Test Theory

Lumsden, James

doi:10.1146/annurev.ps.27.020176.001343

Cited by 99 publications

(48 citation statements)

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“…Analytical results demonstrate that the percentage of explained variation for the first factor exceeded 20% for each dimension. Moreover, the ratio of eigenvalues between the first and second factor exceeded 2, supporting unidimensionality (Lumsden, 1976). These analytical results imply that the data fulfill the unidimensionality assumption, thus meeting the assumption of local independence (Lord and Novick, 1968).…”

Section: Fit Statistics Analysis and Item Parameter Estimatessupporting

confidence: 61%

Perceived accessibility, mobility, and connectivity of public transportation systems

Cheng

Chen

2015

Transportation Research Part A: Policy and Practice

130

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Section: Fit Statistics Analysis and Item Parameter Estimatessupporting

confidence: 61%

Perceived accessibility, mobility, and connectivity of public transportation systems

Cheng

Chen

2015

Transportation Research Part A: Policy and Practice

130

View full text Add to dashboard Cite

“…Lord & Novick, 1968, p. 351). As was pointed out by Lumsden (1976), the notion of unidimensionality has, however, been seriously neglected both by constructors of tests and by test theorists. The unidimensionality assumption of the Rasch model, along with the availability of goodness-of-fit tests makes, in principle at least, this model useful in investigations of the unidimensionality of sets of observations.…”

Section: Evaluating Fit When the Rasch Model Is Wed As A Criterionmentioning

confidence: 99%

Testing and obtaining fit of data to the Rasch model

Gustafsson¹

1980

Brit J Math & Statis

154

113

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Problems and procedures in amessing and obtaining fit of data to the Rasch model are treated in the paper. The assumptions embodied in the model are made explicit and it is concluded that statistical tests are neoded which are sensitive to deviations such that more than one item parameter would be needed for each item, and such that more than one person parameter would be noeded for each person. Statistical goodness-of-fit tests, based on the conditional maximum-likelihood estimates of the item parameters, which can detect these two kinds of deviation are presented. Common sources of deviation are also identified, t w are the tests needed to detect them. Problems in the use of Statistical tests to msess fit are discussed and some investigations of power are presented. In relation to a distinction between use of the Rasch model as a criterion and as an instrument the treatment of the goodness-of-fit problem in different measurement contexts is discussed. Finally it is concluded that items which can be identified as misfitting should not be routinely excluded to obtain fit to the model; instead other actions should often be taken such as grouping of the items into homogeneous subsets.

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“…The two-parameter models have been extensively used (see Bock & Wood, 1971;Lord & Novick, 1968;Lumsden, 1976). Attention has been focused exclusively on scaling from the ICCs, and the PCCs have not been considered.…”

Section: Restrictions Only On the Person Dispersionsmentioning

confidence: 99%

Variations on a Theme by Thurstone

Lumsden

1980

Applied Psychological Measurement

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A test model based on the Thurstone judgmental model is described. By restricting various parameters of the model, 3 Rasch models, 2 pseudoRasch models, 3 two-parameter ICC models, and a Weber's Law model are derived.The thematic model for latent trait approaches to test scaling was developed by Thurstone (1927) from his law of comparative judgment. The model was variously termed the method of successive intervals (Saffir, 1937), the method of graded dichotomies (Attneave, 1949), and the law of categorical judgment (Torgerson, 1958). In the model, stimuli were conceived as having a discriminal dispersion around a central location on an attribute continuum and judgmental categories (or category boundaries) as having a similar distribution on the same continuum. A variant of this model, which will be called Thurstone Model A, is produced by substituting items for stimuli and persons for judgmental categories, as illustrated in Figure 1.Thurstone Model A locates items and persons on the same attribute continuum. Each item and each person has a normal distribution of values on the attribute resulting from moment to moment fluctuation. The standard deviations of APPLIED the distributions may differ from item to item or from person to person. Item and person param_eters are assumed to be independent of each other (ri, = 0). The correlation between location and dispersion parameters is unspecified for either items or persons. A person answers an item correctly if, at the moment of attempting it, his/her momentary attribute value is higher than the momentary attribute value of the item; otherwise he/she answers it incorrectly. Torgerson (1958) suggested certain simplifications of the thematic model in order to overcome the formidable estimation problems. He set the standard deviations for categories (subjects) equal and called the result Condition B; he set standard deviations for stimuli (items) equal and called the result Condition C; finally, he set both the standard deviations of categories and the standard deviations of stimuli equal and called the result Condition D. It is the purpose of this paper to examine more systematically a wider range of simplifying possibilities and to relate these to ancient and modern approaches to test scaling. Restrictions on Both Item and Person Dispersions Torgerson did not consider the cases where item and person dispersions are set to zero. It

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Test Theory

Cited by 99 publications

References 0 publications

Perceived accessibility, mobility, and connectivity of public transportation systems

Perceived accessibility, mobility, and connectivity of public transportation systems

Testing and obtaining fit of data to the Rasch model

Variations on a Theme by Thurstone

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