estimator of Muthén (1984) is also considered for the most severely skewed case. Results show that ML and GLS chi‐square tests are quite robust but obtain too large values for variables that arc severely skewed and kurtotic. ADF, however, performs well.

Parameter estimate bias appears non‐existent for all estimators. Results also show that ML and GLS estimated standard errors are biased downward. For ADF no such standard error bias was found. The CVM estimator appears to work well when applied to severely skewed variables that had been dichotomized. ML and GLS results for a kurtosis only case showed no distortion of chi‐square or parameter estimates and only a slight downward bias in estimated standard errors. The results are compared to those of other related studies.
A fit index for covariance structure models under arbitrary GLS estimation
Authors: Tanaka J. S. , Huba G. J.
Published: August 2011

A general fit index for covariance structure models is obtained for all estimators that can be considered under generalized least squares (GLS) approaches including asymptotically efficient, robust, and resistant methods of estimation. This fit index is expressed as a function of the ratio of two trace functions. Normal theory ordinary least squares (OLS) and maximum likelihood (ML) fit indices previously given by Jöreskog and Sörbom can be derived from this framework. Fit indices for normal theory and generic GLS approaches including robust/resistant estimation methods are also obtained.
On a Stein‐type two‐stage procedure for the general linear model
Authors: Wilcox Rand R.
Published: August 2011

As noted in Wilcox (1984), many Stein‐type two‐stage procedures are based on a ‘generalized’ sample mean, and in a few instances alternative procedures have been proposed that are uniformly better; these alternative procedures are based on the usual sample mean. Using a generalized sample mean, Bishop (1978) extended Stein's technique to the general linear model, but one issue that remains unresolved is determining the conditions under which uniformly better results can be obtained using the usual sample means. This note demonstrates that Bishop's solution can be uniformly improved when the variances are equal.
The Fisher‐Pitman permutation test: A non‐robust alternative to the normal theory F test when variances are heterogeneous
Authors: Boik Robert J.
Published: August 2011

The Fisher–Pitman permutation test is an increasingly popular alternative to the ANOVA F test. As a test of equality of distributions, the permutation test is very attractive because it retains its stated test size without any distributional requirements. As a test of equality of location parameters, however, the permutation test retains its stated test size only under equality of all nuisance parameters. This homogeneity requirement is well known, but often overlooked. As a result, the permutation test is sometimes recommended when, in fact, the distributional requirements are not satisfied. This article examines the robustness of the permutation test to violation of the homogeneity requirement. In particular, the size of the Fisher–Pitman permutation test of equality of means is compared to the size of the normal theory F test in small samples when variances are unequal. Normally distributed populations having equal means are assumed. The size of the permutation test is found to be smaller than the size of the F test when the ratio of the harmonic to the arithmetic mean of the sample sizes is small and vice versa when the ratio is large (i.e. near 1). In either case, the difference between the sizes of the two tests is relatively small, except for extreme heterogeneity. The result is based on a comparison of the moments of the permutation and normal theory sampling distributions and is supported by the results of simulation studies.
Probability inequalities for latent scales
Authors: Rosenbaum Paul R.
Published: August 2011

Certain latent variable models for dichotomous items define a latent scale, in the sense of ordering of the items by difficulty, the same ordering applying to all subpopulations of respondents. These models, which may be either unidimensional or multidimensional, have item characteristic surfaces that do not cross. All models with this property place strong restrictions on the behaviour of the observable distribution of item responses, restrictions which may be compared with empirical data to aid in evaluating whether the items have a latent scale. To this end, two inequalities are obtained for the observable item response distribution: one describes the effects of transpositions of item responses on the distribution, and the other compares the distribution with an exchangeable distribution. An example illustrates some ways in which the inequalities may be used, and briefly discusses the related question of dimensionality. Other applications are briefly discussed.
A general coefficient of determination for covariance structure models under arbitrary GLS estimation
Authors: Tanaka J. S. , Huba G. J.
Published: August 2011

Previous results presented in Tanaka & Huba (1985) introduced a general Fit index for covariance structure models under generalized least squares (GLS) estimation which, in some cases, specialized to the fit indices presented in Jöreskog & Sörbom (1981). Here, it is shown that, for a wide class of models, the general form of this fit index can be expressed as a weighted coefficient of determination. This coefficient is given as the ratio of weighted trace functions of predicted and observed covariance matrix elements.
Sequential item response models with an ordered response
Authors: Tutz Gerhard
Published: August 2011

A stepwise approach to the construction of latent trait models is outlined. As a special case of the derived general sequential model, a sequential Rasch model is considered. The derivation of the models is based on mechanisms of latent random variables. The unconditional maximum likelihood estimation is embedded in the framework of generalized linear models. An alternative estimation procedure which allows for ‘parameter separability’ is considered and its applicability is shown.
Non‐linear redundancy analysis†
Authors: VAN DER Burg Eeke , De Leeuw Jan
Published: August 2011

A non‐linear version of redundancy analysis is introduced. The technique is called REDUNDALS. It is implemented within the computer program for canonical correlation analysis called CANALS (Van der Burg & De Lccuw, 1983). The REDUNDALS algorithm is of an alternating least squares (ALS) type. The technique is defined as minimization of a squared distance between criterion variables and weighted predictor variables. The matrix of weights can be restricted to a specified rank. With the help of optimal scaling the variables are transformed non‐linearly (cf. Young, 1981). An application of redundancy analysis is provided.
Analysing unbalanced repeated measures designs
Authors: Keselman Joanne C. , Keselman H. J.
Published: August 2011

For repeated measures designs containing at least one between‐subjects factor (split‐plot designs), exact univariate F tests of within‐subjects effects depend on the assumption of multisample sphericity. Monte Carlo methods were used to examine univariate and multivariate data‐analytic strategies for unbalanced split‐plot repeated measures designs in which the data do not conform to the condition of multisample sphericity. For varying degrees of assumption violation, empirical Type I error and power rates were determined for varying numbers of levels of the within‐subjects factor, total sample size, and degree of sample size inequality. Only the approximate univariate procedures provided robust tests of within‐subjects main effects in unbalanced designs. Robust univariate and multivariate tests of within‐subjects interaction effects were only achieved when the design was balanced and the number of repeated measurements was moderate.
A logistic mixture distribution model for polychotomous item responses
Authors: Rost Jürgen
Published: August 2011

The polychotomous Rasch model is generalized to a mixture distribution model. It is assumed that the observed data are generated by two or more latent classes of individuals so that within each class the polychotomous Rasch model holds but with different parameters between the classes. Hence, the proposed model is also a generalization of latent class analysis which allows for quantitative individual differences within the classes. A parameter estimation procedure is outlined, employing conditional inference methods for the item parameters within classes and the EM‐algorithm for unmixing the data. The application of the model and control of model fit are illustrated by means of real data and simulated data.
Annotated bibliography of structural equation modelling: Technical work
Authors: Austin James T. , Wolfle Lee M.
Published: August 2011

Researchers must be familiar with a variety of source literature to facilitate the informed use of structural equation modelling. Knowledge can be acquired through the study of an expanding literature found in a diverse set of publishing forums. We propose that structural equation modelling publications can be roughly classified into two groups: (a) technical and (b) substantive applications. Technical materials focus on the procedures rather than substantive conclusions derived from applications. The focus of this article is the former category; included are foundational/major contributions, minor contributions, critical and evaluative reviews, integrations, simulations and computer applications, precursor and historical material, and pedagogical textbooks. After a brief introduction, we annotate 294 articles in the technical category dating back to Sewall Wright (1921).
A comparison of some methodologies for the factor analysis of non‐normal Likert variables: A note on the size of the model
Authors: Muthen Bengt , Kaplan David
Published: August 2011

This paper expands on a recent study by Muthen & Kaplan (1985) by examining the impact of non‐normal Likert variables on testing and estimation in factor analysis for models of various size. Normal theory GLS and the recently developed ADF estimator are compared for six cases of non‐normality, two sample sizes, and four models of increasing size in a Monte Carlo framework with a large number of replications. Results show that GLS and ADF chi‐square tests are increasingly sensitive to non‐normality when the size of the model increases. No parameter estimate bias was observed for GLS and only slight parameter bias was found for ADF. A downward bias in estimated standard errors was found for GLS which remains constant across model size. For ADF, a downward bias in estimated standard errors was also found which became increasingly worse with the size of the model.
Prior distribution for item response curves
Authors: Tsutakawa Robert K.
Published: August 2011

The paper examines the use of the ordered Dirichlet prior for binary logistic item response models. This prior is based on the investigator's prior information about the probabilities of correct response to items from examinees at several ability levels. The effect of the prior is examined in terms of the posterior mode of the item parameters computed via the EM algorithm. An illustration is used to explore the application of a 1981 ACT math test to form a prior that is then used on a similar 1987 test. A novel feature of the paper is the emphasis placed on the entire item response curves, rather than the item parameters per se. Detailed computational expressions for the three‐parameter logistic model are summarized in an Appendix.
Type I error rates for James's second‐order test and Wilcox's Hm test under heteroscedasticity and non‐normality
Authors: Oshima T. C. , Algina James
Published: August 2011

Actual Type I error rates (τ) for James's second‐order test and Wilcox's Hm test on means were estimated for various conditions in which variances were either homoscedastic or heteroscedastic and distributions were either normal or non‐normal. Actual Type I error rates for both James's second‐order and Wilcox's Hm tests were affected by non‐normality. However, the two tests tended to have τ near the nominal Type I error rate (α) when applied to data sampled from symmetric non‐normal distributions. When applied to data sampled from asymmetric distributions, larger values of τ‐α occurred and τ‐α tended to increase as the degree of asymmetry increased.
Type I error rates for Huynh's general approximation and improved general approximation tests
Authors: Algina James , Oshima T. C.
Published: August 2011

For split plot designs exact univariate F tests of the within‐subjects main effect and the between × within interaction are based on the assumption of multi‐sample sphericity. Type I error rates are reported for three tests designed for use when multisample sphericity is violated: the general approximation test, the improved general approximation test and a revised improved general approximation test. The results indicate that when sample sizes are unequal and dispersion matrices are unequal, using the improved general approximation or revised improved general approximation test of the interaction allows better control of the Type I error rate than does the ‐adjusted test.
Estimating Winsorized correlations in a univariate or bivariate random effects model
Authors: Wilcox Rand R.
Published: August 2011

A well‐known result is that slight departures from normality can have a large effect on the usual correlation coefficient rendering the magnitude of the correlation difficult to interpret and potentially misleading. In the context of a random effects model, which is the focus of attention in this paper, this means that effect size, as measured by the intraclass correlation, might be small due to outliers or heavy‐tailed distributions rather than a lack of differences among the groups being compared. Similarly, a large intraclass correlation might be due to trivial shifts away from normality which would become small if an adjustment for non‐normality were made. Moreover, this problem has to do with the effects of non‐normality on population parameters, not just statistics, so problems can arise even with large sample sizes. This follows almost immediately from results in Tukey (1960), and it is briefly illustrated here. One approach to this problem is to use a Winsorized analogue of the intraclass correlation. This paper suggests three ways the Winsorized intraclass correlation might be estimated and compares them via simulations. A bivariate generalization of the random effects model is also considered, and two methods of estimating the group‐level correlation are described and compared. Alternatives to Winsorization are also discussed.
Parameter estimation and goodness‐of‐fit testing in multinomial models
Authors: García‐Pérez Miguel A.
Published: August 2011

The application of multinomial models to describe psychological data usually involves small sample sizes. In these circumstances, the asymptotic properties of the parameter estimation method and goodness‐of‐fit statistics designed for use with multinomial models may not hold up. This paper illustrates the design of a simulation study that will allow researchers and practitioners to determine which of the available estimation methods and goodness‐of‐fit statistics for multinomial models has better finite‐sample properties for the model and sample size of concern. All of the estimation methods and goodness‐of‐fit statistics considered are members of the family of power divergence measures defined by Cressie & Read (1984), which include maximum likelihood and minimum chi‐square among other estimation methods. Criteria for comparing the methods and statistics include the accuracy of the estimates and the closeness of the asymptotic significance levels of the statistics to their exact finite‐sample levels. A number of simulations are carried out in order to investigate these properties for different models and sample sizes. In addition to illustrating the procedure for carrying out the comparison, the results found along the way indicate that the optimal choices are not always the maximum likelihood estimation method and the log‐likelihood ratio statistic.
Contrast analysis for additive non‐orthogonal two‐factor designs in unequal variance cases
Authors: Hsiung Tung‐Hsing , Olejnik Stephen
Published: August 2011

This study considered the problem of performing all pairwise comparisons of column means for an additive non‐orthogonal two‐by‐four factorial ANOVA model where cell variances were heterogeneous. Extensions of the Games & Howell (1976) procedure, the Dunnett (1980) T3 and C procedures, the Holland & Copenhaver (1987) technique, the Hayter (1986) procedure, and the James (1951) second‐order test were considered. Using computer‐simulated data, Type I error rates and statistical power for these multiple comparison procedures were estimated. Examined in this study were 132 different combinations of sample size, variance patterns, group mean patterns, and design types. The family‐wise Type I error rate for each of these procedures was generally maintained under the nominal .05 level. In terms of statistical power, the Games—Howell procedure generally provided the greatest any‐pair power, while the extension of the Hayter technique provided the greatest average power per contrast and was most efficient in identifying all significant pairwise differences (all‐pairs power).
A stage‐theory model of cognitive development
Authors: Preece Peter F. W. , Read Kenneth L. Q.
Published: August 2011

A model of the proportions of the population at various stages of cognitive development as a function of age is proposed. It is shown that a number of weaknesses in an earlier model proposed by‐Eckstein & Shemesh (1992a) are avoided. The new model accounts well for empirical data for the age range 13–18 years. The uses of such models in research are discussed.
Skills and knowledge structures†
Authors: Düntsch Ivo , Gediga Günther
Published: August 2011

Suppose that Q is a set of problems and S is a set of skills. A skill function assigns to each problem q i.e. to each element of Q — those sets of skills which are minimally sufficient to solve q; a problem function assigns to each set X of skills the set of problems which can be solved with these skills (a knowledge state). We explore the natural properties of such functions and show that these concepts are basically the same. Furthermore, we show that for every family K of subsets of Q which includes the empty set and Q, there are a set S of (abstract) skills and a problem function whose range is just K. We also give a bound for the number of skills needed to generate a specific set of knowledge states, and discuss various ways to supply a set of knowledge states with an underlying skill theory. Finally, a procedure is described to determine a skill function using coverings in partial orders which is applied to set A of the Coloured Progressive Matrices test (Raven, 1965).
Replicated paired comparisons at the individual level
Authors: Bechtel Gordon G. , Ofir Chezy , Khuri André I.
Published: August 2011

A model and generalized least squares (GLS) analysis is presented for paired comparisons replicated within individuals. This analysis is applicable to any pairwise judgement or datum that is interprétable as a preference or perceptual difference, and it permits any (unknown) pattern of correlations among the paired comparisons. Exact individual‐level hypothesis tests and GLS estimates are developed from Wishart distribution theory and applied to a consumer taste panel.
The analysis of repeated measurements: Univariate tests, multivariate tests, or both?
Authors: Keselman H. J. , Keselman Joanne C. , Lix Lisa M.
Published: August 2011

One strategy which has been recommended for examining effects in repeated measures designs combines a degrees of freedom (d.f.)‐adjusted univariate F test and a multivariate test. The results of a simulation study for a groups × trials repeated measures design are presented, and demonstrate that for balanced designs this combined strategy rarely provided superior Type I error control to that afforded by uniformly adopting either a univariate or multivariate test. For unbalanced repeated measures designs, all three strategies typically resulted in very conservative or very liberal Type I error rates when covariance matrices and group sizes were positively and negatively paired, respectively. For such designs, the approximate d.f. Welch‐James (James, 1951, 1954; Welch, 1947, 1951) multivariate statistic developed by Johansen (1980) is preferable to any of the other strategies investigated in this paper. Power comparisons also favour the use of the Welch‐James test.
The goals and strategies of robust methods
Authors: Wilcox Rand R.
Published: August 2011

The general theme of this paper is that we have the technology to vastly improve psychological research in any situation where ANOVA, regression, and correlation are used. Modern methods, which include robust methods as a special case, are important to applied researchers because they substantially increase our chances of detecting true differences between groups and true associations between variables, and they provide a more revealing description of how groups differ and how variables are related. Put another way, if the goal is to collect data and avoid discovering differences between groups and associations between variables, use standard methods and avoid robust techniques. Standard methods work well when conventional assumptions are true, but under arbitrarily small departures from normality, their power can be relatively poor and confidence intervals can have probability coverage that differs substantially from the nominal level. However, misconceptions about the goals and strategies of robust methods are common, perhaps because typical descriptions about them are written at a rather technical level, or because the methods are not intuitive. Consequently, one goal in this paper is to provide a relatively non‐technical summary of the foundations of robust methods and hopefully to correct many of the misconceptions that arise. Another goal is to illustrate the advantages of robust methods by re‐analysing data from various studies and demonstrating that they can lead to substantially different conclusions versus standard techniques. Yet another goal is to supplement recent reviews of robust methods by describing some recent advances.
Spotlight on Plasmon Lasers
Authors: Sorger Volker J. , Zhang Xiang
Published: August 2011

A plasmonics-based design approach is enabling coherent light sources to be built at the nanometer scale.
High-Speed Atomic Force Microscopy Reveals Rotary Catalysis of Rotorless F
1
-ATPase
Authors: Uchihashi Takayuki , Iino Ryota , Ando Toshio , Noji Hiroyuki
Published: August 2011

Intrinsic cooperativity drives cyclic propagation of conformational states in the stator ring of an adenosine triphosphate–driven rotary motor.
Unbiased Parallel Detection of Viral Pathogens in Clinical Samples by Use of a Metagenomic Approach
Authors: Yang Jian , Yang Fan , Ren Lili , Xiong Zhaohui , Wu Zhiqiang , Dong Jie , Sun Lilian , Zhang Ting , Hu Yongfeng , Du Jiang , Wang Jianwei , Jin Qi
Published: August 2011

Viral infectious diseases represent a major threat to public health and are among the greatest disease burdens worldwide. Rapid and accurate identification of viral agents is crucial for both outbreak control and estimating regional disease burdens. Recently developed metagenomic methods have proven to be powerful tools for simultaneous pathogen detection. Here, we performed a systematic study of the capability of the short-read-based metagenomic approach in the molecular detection of viral pathogens in nasopharyngeal aspirate samples from patients with acute lower respiratory tract infections (
n
= 16). Using the high-throughput capacity of ultradeep sequencing and a dedicated data interpretation method, we successfully identified seven species of known respiratory viral agents from 15 samples, a result that was consistent with results of conventional PCR assays. We also detected a coinfected case that was missed by regular PCR testing. Using the metagenomic data, 11 draft genomes of the abundantly detected viruses in the samples were reconstructed with 21.84% to 98.53% coverage. Our results show the power of the short-read-based metagenomic approach for accurate and parallel screening of viral pathogens. Although there are some inherent difficulties in applying this approach to clinical samples, including a lack of controls, limited specimen quantity, and high contamination rate, our work will facilitate further application of this unprecedented high-throughput method to clinical samples.