A Theory and Procedure of Scale Analysis: With Applications in Political Research (Methods and Models in the Social Sciences)

This study is a result of my activities at three academic institutes in Amsterdam: the Department of Mathematical Statistics of the Mathematical Centre and the Institutes of Mass Communications and for Political Science of the University of Amsterdam. It served as a dissertation in the Faculty of Social Sciences of the University of Amsterdam. Much gratitude is owed by me to my nearest colleagues and numerous former colleagues for their kind cooperation and assistance as well as for the opportunities they have given me. I benefited much from the critical comments and general guidance of Professor H. Daudt of the Institute for Political Science during the preparation of the manuscript. Special thanks are due to Drs. W. van Nooten of the Mathematical Centre for our thorough and frequent discussions about chapters 3 and 4 which led to many improvements. With pleasure I also acknowledge the collaboration with Drs. F. Bergsma and Drs. F. N. Stokman in the research, some results of which are reported in chapters 6 and 9, and that with Drs. Constance E. van der Maesen and O. Schmidt in the research, reported in chapters 7, 8 and 9. For the typing of the manuscript I owe much to the concerted efforts of Miss Anke Faddegon, Miss N. Kool and, last but not least, of my wife Thelma. The author's English was corrected skilfully by Mrs. C. M. van Staalen. I also wish to thank the Netherlands Organization for the Advancement of Pure Research (Z.W.O.) for their contribution in the costs of publication. Robert J. Mokken Badhoevedorp, November 1970 CHAPTER 1 The scopet)f the study 1.1 PART I Theory and method CHAPTER 2 The deterministic model: the Guttman scale ## 2. 1 Two examples borrowed from Measurement and Prediction (Suchman, 1950a, 125) are given to illustrate the procedure. They concern two items from a scale measuring "Satisfaction with One's Army Job". First an item of the Yes-No variety. "Would you change to some other Army job if given a chance?" 1 -Yes 2 -No 3 -Undecided In this case 2: "No" may be considered to be the scale alternative (the "positive" answer), "Yes" and "Undecided" forming the complementary alternative. Next a multicategory item: "Which of the following would you say best applies to your job?" 1 -Time always passes quickly. 2 -Time passes quickly most of the time. 3 -Enjoy working part of the time, but it drags at other times. 4 -Time drags most of the time. 5 -Time always drags. ("No answers" were all coded 0). Here alternative 1 may be the scale alternative. However, one might also combine several alternatives to form the scale alternative, e.g. alternatives 1 and 2. The other alternatives together form the second complementary alternative. Guttman's original method was also designed to scale multicategory items without dichotomizing them. We shall not consider these items in this study, and again refer the reader to Torgerson (1958) or Matalon (1965). This restriction does not seem too severe when we consider that dichotomized data are used very frequently in measurement and analysis in the behavioral sciences. #### 2.2.2 Monotone items and trace lines It has been said that each subject "measures" himself against each item in terms of the variable we want to measure, his response giving the result of this comparison. The content of the item determines this response behavior. Now this response behavior can be partially classified into two \*In conformance with common practice in mathematical statistics, Greek symbols will be used for the (unknown) parameters of stochastic models. \*Torgerson seems to confuse these two definitions, as many others did (Torgerson, 1958,. ""max J values he gives will be reached when every subject with a particular \*Galtung's formula contains a misprint: the upper limit of summation is erroneously given as k -1. \* Vectors and matrices will be given in bold print. \* Lazarsfeld (1959 a, 498) reverses the situation by defining a homogeneous class as one in which this statistical independence prevails. \* Another term used is item characteristic function (Lord and Novick, 1968, 360). This terminology seems rather unfortunate, as characteristic functions have a very specific meaning in probabilistic contexts. \* \* \* \* Van der Maesen (-) will suggest the term "personal political effectiveness". \* Non-scale item. \*\*Numbering of statements follows that of the questionnaire. Item numbering is that of section 9.2. ACKNOWLEDGEMENTS 1. THE SCOPE OF THE STUDY 1.1 Introduction 1.2 Data models 1.3 Measurement models 1.4 Outline of the study PART I. THEORY AND METHOD 2. THE DETERMINISTIC MODEL: THE GUTTMAN SCALE 2.1 Introduction 2.2 The perfect scale 2.3 The two sets as populations 2.4 The imperfect scale: the problem of “error” 2.5 Coefficients of scalability 2.6 Procedures of scale analysis 2.7 The quasi-scale: a stochastic model 3. PROBABILISTIC RESPONSE: LATENT STRUCTURE MODELS 3.1 Latent structure analysis 3.2 Latent structure models for dichotomous data 4. HOMOGENEITY AND HOLOMORPHISM IN SCALING MODELS: SOME SIMPLE PROPERTIES 4.1 Holomorphic two-parameter models 4.2 Scale statistics: score, reliability, scalability and patterns 4.3 Approximate sampling distributions 5. A CLASS OF SCALING PROCEDURES 5.1 Summary and evaluation of the findings 5.2 Description of scaling procedures PART II. APPLICATIONS IN POLITICAL RESEARCH 6. CROSS-CULTURAL COMPARISON: THE DISCOVERY OF DIMENSIONAL IDENTITY 6.1 On cross-cultural comparison 6.2 The study 6.3 The study 6.4 A Dutch study (Amsterdam, 1964) 6.5 A second Dutch study (Amsterdam, 1965) 6.6 A scale of political interest 6.7 Conclusions 7. THE CROSS-CULTURAL ROBUSTNESS OF SCALES: POLITICAL EFFICACY 7.1 Dutch-American comparisons of the “sense of political efficacy” 7.2 Some further possibilities 8. AN EXPLORATION OF POLITICAL EFFICACY 8.1 A Dutch extension of the efficacy scale 8.2 An analysis across sub-groups 8.3 A broader efficacy dimension: a combined scale (17 items) 8.4 Investigating the double monotony of scales 8.5 The reliability of doubly monotone scales 9. APPLICATIONS OF MULTIPLE SCALING 9.1 Scaling opinion leadership 9.2 The sense of civic competence and the sense of political efficacy 9.3 Influence stereotypes 9.4 Scaling political participation APPENDIX 1 Sampling design 2 The Dutch text of the scales REFERENCES INDEX

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