198,269 research outputs found
On the Wedderburn–Guttman theorem
No full textAbstractLet A be a u by v matrix of rank a, and let M and N be u by g and v by g matrices, respectively, such that M′AN is nonsingular. Then, rank(A−N(M′AN)−1M′A)=a−g, where g=rank(AN(M′AN)−1M′A)=rank(M′AN). This is called Wedderburn–Guttman theorem. What happens if M′AN is rectangular and/or singular? In this paper we investigate conditions under which the regular inverse (M′AN)−1 can be replaced by a g-inverse (M′AN)− of some kind, thereby extending the Wedderburn–Guttman theorem. The resultant conditions look similar to those arising in seemingly unrelated contexts, namely Cochran’s and related theorems on distributions of quadratic forms involving a normal random vector
Weighted Guttman errors: Handling ties and two-level data
No full textWe provide an introduction to weighted Guttman errors and discuss two problems in computing weighted Guttman errors that are currently not handled correctly by all software: Handling ties—that is, computing weighted Guttman errors when two items have the same estimated popularity—and computing weighted Guttman errors when the data have a two-level structure. Handling ties can be incorporated easily in existing software. For computing weighted Guttman errors for two-level data, we provide an R function
The Use of the Guttman Scale in Development of a Family Business Index
No full textThe purpose of this paper is to introduce a new approach for operationalising family-business variables. It is consistent with multidimensional definitions of family business such as the F-PEC scale. This paper demonstrates the use of the Guttman-scaling procedure, on a random sample of 885 Dutch SMEs. More specifically, the research question is as follows: Can various indicators of family business be validly combined using a Guttman scale? After reviewing the different definitions dealt with in the family business research literature, the paper presents the results of an analysis of various items available for this particular dataset. In particular, the index assigns a value of family-relatedness to a company depending upon the criteria that it meets. The study uses a series of statistical procedures, including factor analysis and cross-tabulations, to identify a potential ordering of criteria varying in difficulty. The least difficult criterion, that one or more of the management team is drawn from the family that owns the business, is met by 77.6% of the responding firms. The most difficult of the criteria, met by only 26% of the firms, is that current management plans to transfer the enterprise to the next generation. 85% of the sample can be classified properly according to this Guttman scale: If a company meets one of the more difficult criteria, it also meets all the easier criteria. In the second part of the paper, the proposed Guttman Scale is compared with the individual criteria making up the scale as well as other family business variables to predict self-perceptions of family business. In particular, the scale is positively correlated with the outcome of the question, 'Would you consider your firm a family business?' In addition, a multiple regression of the individual criteria on the dependent variable is compared with the use of the index. The paper sums up with further discussion of the possible advantages and disadvantages of the Guttman scale technique, both for theoretical and empirical development in family business research.
Alternative characterizations of the extended Wedderburn–Guttman theorem
No full textAbstractLet A be a u by v matrix of rank a, and let M and N be u by p and v by q matrices, respectively, where p is not necessarily equal to q or rank(M′AN)<min(p,q). Takane and Yanai [Y. Takane, H. Yanai, On the Wedderburn–Guttman theorem, Linear Algebra Appl. 410 (2005) 267–278] investigated the conditions under which rank(A-AN(M′AN)-M′A)=rank(A)-rank(AN(M′AN)-M′A). This is called the extended Wedderburn–Guttman theorem. In this paper, we give alternative characterizations of these conditions using the product singular value decomposition (PSVD) of matrix triplets
Scaling indices of disablement
No full textWilliams et al. (1976) have suggested the use of Guttman scaling for scoring an index of disability. Two examples confirm the applicability of this method in the context of survey research. One of these examples is of a disablement scale widely employed in local authority social services research. For the purpose of survey assessment of disabled populations, the precise choice of scaling method for scoring disability is often of little consequence
Weighted Guttman errors: Handling ties and two-level data
No full textWe provide an introduction to weighted Guttman errors and discuss two problems in computing weighted Guttman errors that are currently not handled correctly by all software: Handling ties—that is, computing weighted Guttman errors when two items have the same estimated popularity—and computing weighted Guttman errors when the data have a two-level structure. Handling ties can be incorporated easily in existing software. For computing weighted Guttman errors for two-level data, we provide an R function
The longitudinal Guttman simplex: A new methodology for measurement of dynamic constructs in longitudinal panel studies
No full textTraditional psychometric procedures can be inadequate
for the measurement of dynamic constructs in
longitudinal panel studies. This paper introduces an alternative
based on the longitudinal Guttman simplex
(LGS) model,a measurement model developed especially
for dynamic constructs measured longitudinally.
The LGS is a model of cumulative, unitary development.
It is cumulative in the sense that as persons acquire
new skills (or abilities, or opinions), earlier obtained
skills are retained; it is unitary in the sense that
all persons progress through a sequence of skills in the
same skill order. CL, a consistency index that gives
the researcher a measure of the extent to which the
LGS model axioms are obeyed in a given dataset, is
introduced. By making use of this consistency index,
the researcher can develop scales uniquely sensitive to
cumulative, unitary development. LGSCLUS, an exploratory
procedure to find longitudinal Guttman scales in
empirical datasets, is described. An artificial data
study is reported, the purpose of which was to test the
performance of LGSCLUS under controlled conditions.
The artificial data study showed that, in general,
LGSCLUS recovers longitudinal Guttman scales with a
high degree of accuracy. There remains a need for
measurement procedures for dynamic constructs exhibiting
types of development other than cumulative and
unitary. Index terms: Dynamic constructs, Guttman
simplex, Longitudinal panel studies, Mathematical
models, Measurement theory, Scaling, Three-set data.Collins, Linda M.; Cliff, Norman; Dent, Clyde W.. (1988). The longitudinal Guttman simplex: A new methodology for measurement of dynamic constructs in longitudinal panel studies. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/104227
The development of a scale of the Guttman Type for the assessment of mobility disability in multiple sclerosis
No full textObjective: The aim of the study was to develop a valid and reliable unidimensional scale of the Guttman type for the assessment of mobility disability in multiple sclerosis (MS).
Subjects: Sixty-eight subjects with a definite diagnosis of MS participated.They were attending as outpatients at a MS unit at a District General Hospital. Thirty had the primary progressive pattern of disease, and 38 had the relapsing-remitting pattern.
Methods: Formal assessments used for neurological disability were inspected, and 14 test items of gross motor function were extracted and ordered according to two criteria. These were that actions progressed from lying, to sitting, to standing and walking tasks, and that they progressed from broader to narrower bases of support. All subjects carried out all test items which were scored as ‘pass’ or ‘fail’.
Analysis: Data were tested for internal consistency, reliability, inter item correlation, reproducibility and scalability. On the basis of the results, the items were re-ordered in rank, and reduced to eleven tests. The eleven item scale was re-analysed.
Results: Results showed that the scale had an internal consistency of 0.88 (alpha coefficient) and a coefficient of reproducibility (CR) of 0.95 and above for both MS subject groups. The coefficient of scalability (CS) for items was 0.78 for primary progressive subjects and 0.74 for the relapsing-remitting group. Reliability ranged from good (kappa = 0.49) for one item, to perfect for six items.
Conclusion: The scale was demonstrated to be a hierarchical scale of the Guttman type exhibiting homogeneous unidimensionality and good reliability. The high CR indicated that scores may be summed, and the very acceptable levels of CS indicated that the cumulative scores are meaningful within the defined concept of hierarchy used in this study
Schematic representation of Guttman/Rasch data structure.
No full text<p>Representation of the raw data (top) and after sorting of the columns (health states) and the rows (patients) in order to arrive at the hierarchical Guttman/Rasch data structures (the check mark indicates that this health state is preferred over the next health state, the cross mark indicates a misfit) (from: <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0079494#pone.0079494-Arons1" target="_blank">[33]</a>).</p
Dr. Duane M. Jackson, Morehouse College, July 2011
No full textThis video is a conversation with Dr. Duane M. Jackson. Dr. Jackson talks about his paper, "Recall and the Serial Position Effect: The Role of Primacy and Recency on Accounting Students' Performance." Jackie Daniel, AUC Woodruff Library, is the interviewer
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