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1.
Two well-known lower bounds to the reliability in classical test theory, Guttman's 2 and Cronbach's coefficient alpha, are shown to be terms of an infinite series of lower bounds. All terms of this series are equal to the reliability if and only if the test is composed of items which are essentially tau-equivalent. Some practical examples, comparing the first 7 terms of the series, are offered. It appears that the second term (2) is generally worth-while computing as an improvement of the first term (alpha) whereas going beyond the second term is not worth the computational effort. Possibly an exception should be made for very short tests having widely spread absolute values of covariances between items. The relationship of the series and previous work on lower bound estimates for the reliability is briefly discussed.The authors are obliged to Henk Camstra for providing a computer program that was used in this study. 相似文献
2.
In theory, the greatest lower bound (g.l.b.) to reliability is the best possible lower bound to the reliability based on single test administration. Yet the practical use of the g.l.b. has been severely hindered by sampling bias problems. It is well known that the g.l.b. based on small samples (even a sample of one thousand subjects is not generally enough) may severely overestimate the population value, and statistical treatment of the bias has been badly missing. The only results obtained so far are concerned with the asymptotic variance of the g.l.b. and of its numerator (the maximum possible error variance of a test), based on first order derivatives and the asumption of multivariate normality. The present paper extends these results by offering explicit expressions for the second order derivatives. This yields a closed form expression for the asymptotic bias of both the g.l.b. and its numerator, under the assumptions that the rank of the reduced covariance matrix is at or above the Ledermann bound, and that the nonnegativity constraints on the diagonal elements of the matrix of unique variances are inactive. It is also shown that, when the reduced rank is at its highest possible value (i.e., the number of variables minus one), the numerator of the g.l.b. is asymptotically unbiased, and the asymptotic bias of the g.l.b. is negative. The latter results are contrary to common belief, but apply only to cases where the number of variables is small. The asymptotic results are illustrated by numerical examples.This research was supported by grant DMI-9713878 from the National Science Foundation. 相似文献
3.
In the last decade several algorithms for computing the greatest lower bound to reliability or the constrained minimum-trace communality solution in factor analysis have been developed. In this paper convergence properties of these methods are examined. Instead of using Lagrange multipliers a new theorem is applied that gives a sufficient condition for a symmetric matrix to be Gramian. Whereas computational pitfalls for two methods suggested by Woodhouse and Jackson can be constructed it is shown that a slightly modified version of one method suggested by Bentler and Woodward can safely be applied to any set of data. A uniqueness proof for the solution desired is offered.The authors are obliged to Charles Lewis and Dirk Knol for helpful comments, and to Frank Brokken and Henk Camstra for developing computer programs. 相似文献
4.
We derive several relationships between communalities and the eigenvalues for ap ×p correlation matrix under the usual factor analysis model. For suitable choices ofj,
j
(), where
j
() is thej-th largest eigenvalue of , provides either a lower or an upper bound to the communalities for some of the variables. We show that for at least one variable, 1 -
p
() improves on the use of squared mulitiple correlation coefficient as a lower bound.This research was done while the second author was at Tokyo Institute of Technology. 相似文献
5.
Let Σ
x
be the (population) dispersion matrix, assumed well-estimated, of a set of non-homogeneous item scores. Finding the greatest
lower bound for the reliability of the total of these scores is shown to be equivalent to minimizing the trace of Σ
x
by reducing the diagonal elements while keeping the matrix non-negative definite. Using this approach, Guttman's bounds are
reviewed, a method is established to determine whether his λ4 (maximum split-half coefficient alpha) is the greatest lower bound in any instance, and three new bounds are discussed. A
geometric representation, which sheds light on many of the bounds, is described.
Present affiliation of the second author: Department of Statistics, University of Nigeria (Nsukka Campus). Work on this paper
was carried out while on study leave in Aberystwyth. 相似文献
6.
W. Alan Nicewander 《Psychometrika》1990,55(1):65-74
An estimate and an upper-bound estimate for the reliability of a test composed of binary items is derived from the multidimensional latent trait theory proposed by Bock and Aitkin (1981). The estimate derived here is similar to internal consistency estimates (such as coefficient alpha) in that it is a function of the correlations among test items; however, it is not a lowerbound estimate as are all other similar methods.An upper bound to reliability that is less than unity does not exist in the context of classical test theory. The richer theoretical background provided by Bock and Aitkin's latent trait model has allowed the development of an index (called here) that is always greater-than or equal-to the reliability coefficient for a test (and is less-than or equal-to one). The upper bound estimate of reliability has practical uses—one of which makes use of the greatest lower bound. 相似文献
7.
W. Alan Nicewander 《Psychometrika》1993,58(1):139-141
It is shown that IRTs information function for an item is functionally related to local versions of classical test theories' signal/noise ratio and reliability coefficient. 相似文献
8.
Finding the greatest lower bound for the reliability of the total score on a test comprisingn non-homogenous items with dispersion matrix Σ
x
is equivalent to maximizing the trace of a diagonal matrix Σ
E
with elements θ
I
, subject to Σ
E
and Σ
T
=Σ
x
− Σ
E
being non-negative definite. The casesn=2 andn=3 are solved explicity. A computer search in the space of the θ
i
is developed for the general case. When Guttman's λ4 (maximum split-half coefficient alpha) is not the g.l.b., the maximizing set of θ
i
makes the rank of Σ
T
less thann − 1. Numerical examples of various bounds are given.
Present affiliation of the first author: St. Hild's College of Education, Durham City, England. 相似文献
9.
Coefficients Alpha,Beta, Omega,and the glb: Comments on Sijtsma 总被引:2,自引:1,他引:1
There are three fundamental problems in Sijtsma (Psychometrika, 2008): (1) contrary to the name, the glb is not the greatest lower bound of reliability but rather is systematically less than
ω
t
(McDonald, Test theory: A unified treatment, Erlbaum, Hillsdale, 1999), (2) we agree with Sijtsma that when considering how well a test measures one concept, α is not appropriate, but recommend ω
t
rather than the glb, and (3) the end user needs procedures that are readily available in open source software. 相似文献
10.
To assess the reliability of congeneric tests, specifically designed reliability measures have been proposed. This paper emphasizes
that such measures rely on a unidimensionality hypothesis, which can neither be confirmed nor rejected when there are only
three test parts, and will invariably be rejected when there are more than three test parts. Jackson and Agunwamba's (1977)
greatest lower bound to reliability is proposed instead. Although this bound has a reputation for overestimating the population
value when the sample size is small, this is no reason to prefer the unidimensionality-based reliability. Firstly, the sampling
bias problem of the glb does not play a role when the number of test parts is small, as is often the case with congeneric
measures. Secondly, glb and unidimensionality based reliability are often equal when there are three test parts, and when
there are more test parts, their numerical values are still very similar. To the extent that the bias problem of the greatest
lower bound does play a role, unidimensionality-based reliability is equally affected. Although unidimensionality and reliability
are often thought of as unrelated, this paper shows that, from at least two perspectives, they act as antagonistic concepts.
A measure, based on the same framework that led to the greatest lower bound, is discussed for assessing how close is a set
of variables to unidimensionality. It is the percentage of common variance that can be explained by a single factor. An empirical
example is given to demonstrate the main points of the paper.
The authors are obliged to Henk Kiers for commenting on a previous version. Gregor Sočan is now at the University of Ljubljana. 相似文献
11.
TENKO RAYKOV 《Scandinavian journal of psychology》1993,34(1):94-96
This note is concerned with differences and similarities between structural models for analyzing change, which are conceptualized within two different modelling traditions: the one based on the classical test theory, and that within the factor-analytic approach. It is shown that these two possibilities lead to models for studying change, which are indistinguishable when using for data analytic purposes structural modeling programs, such as LISREL, EQS, COSAN, LISCOMP, RAMONA, EzPATH, SAS PROC CALIS. The reason for this data-analytic equivalence of the two conceptually different types of models is the confounding of their differences in the corresponding implied covariance matrix structures. 相似文献
12.
Expressions involving optimal sign vectors are derived so as to yield two new applications. First, coefficient alpha for the sign-weighted composite is maximized in analogy to Lord's scale-independent solution with differential weights. Second, optimal sign vectors are used to define two groups of objects that are maximally distinct in terms of a function of the squared euclidean distances between groups. An efficient computing algorithm is described along with several examples.This research was supported in part by a research grant (DA 01070) from the U. S. Public Health Service. 相似文献
13.
In the classical test theory, a high-reliability test always leads to a precise measurement. However, when it comes to the prediction of test scores, it is not necessarily so. Based on a Bayesian statistical approach, we predicted the distributions of test scores for a new subject, a new test, and a new subject taking a new test. Under some reasonable conditions, the predicted means, variances, and covariances of predicted scores were obtained and investigated. We found that high test reliability did not necessarily lead to small variances or covariances. For a new subject, higher test reliability led to larger predicted variances and covariances, because high test reliability enabled a more accurate prediction of test score variances. Regarding a new subject taking a new test, in this study, higher test reliability led to a large variance when the sample size was smaller than half the number of tests. The classical test theory is reanalyzed from the viewpoint of predictions and some suggestions are made. 相似文献
14.
Augustine Osman Peter M. Gutierrez Francisco X. Barrios Beverly A. Kopper Christine E. Chiros 《Journal of psychopathology and behavioral assessment》1998,20(3):249-264
The present investigations examined the factor structure and psychometric properties of two new self-report measures of social phobia, the Social Interaction Anxiety Scale (SIAS) and the Social Phobia Scale (SPS). A confirmatory factor analysis in Study I provided support for the fit of a two-factor model of the SIAS and SPS. Internal consistency estimates were high for the original two scales with a sample of 200 undergraduates. Also, using an item parceling procedure, the obtained internal consistency reliability indices for each parcel were acceptable. Results of the CFA in Study II provided support for the factorial stability of the model identified in Study I. Furthermore, multisample analyses showed invariant patterns for factor loadings and factor correlations across 138 men and 272 women. Gender differences were not observed in the mean SIAS and SPS scale and item scores. Both scales correlated negatively and significantly with measures of social desirability. Concurrent validity was established for the scales. The SPS was less specific than the SIAS to symptoms of social phobia. 相似文献
15.
16.
The factor structure and composite reliability of the Rosenberg Self-Esteem Scale among ex-prisoners
Daniel Boduszek Philip Hyland Katie Dhingra John Mallett 《Personality and individual differences》2013
The aim of this study was to examine the factor structure and composite reliability of the Rosenberg Self-Esteem Scale (RSES) using a sample of 669 ex-prisoners identified in the National Survey of American Life. Six distinct factor models, with uncorrelated measurement error terms, were specified and tested using confirmatory factor analysis (CFA). Results indicated that the two-factor model consisting of positive and negative latent variables provided a better fit to the data than the alternative models. Moreover, only positive self-esteem was a significant predictor of recidivism. Composite reliability indicated that the two factors were measured with very good reliability. The results consequently provide additional support for a two-dimensional model of the RSES within offender populations. 相似文献
17.
A closed form estimator of the uniqueness (unique variance) in factor analysis is proposed. It has analytically desirable properties—consistency, asymptotic normality and scale invariance. The estimation procedure is given through the application to the two sets of Emmett's data and Holzinger and Swineford's data. The new estimator is shown to lead to values rather close to the maximum likelihood estimator. 相似文献
18.
Vernon L. Greene 《Psychometrika》1978,43(2):273-275
P. M. Bentler has shown that Rao's canonical factor analysis is in effect a psychometric analysis, leading to factors that are maximally assessible from the data. He contrasts this with Kaiser and Caffrey's alpha factor analysis that leads to factors that maximally represent the true factors in the content domain. Noting the problems associated with factors that may be highly assessible, but not very representative, or vice versa, Bentler suggests the need for a technique that would, insofar as possible, be optimal with respect to both criteria. Such a technique is presented here, and is shown to resolve into a traditional scaling method, which in turn acquires a richer psychometric interpretation.The author would like to gratefully acknowledge support for this research from the Workshop in Political Theory and Policy Analysis (Indiana University) and Esco Research Associates. The paper benefitted substantially from the criticisms and suggestions of an anonymous referee. 相似文献
19.
Pallesen S Nordhus IH Carlstedt B Thayer JF Johnsen TB 《Scandinavian journal of psychology》2006,47(4):281-291
A Norwegian version of the Penn State Worry Questionnaire (PSWQ) was administered to 304 undergraduate students together with the Beck Depression Inventory (BDI), the State-Trait Anxiety Inventory (STAI) and the Maudsley Obsessive Compulsive Inventory (MOCI). The PSWQ was also administered to a community sample comprising 879 subjects, together with the Beck Anxiety Inventory (BAI), the Beck Depression Inventory II (BDI II) and the White Bear Suppression Inventory (WBSI). Structural equation modeling showed that a three-factor solution of the PSWQ gave the best goodness of fit. The Norwegian version of the PSWQ demonstrated adequate psychometric properties in terms of reliability and validity in both samples. Females scored higher than males on PSWQ. 相似文献
20.
Recent work on reliability coefficients has largely focused on continuous items, including critiques of Cronbach’s alpha. Although two new model-based reliability coefficients have been proposed for dichotomous items (Dimitrov, 2003a,b; Green & Yang, 2009a), these approaches have yet to be compared to each other or other popular estimates of reliability such as omega, alpha, and the greatest lower bound. We seek computational improvements to one of these model-based reliability coefficients and, in addition, conduct initial Monte Carlo simulations to compare coefficients using dichotomous data. Our results suggest that such improvements to the model-based approach are warranted, while model-based approaches were generally superior. 相似文献