Part I. Experimental Studies: 2. Experiment in psychology 3. Experiments on perceiving III Experiments on imaging 4-8. Experiments on remembering: (a) The method of description (b) The method of repeated reproduction (c) The method of picture writing (d) The method of serial reproduction (e) The method of serial reproduction picture material 9. Perceiving, recognizing, remembering 10. A theory of remembering 11. Images and their functions 12. Meaning Part II. Remembering as a Study in Social Psychology: 13. Social psychology 14. Social psychology and the matter of recall 15. Social psychology and the manner of recall 16. Conventionalism 17. The notion of a collective unconscious 18. The basis of social recall 19. A summary and some conclusions.

Remembering. A Study in Experimental and Social Psychology, Cambridge (University Press) 1964.

The brms package implements Bayesian multilevel models in R using the probabilistic programming language Stan. A wide range of distributions and link functions are supported, allowing users to fit - among others - linear, robust linear, binomial, Poisson, survival, ordinal, zero-inflated, hurdle, and even non-linear models all in a multilevel context. Further modeling options include autocorrelation of the response variable, user defined covariance structures, censored data, as well as meta-analytic standard errors. Prior specifications are flexible and explicitly encourage users to apply prior distributions that actually reflect their beliefs. In addition, model fit can easily be assessed and compared with the Watanabe-Akaike information criterion and leave-one-out cross-validation.

brms: An R Package for Bayesian Multilevel Models Using Stan

The detection of psychiatric illness by questionnaire

SUMMARY A general class of regression models for ordinal data is developed and discussed. These models utilize the ordinal nature of the data by describing various modes of stochastic ordering and this eliminates the need for assigning scores or otherwise assuming cardinality instead of ordinality. Two models in particular, the proportional odds and the proportional hazards models are likely to be most useful in practice because of the simplicity of their interpretation. These linear models are shown to be multivariate extensions of generalized linear models. Extensions to non-linear models are discussed and it is shown that even here the method of iteratively reweighted least squares converges to the maximum likelihood estimate, a property which greatly simplifies the necessary computation. Applications are discussed with the aid of examples.

https://rss.onlinelibrary.wiley.com/doi/pdf/10.1111/j.2517-6161.1980.tb01109.x

Regression Models for Ordinal Data

A unidimensional latent trait model for responses scored in two or more ordered categories is developed. This “Partial Credit” model is a member of the family of latent trait models which share the property of parameter separability and so permit “specifically objective” comparisons of persons and items. The model can be viewed as an extension of Andrich's Rating Scale model to situations in which ordered response alternatives are free to vary in number and structure from item to item. The difference between the parameters in this model and the “category boundaries” in Samejima's Graded Response model is demonstrated. An unconditional maximum likelihood procedure for estimating the model parameters is developed.

A Rasch Model for Partial Credit Scoring.

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 of the Rasch model for polychotomous responses in which the latent trait is assumed uni-dimensional. In the case where the threshold discriminations are equal, the scoring of successive categories by the familiar assignment of successive integers is justified. In the case where distances between thresholds are also equal, a simple pattern of category coefficients is shown to follow.

A rating formulation for ordered response categories

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 have been considerably improved if space could have been found for even a brief discussion of the inter-relationships between the variables. The lack of such an exploration has at least three disadvantages. First, as the author recognises, it makes his discussion of the substantive findings in the central chapter of the book extremely heavy going, since the elements in the discussion are all so abstract. (As he rightly says, "This has been an exceedingly difficult chapter"!) Secondly, it leaves unanswered the intriguing question as to why, in linguistic terms, an analysis using these variables should work at all-an inevitable question if only because, in an inflected language like classical Greek, his 'last letter' variables usually have direct grammatical significance. Thirdly, it will leave those who would wish to carry further the work in this field, which, as the author says, is "deficient still in its theoretical content", with very few further basic principles to guide their work. So one must hope that the author will find time and resources to explore in much more detail the workings of the methodology which he has so successfully introduced to this intriguing field of enquiry.

Rasch models for measurement

Rating Scale Analysis

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 different. Because these different perspectives continue to manifest themselves in various ways, it seems relevant to understand the source of the original controversy. This paper attempts to do so by invoking Kuhn's studies in the history and philosophy of science at 3 levels. First, it suggests that the 2 perspectives reflect Kuhn's concept of legitimate, incompatible paradigms in which controversy is a typical manifestation. Second, because Kuhn recognizes individual histories in the development of paradigms, Rasch's own shift in perspective is summarized. Third, because proponents of the Rasch models emphasize the models' compatibility with fundamental measurement found in physical science, an analogy is made between how Kuhn explains the role of measurement in the physical sciences and how proponents of Rasch models explain the role of these models in the social sciences. In particular, these roles cannot be gleaned from textbooks in science and statistics, respectively.

Controversy and the Rasch model: a characteristic of incompatible paradigms?

A latent trait measurement model in which ordered response categories are both parameterized and scored with successive integers is investigated and applied to a summated rating or Likert ques tionnaire In addition to each category, each item of the questionnaire and each subject are para meterized in the model; and maximum likelihood estimates for these parameters are derived Among the features of the model which make it attractive for applications to Likert questionnaires is that the total score is a sufficient statistic for a subject's at titude measure Thus, the model provides a formal ization of a familiar and practical procedure for measuring attitudes

/pdf/application-of-a-psychometric-rating-model-to-ordered-14qbkhf8oc.pdf

David Andrich

Papers

A rating formulation for ordered response categories

Rasch models for measurement

Rating Scale Analysis

Controversy and the Rasch model: a characteristic of incompatible paradigms?

Application of a psychometric rating model to ordered categories which are scored with successive integers