Application of the Double Monotonicity Model to Polytomous Items
Abstract
Abstract. This paper investigates the item scalability of the Beck Depression Inventory (BDI) in 252 subjects; 126 with and 126 without eating disorders. To do so, an order was established regarding the BDI items according to the clinical characteristics of the subjects with eating disorders. The nonparametric Item Response Theory (NIRT) model was applied to evaluate Monotone Homogeneity and Double Monotonicity of items, as well as the reliability of the scale in both groups. The results show that the order of the items is satisfied in the group with eating disorders, but not in the control group. Therefore, the results obtained allow the ordering of depression scores of subjects with eating disorders according to their clinical characteristics. This order is not valid for the depression scores of subjects who did not have eating disorders. It should be noted that the application of the Double Monotonicity model to polytomous items provides new and relevant information when compared to the data provided by the Classical Test Model. In addition, it is very useful for other items and subjects having certain characteristics.
References
(1994). Diagnostic and statistical manual of mental disorders (DSM-IV) . Washington, DC: Author
Beck, A.T. (1967). Depression: Clinical, experimental, and theoretical aspects . New York: Harper & RowBeck, A.T. Rush, A.J. Shaw, B.F. Emery, G. (1979). Cognitive therapy of depression . New York: GuilfordBeck, A.T. Steer, R.A. Garbin, M.G. (1988). Psychometric properties of the Beck Depression Inventory: Twenty-five years of evaluation. Clinical Psychology Review, 8, 77– 100Beck, A.T. Ward, C.H. Mendelson, M. Mock, J. Erbaugh, J. (1961). An inventory for measuring depression. Archives of General Psychiatry, 4, 561– 571Canals, J. Blade, J. Carbajo, G. Domenech, E. (2001). The Beck Depression Inventory: Psychometric characteristics and usefulness in nonclinical adolescents. European Journal of Psychological Assessment, 17, 63– 68Cooper, P.J. (1995). Eating disorders and their relationship to mood and anxiety disorders. In K.D. Brownell & C.G. Fairburn (Eds.), Eating disorders and obesity. A comprehensive handbook (pp. 159-164). New York: GuilfordDohrenwend, B.P. Shrout, P.E. Egri, G. Mendelsohn, F.S. (1980). Nonspecific psychological distress and other dimensions of psychopathology. Archives of General Psychiatry, 37, 1229– 1236Dykens, E.M. Gerard, M. (1986). Psychological profiles of purging bulimics, repeat dieters, and controls. Journal of Consulting and Clinical Psychology, 54, 283– 288Edelstein, C.K. Yager, J. (1992). Eating disorders and affective disorders. In J. Yager & H.E. Gwirtsman (Eds.), Special problems in managing eating disorders (pp. 15-50). Washington, DC: American Psychiatric PressFairburn, C.G. Garner, D.M. (1988). Diagnostic criteria for anorexia nervosa and bulimia nervosa: The importance of attitude to shape and weight. In D.M. Garner & P.E. Garfinkel (Eds.), Diagnostic issues in anorexia nervosa and bulimia nervosa (pp. 36-65). New York: Brunner/MazelGarfinkel, P.E. (1992). Evidence in support of attitudes to shape and weight as a diagnostic criterion of bulimia nervosa. International Journal of Eating Disorders, 11, 321– 325Halmi, K. Eckert, E. Marchi, P. Sampugnaro, V. Apple, R. Cohen, J. (1991). Comorbidity of psychiatric diagnoses in anorexia nervosa. Archives of General Psychiatry, 48, 712– 718Hammond, S.M. (1995). An IRT investigation of the validity of nonpatient analog research using the Beck Depression Inventory. European Journal of Psychological Assessment, 11, 14– 20Hemker, B.T. Sijtsma, K. Molenaar, I.W. (1995). Theoretical results and item selection from multidimensional item bank in the Mokken IRT model for polytomous items. Applied Psychological Measurement, 19, 337– 352Hemker, B.T. Sijtsma, K. Molenaar, I.W. Junker, B.W. (1997). Stochastic ordering using the latent trait and the sum score in polytomous IRT models. Psychometrika, 62, 331– 347Hinz, L.D. Williamson, D.A. (1987). Bulimia and depression: A review of the affective variant hypothesis. Psychological Bulletin, 102, 150– 158Hoffman, L. Halmi, K.A. (1993). Depression and eating disorders. In H.S. Koplewicz & E. Klass, Depression in children and adolescents. Monographs in clinical pediatrics, (vol. 6., pp. 149-174). Philadelphia, PA: HarwoodKaplan, A.S. Garfinkel, P.E. (1993). Medical issues in the eating disorders . New York: Brunner/MazelLee, N.F. Rush, A.J. Mitchel, J.E. (1985). Bulimia and depression. Journal of Affective Disorders, 9, 231– 238Martínez Arias, R. (1995). Psicometría: Teoría de los tests psicológicos y educativos . [Psychometrics: Educational and psychological test theory]. Madrid: SíntesisMintz, L.B. O'Halloran, M.S. Mulholland, A.M. Schneider, P.A. (1997). Questionnaire for eating disorder diagnoses: Reliability and validity of operationalizing DSM-IV criteria into a self-report format. Journal of Counseling Psychology, 44, 63– 79Mokken, R.J. (1971). A theory and procedure of scale analysis with applications in political research . Berlin: Walter de Gruyter, MoutonMokken, R.J. (1997). Nonparametric models for dichotomous responses. In W.J. Van der Linden & R.K. Hambleton (Eds.), Handbook of modern item response theory (pp. 351-367). New York: SpringerMolenaar, I.W. (1982). Mokken scaling revised. Kwantitatieve Methoden, 3, 145– 164Molenaar, I.W. (1986). A dexterity exercise in IRT for three ordered answer categories. In G.F. Pikkemaat & J.J.A. Moors (Eds.), Liber amicorum Jaap Muilwijk. Groningen: Econometrisch InstituutMolenaar, I.W. (1991a). A weighted Loevinger H coefficient extending Mokken scaling to multicategory items. Kwantitatieve Methoden, 12, 97– 117Molenaar, I.W. (1991b). Fit investigation in the multicategory Mokken scale . Unpublished manuscriptMolenaar, I.W. (1997). Nonparametric models for polytomous responses. In W.J. Van der Linden & R.K. Hambleton (Eds.), Handbook of modern item response theory (pp. 369-380). New York: SpringerMolenaar, I.W. Debets, P. Sijtsma, K. Hemker, B.T. (1994). MSP 3.0. A program for Mokken Scale Analysis for polytomous items . Groningen: Iec ProGAMMAMolenaar, I.W. Sijtsma, K. (2000). User's manual MSP5 for Windows . Groningen: Iec ProGAMMAMolenaar, I.W. Sijtsma, K. van Schuur, W.H. Mokken, R.J. (2000). MSP5 for Windows. A program for Mokken Scale Analysis for polytomous items . Groningen: Iec ProGAMMAPope, H.G. Hudson, J.I. (1985a). New hope for binge eaters . New York: Harper & RowPope, H.G. Hudson, J.I. (1985b). Biological treatments of eating disorders. In S.W. Emmett (Ed.), Theory and treatment of anorexia nervosa and bulimia: Biomedical, sociocultural, and psychosocial perspectives (pp. 73-92). New York: Brunner/MazelPulos, S. (1996). Validity of the Beck Depression Inventory with eating disorder patients. Educational and Psychological Measurement, 56, 139– 141Rivas, T. Bersabé, R. Castro, S. (2001). Propiedades psicométricas del cuestionario para el diagnóstico de los trastornos de la conducta alimentaria (Q-EDD). [Psychometric properties of the Questionnaire for Eating Disorder Diagnoses (Q-EDD)] Psicología Conductual, 9, 255– 266Rivas, T. Bersabé, R. Berrocal, C. (2001, September). Item scalability of the Beck Depression Inventory on subjects with eating disorders . Paper presented at the 6th European Conference on Psychological Assessment, Aachen, GermanyRosenbaum, P.R. (1984). Testing the conditional independence and monotonicity assumptions of item response theory. Psychometrika, 49, 425– 435Rosenbaum, P.R. (1987). Comparing item characteristic curves. Psychometrika, 52, 217– 233Schlesier-Carter, B. Hamilton, S.A. O'Neil, P.M. Lydiard, R.B. Malcolm, R. (1989). Depression and bulimia: The link between depression and bulimic cognitions. Journal of Abnormal Psychology, 98, 322– 325Sijtsma, K. (1998). Methodology review: Nonparametric IRT approaches to the analysis of dichotomous item scores. Applied Psychological Measurement, 22, 3– 31Sijtsma, K. (2001). Developments in measurement of persons and items by means of item response models. Behaviormetrika, 28, 65– 94Sijtsma, K. Meijer, R.R. (1992). A method for investigating the intersection of item response functions in Mokken's nonparametric IRT model. Applied Psychological Measurement, 16, 149– 157Sijtsma, K. Molenaar, I.W. (2002). Introduction to nonparametric item response theory . London: SageSijtsma, K. Junker, B.W. (1996). A survey of theory and methods of invariant item ordering. British Journal of Mathematical and Statistical Psychology, 49, 79– 105Slade, P. (1982). Toward a functional analysis of anorexia nervosa and bulimia nervosa. British Journal of Clinical Psychology, 21, 167– 179Swift, W.J. Andrew, D. Barklage, N.E. (1986). The relationship between affective disorder and eating disorders: A review of the literature. American Journal of Psychiatry, 143, 290– 299Welch, G. Hall, A. Walkey, F. (1990). The replicable dimensions of the Beck Depression Inventory. Journal of Clinical Psychology, 46, 817– 827
