David Andrich
Biographic Data
| ID | 374265 |
|---|---|
| NAME | David Andrich |
| GIVEN NAMES | David |
| FAMILY NAME | Andrich |
| SIGNATURE | ANDRICH D |
| AFFILIATIONS | Murdoch University |
| ORCID | 0000-0003-2085-6167 |
| VERIFIED | Yes |
| TOTAL WORKS | 21 |
| TOTAL CITATIONS | 140 |
| AUTHOR COUNT | 21 |
| EDITOR COUNT | 0 |
| FIRST PUBLICATION YEAR | 1978 |
| LATEST PUBLICATION YEAR | 2016 |
| H-INDEX | 2 |
Georg Rasch and Benjamin Wright’s Struggle With the Unidimensional Polytomous Model With Sufficient Statistics
This article reproduces correspondence between Georg Rasch of The University of Copenhagen and Benjamin Wright of The University of Chicago in the period from January 1966 to July 1967. This correspondence reveals their struggle to operationalize a unidimensional measurement model with sufficient statistics for responses in a set of ordered categories. The article then explains the original approach taken by Rasch, Wright, and Andersen, and then …
Controlling Guessing Bias in the Dichotomous Rasch Model Applied to a Large-Scale, Vertically Scaled Testing Program
Recent research has shown how the statistical bias in Rasch model difficulty estimates induced by guessing in multiple-choice items can be eliminated. Using vertical scaling of a high-profile national reading test, it is shown that the dominant effect of removing such bias is a nonlinear change in the unit of scale across the continuum. The consequence is that the proficiencies of the more proficient students are increased relative to those of th…
Real and Artificial Differential Item Functioning in Polytomous Items
Differential item functioning (DIF) for an item between two groups is present if, for the same person location on a variable, persons from different groups have different expected values for their responses. Applying only to dichotomously scored items in the popular Mantel–Haenszel (MH) method for detecting DIF in which persons are classified by their total scores on an instrument, Andrich and Hagquist articulated the concept of artificial DIF an…
The Legacies of R. A. Fisher and K. Pearson in the Application of the Polytomous Rasch Model for Assessing the Empirical Ordering of Categories
Assessments in response formats with ordered categories are ubiquitous in the social and health sciences. Although the assumption that the ordering of the categories is working as intended is central to any interpretation that arises from such assessments, testing that this assumption is valid is not standard in psychometrics. This is surprising given that it has been known for some 35 years that this assumption can be checked routinely using the…
An Expanded Derivation of the Threshold Structure of the Polytomous Rasch Model That Dispels Any “Threshold Disorder Controversy”
Responses to items with formats in more than two ordered categories are ubiquitous in education and the social sciences. Because the putative ordering of the categories reflects an understanding of what it means to have more of the variable, it seems mandatory that the ordering of the categories is an empirical property of the assessments and not merely a property of the model used to analyze them. To provide an unequivocal interpretation of cate…
Controversy and the Rasch Model
The development of Rasch models in educational and psychologic measurement in the 1960s coincided with the introduction of other similar models, now described as models of item response theory (IRT). The application of IRT models has now extended to other social sciences, including health. Originally, there was substantial controversy between those who saw Rasch models as simply special cases of IRT models and those who saw them as essentially di…
Measuring subjective health among adolescents in Sweden
On the Distribution of Measurements in Units that are not Arbitrary
Measurement achieved in the physical sciences as some kind of mapping on a continuum partitioned into equal units from an origin is understood readily. However, measurement is also an advanced concept, the achievement of which has been integral to the remarkable progress of physical science. This article specializes the probabilistic Rasch model for a finite number of ordered response categories to a response structure which is analogous to measu…
A framework relating outcomes based education and the taxonomy of educational objectives
Implications and applications of modern test theory in the context of outcomes based education
Differential Subject Performance and the Problems of Selection
Methods of test equating and scaling have been studied in the statistically advanced literature of educational and psychological measurement, and applied extensively where mass testing and selection procedures are required; for example, selection for tertiary study. Usually the procedures themselves require large data sets, and they are applied in order to ensure that students are not advantaged or disadvantaged because of the arbitrary features …
Psychometric Evidence of Intellectual Growth Spurts in Early Adolescence
A tantalizing idea indicated by both qualitative psychological research and brain research is that intellectual growth includes spurts. Intellectual growth spurts have been difficult to confirm quantitatively because of the lack of a constant unit of measurement for an intellectual variable applicable across different ages and because of problems in conducting longitudinal studies. This article reports quantitative evidence of an intellectual gro…
Linking the Standard and Advanced forms of the Raven'S Progressive Matrices in both the Pencil-And-Paper and Computer-Adaptive-Testing Formats
The concepts of adaptive testing, already used by Binet, and concepts of modern or latent trait theory, already extended from psychophysics by Thurstone, have been brought together by the advent of the computer, particularly the PC. With these developments, it is likely that to test specific abilities, special tests will be constructed for administration only by a computer and not in pencil and paper format. In the meantime, many existing paper-a…
Rasch Models for Measurement
It is true that, in his interpretation of the results of these analyses, the author implicitly accepts the limitation which this unexplored level of collinearity in his variables imposes: his interpretation is almost entirely carried out in terms of the values on the left-hand side of his equations and he properly refrains from any attempt to interpret the individual coefficients on the right-hand side. Nevertheless I think that the book would ha…
An Elaboration of Guttman Scaling with Rasch Models for Measurement
Permission from M. Dynan, L. H. Parker, and A. Ryan to use data from the evaluation of a new subject introduced into some secondary schools in Western Australia is gratefully acknowledged, as are discussions about the theoretical implications of the data with L. H. Parker. Alan Lyne wrote the computer programs used in the analysis of the data. Helpful comments on earlier versions of the chapter were provided by G. A. Douglas, 0. D. Duncan, G. N. …
Recognizing a Violation of the Assumption of Local Independence in the Analysis of Test Data
A computer program for analysing test data according to a latent trait model which allows for dependencies among responses is described briefly. The model allows for dependencies among a subset of dichotomously scored items through a dispersion parameter associated with the subtest. The smaller the value for this parameter, the greater the dependence. In addition to the estimates of the difficulty and dependence parameters of subtests and the est…
Within and Among Population Item Fit with the Simple Logistic Model
The Rasch simple logistic model is used to examine the relative item parameter values of a personality inventory with respect to populations cross classified by sex and country. If the model holds across populations these values should be statistically equivalent. However, while the items conform to the model within each of the populations, half the items show significant discrepancies among the populations. These discrepancies are interpreted bo…
Stability of Response, Reliability, and Accuracy of Measurement
A study on response stability when a subject encounters personality inventory items is re-examined in terms of the latent trait model used. This re-examination shows, firstly that the study demonstrates an important type of validity for the application of latent trait models to such items, and secondly that the original recommendations for test construction based on the study require modification. A key aspect of the paper is an amplication of th…
Scaling Attitude Items Constructed and Scored in the Likert Tradition
The statement scaling emphasis associated with the Thurstone tradition for the study of attitude provides no direct consequence for attitude measurement, while conversely, the attitude measurement emphasis in the Likert tradition provides no direct consequence for statement scaling. Both aspects of the study of attitude are unified by a generalisation of Rasch's simple logistic model for dichotomously scored achievement items. The generalized mod…
Hierarchies in the Skills of Davis' 'Reading Comprehension Test', Form D
David Andrich, John R. Godfrey, Hierarchies in the Skills of Davis' 'Reading Comprehension Test', Form D: An Empirical Investigation Using a Latent Trait Model, Reading Research Quarterly, Vol. 14, No. 2 (1978 - 1979), pp. 182-200
A rating formulation for ordered response categories
A rating response mechanism for ordered categories, which is related to the traditional threshold formulation but distinctively different from it, is formulated. In addition to the subject and item parameters two other sets of parameters, which can be interpreted in terms of thresholds on a latent continuum and discriminations at the thresholds, are obtained. These parameters are identified with the category coefficients and the scoring function …
A rating formulation for ordered response categories
A rating response mechanism for ordered categories, which is related to the traditional threshold formulation but distinctively different from it, is formulated. In addition to the subject and item parameters two other sets of parameters, which can be interpreted in terms of thresholds on a latent continuum and discriminations at the thresholds, are obtained. These parameters are identified with the category coefficients and the scoring function …
Measuring subjective health among adolescents in Sweden
Psychometric Evidence of Intellectual Growth Spurts in Early Adolescence
A tantalizing idea indicated by both qualitative psychological research and brain research is that intellectual growth includes spurts. Intellectual growth spurts have been difficult to confirm quantitatively because of the lack of a constant unit of measurement for an intellectual variable applicable across different ages and because of problems in conducting longitudinal studies. This article reports quantitative evidence of an intellectual gro…
On the Distribution of Measurements in Units that are not Arbitrary
Measurement achieved in the physical sciences as some kind of mapping on a continuum partitioned into equal units from an origin is understood readily. However, measurement is also an advanced concept, the achievement of which has been integral to the remarkable progress of physical science. This article specializes the probabilistic Rasch model for a finite number of ordered response categories to a response structure which is analogous to measu…
An Elaboration of Guttman Scaling with Rasch Models for Measurement
Permission from M. Dynan, L. H. Parker, and A. Ryan to use data from the evaluation of a new subject introduced into some secondary schools in Western Australia is gratefully acknowledged, as are discussions about the theoretical implications of the data with L. H. Parker. Alan Lyne wrote the computer programs used in the analysis of the data. Helpful comments on earlier versions of the chapter were provided by G. A. Douglas, 0. D. Duncan, G. N. …
Scaling Attitude Items Constructed and Scored in the Likert Tradition
The statement scaling emphasis associated with the Thurstone tradition for the study of attitude provides no direct consequence for attitude measurement, while conversely, the attitude measurement emphasis in the Likert tradition provides no direct consequence for statement scaling. Both aspects of the study of attitude are unified by a generalisation of Rasch's simple logistic model for dichotomously scored achievement items. The generalized mod…
Hierarchies in the Skills of Davis' 'Reading Comprehension Test', Form D
David Andrich, John R. Godfrey, Hierarchies in the Skills of Davis' 'Reading Comprehension Test', Form D: An Empirical Investigation Using a Latent Trait Model, Reading Research Quarterly, Vol. 14, No. 2 (1978 - 1979), pp. 182-200
A rating formulation for ordered response categories
A rating response mechanism for ordered categories, which is related to the traditional threshold formulation but distinctively different from it, is formulated. In addition to the subject and item parameters two other sets of parameters, which can be interpreted in terms of thresholds on a latent continuum and discriminations at the thresholds, are obtained. These parameters are identified with the category coefficients and the scoring function …
Within and Among Population Item Fit with the Simple Logistic Model
The Rasch simple logistic model is used to examine the relative item parameter values of a personality inventory with respect to populations cross classified by sex and country. If the model holds across populations these values should be statistically equivalent. However, while the items conform to the model within each of the populations, half the items show significant discrepancies among the populations. These discrepancies are interpreted bo…
Stability of Response, Reliability, and Accuracy of Measurement
A study on response stability when a subject encounters personality inventory items is re-examined in terms of the latent trait model used. This re-examination shows, firstly that the study demonstrates an important type of validity for the application of latent trait models to such items, and secondly that the original recommendations for test construction based on the study require modification. A key aspect of the paper is an amplication of th…
Recognizing a Violation of the Assumption of Local Independence in the Analysis of Test Data
A computer program for analysing test data according to a latent trait model which allows for dependencies among responses is described briefly. The model allows for dependencies among a subset of dichotomously scored items through a dispersion parameter associated with the subtest. The smaller the value for this parameter, the greater the dependence. In addition to the estimates of the difficulty and dependence parameters of subtests and the est…
An Elaboration of Guttman Scaling with Rasch Models for Measurement
Permission from M. Dynan, L. H. Parker, and A. Ryan to use data from the evaluation of a new subject introduced into some secondary schools in Western Australia is gratefully acknowledged, as are discussions about the theoretical implications of the data with L. H. Parker. Alan Lyne wrote the computer programs used in the analysis of the data. Helpful comments on earlier versions of the chapter were provided by G. A. Douglas, 0. D. Duncan, G. N. …
Rasch Models for Measurement
It is true that, in his interpretation of the results of these analyses, the author implicitly accepts the limitation which this unexplored level of collinearity in his variables imposes: his interpretation is almost entirely carried out in terms of the values on the left-hand side of his equations and he properly refrains from any attempt to interpret the individual coefficients on the right-hand side. Nevertheless I think that the book would ha…
Linking the Standard and Advanced forms of the Raven'S Progressive Matrices in both the Pencil-And-Paper and Computer-Adaptive-Testing Formats
The concepts of adaptive testing, already used by Binet, and concepts of modern or latent trait theory, already extended from psychophysics by Thurstone, have been brought together by the advent of the computer, particularly the PC. With these developments, it is likely that to test specific abilities, special tests will be constructed for administration only by a computer and not in pencil and paper format. In the meantime, many existing paper-a…
Psychometric Evidence of Intellectual Growth Spurts in Early Adolescence
A tantalizing idea indicated by both qualitative psychological research and brain research is that intellectual growth includes spurts. Intellectual growth spurts have been difficult to confirm quantitatively because of the lack of a constant unit of measurement for an intellectual variable applicable across different ages and because of problems in conducting longitudinal studies. This article reports quantitative evidence of an intellectual gro…
Differential Subject Performance and the Problems of Selection
Methods of test equating and scaling have been studied in the statistically advanced literature of educational and psychological measurement, and applied extensively where mass testing and selection procedures are required; for example, selection for tertiary study. Usually the procedures themselves require large data sets, and they are applied in order to ensure that students are not advantaged or disadvantaged because of the arbitrary features …
A framework relating outcomes based education and the taxonomy of educational objectives
Implications and applications of modern test theory in the context of outcomes based education
On the Distribution of Measurements in Units that are not Arbitrary
Measurement achieved in the physical sciences as some kind of mapping on a continuum partitioned into equal units from an origin is understood readily. However, measurement is also an advanced concept, the achievement of which has been integral to the remarkable progress of physical science. This article specializes the probabilistic Rasch model for a finite number of ordered response categories to a response structure which is analogous to measu…
Controversy and the Rasch Model
The development of Rasch models in educational and psychologic measurement in the 1960s coincided with the introduction of other similar models, now described as models of item response theory (IRT). The application of IRT models has now extended to other social sciences, including health. Originally, there was substantial controversy between those who saw Rasch models as simply special cases of IRT models and those who saw them as essentially di…
Measuring subjective health among adolescents in Sweden
The Legacies of R. A. Fisher and K. Pearson in the Application of the Polytomous Rasch Model for Assessing the Empirical Ordering of Categories
Assessments in response formats with ordered categories are ubiquitous in the social and health sciences. Although the assumption that the ordering of the categories is working as intended is central to any interpretation that arises from such assessments, testing that this assumption is valid is not standard in psychometrics. This is surprising given that it has been known for some 35 years that this assumption can be checked routinely using the…
An Expanded Derivation of the Threshold Structure of the Polytomous Rasch Model That Dispels Any “Threshold Disorder Controversy”
Responses to items with formats in more than two ordered categories are ubiquitous in education and the social sciences. Because the putative ordering of the categories reflects an understanding of what it means to have more of the variable, it seems mandatory that the ordering of the categories is an empirical property of the assessments and not merely a property of the model used to analyze them. To provide an unequivocal interpretation of cate…
Real and Artificial Differential Item Functioning in Polytomous Items
Differential item functioning (DIF) for an item between two groups is present if, for the same person location on a variable, persons from different groups have different expected values for their responses. Applying only to dichotomously scored items in the popular Mantel–Haenszel (MH) method for detecting DIF in which persons are classified by their total scores on an instrument, Andrich and Hagquist articulated the concept of artificial DIF an…
Georg Rasch and Benjamin Wright’s Struggle With the Unidimensional Polytomous Model With Sufficient Statistics
This article reproduces correspondence between Georg Rasch of The University of Copenhagen and Benjamin Wright of The University of Chicago in the period from January 1966 to July 1967. This correspondence reveals their struggle to operationalize a unidimensional measurement model with sufficient statistics for responses in a set of ordered categories. The article then explains the original approach taken by Rasch, Wright, and Andersen, and then …
Controlling Guessing Bias in the Dichotomous Rasch Model Applied to a Large-Scale, Vertically Scaled Testing Program
Recent research has shown how the statistical bias in Rasch model difficulty estimates induced by guessing in multiple-choice items can be eliminated. Using vertical scaling of a high-profile national reading test, it is shown that the dominant effect of removing such bias is a nonlinear change in the unit of scale across the continuum. The consequence is that the proficiencies of the more proficient students are increased relative to those of th…
Psychology (18 works) · Item response theory (14 works) · Mathematics (14 works) · Psychometric Methodologies and Testing (14 works) · Psychometrics (14 works) · Rasch model (14 works) · Developmental psychology (13 works) · Computer Science (12 works) · Statistics (12 works) · Polytomous Rasch model (9 works)