Classification analysis is used widely to detect classification errors determined by evaluating a screening or diagnostic instrument against a criterion measure. The usefulness of classification analysis is limited because it assumes an error-free criterion and provides no statistical test of the validity of that assumption. The classification-analysis model is a special case of a general latent-class model. This paper presents latent-class models that fall within the purview of the general model presented by Clogg & Goodman (1984, 1985) and Walter & Irwig (1988). Variations on the general latent-class model allowthe investigator to determine whether the criterion measure and/or the diagnostic or screening procedure for multiple groups can be considered error-free. Analogous to the problem of differential item functioning, the general model makes it possible to test assumptions regarding classification errors that could occur across groups. The proportion of individuals who may be misclassified by a screening instrument or diagnostic procedure can also be determined using latent structure techniques.
Get full access to this article
View all access options for this article.
References
1.
Anderson, R. E. , Hill, R. B., & Key, C. R. (1989). The sensitivity and specificity of clinical diagnostics during five decades. Journal of the American Medical Association, 261, 1610–1617.
2.
Bergan, J. R. (1983). Latent class models in educational research. In E. W. Gordon (Ed.) Review of Research in Education, 10, (pp. 305–360). Washington, D.C.: American Educational Research Association.
3.
Bergan, J. R. , Cancelli, A. A., & Luiten, J. (1980). Mastery assessment with latent class and quasiindependence models representing homogeneous item domains. Journal of Educational Statistics, 5, 65–81.
4.
Cadman, D. , Chambers, L. W., Walter, S. D., Feldman, W., Smith, K., & Ferguson, R. (1984). The usefulness of the Denver Developmental Screening Test to predict kindergarten problems in a general community population. American Journal of Public Health, 74, 1093–1097.
5.
Clogg, C. C. (1979). Some latent structure models for the analysis of Likert-type data. Social Science Research, 86, 836–868.
6.
Clogg, C. C. (1981). Latent structure models of mobility. American Journal of Sociology, 86, 836–868.
7.
Clogg, C. C. , & Eliason, S. R. (1987). Unrestricted and restricted maximum likelihood latent structure analysis: A manual for users (Working Paper 1977-09). University Park, PA: Population Issues Research Office.
8.
Clogg, C. C. ,& Goodman, L. A. (1984). Latent structure analysis of a set of multidimensional contingency tables. Journal of the American Statistical Association, 79, 762–771.
9.
Clogg, C. C. , & Goodman, L. A. (1985). Simultaneous latent structure analysis in several groups. In N. B. Tuma (Ed.), Sociological methodology. San Francisco: Jossey-Bass.
10.
Cronbach, L. J. , Gleser, G. C., Nanda, H., & Rajaratnam, N. (1972). The dependability of behavioral measurements: Theory of generalizability for scores and profiles. New York: Wiley.
11.
Dempster, A. P. , Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm (with discussion). Journal of the Royal Statistical Association, 56, 335–349.
12.
Espeland, M. A. , & Handelman, S. L. (1989). Using latent class models to characterize and assess relative error in discrete measurements. Biometrics, 45, 587–599.
13.
Frankenburg, W. K. , Goldstein, A. D., & Camp, B. W. (1971). The revised Denver Development Screening Test: Its accuracy as a screening instrument. The Journal of Pediatrics, 79, 988–995.
14.
Fulop, G. , Strain, J., & Vita, J. (1987). Impact of psychiatric co-morbidity on length of hospital stay for medical/surgical patients: A preliminary report. American Journal of Psychology, 144, 878–878.
15.
Galen, R. S. (1982). Application of the predictive value model in the analysis of test effectiveness. Clinical Laboratory Methodology, 2, 685–699.
16.
Galen, R. S. , & Gambino, S. R. (1975). Beyond normality: The predictive value and efficiency of medical diagnoses. New York: Wiley.
17.
Goodman, L. A. (1974a). The analysis of systems of quantitative variables when some of the variables are unobservable: Part I. A modified latent structure approach. American Journal of Sociology, 79, 179–259.
18.
Goodman, L. A. (1974b). Exploratory latent structure analysis using both identifiable and unidentifiable models. Biometrika, 61, 215–231.
19.
Hui, S. L. , & Walter, S. D. (1980). Estimating the error rates of diagnostic tests. Biometrics, 36, 167–171.
20.
Kelderman, H. & Macready, G. B. (1990). The use of loglinear models for assessing differential item functioning across manifest and latent examinee groups. Journal of Educational Measurement, 27, 307–327.
21.
Koenig, H. G. , Meador, K. G., Cohen, H. J., & Blazer,D. G. (1988). Self-rated depression scales and screening for major depression in the older hospitalized patient with medical illnesses. American Geriatrics Society, 88, 699–706.
22.
Lazarsfeld, P. F. ,& Henry, N. W. (1968). Latent structure analysis. Boston: Houghton-Mifflin.
23.
Macready, G. B. , & Dayton, C. M. (1977). The use of probabilistic models in the assessment of mastery. Journal of Educational Statistics, 2, 99–120.
24.
Murden, R. A. , McRae, T. D., Kaner, S., & Bucknam, M. E. (1991). Mini-mental state exam scores vary with education in blacks and whites. Journal of American Geriatrics Society, 39, 149–155.
25.
Rindskopf, D. , & Rindskopf, W. (1986). The value of latent class analysis in medical diagnosis. Statistics in Medicine, 5, 21–27.
26.
Roberts, R. E. , Vernon, S. W., & Rhoades, H. M. (1989). Effects of language and ethnic status on reliability and validity of the Center for Epidemiologic Studies Depression Scale with psychiatric patients. Journal of Nervous and Mental Disease, 177, 581–592.
27.
Sackett, D. L. , Haynes, R. B., & Tugwell, P. (1985). Clinical epidemiology: A basic science for clinical medicine. Boston: Little Brown & Co.
28.
Sturner, R. A. , Green, J. A., & Funk, S. G. (1985). Preschool Denver developmental screening tests as a predictor of later school problems.Behavioral Pediatrics, 107, 615–621.
29.
Tanner, M. A. , & Young, M. A. (1985). Modeling agreement among raters. Journal of the American Statistical Association, 80, 175–180.
30.
Terman, L. M. , & Merrill, M. A. (1972). Stanford-Binet Intelligence Scale Manual for the Third Revision Form L-M. Boston: Houghton-Mifflin.
31.
Thissen, D. , Steinberg, L., & Wainer, H. (1993). Detection of differential item functioning using the parameters of item response models. In P. Holland & H. Wainer (Eds.), Differential item functioning (pp. 67–114). Hillsdale, NJ: Erlbaum.
32.
Uebersax, J. S. , & Grove, W. M. (1990). Latent class analysis of diagnostic agreement. Statistics in Medicine, 9, 559–572.
33.
Walter, S. D. , & Irwig, L. M. (1988). Estimation of test error rates, disease prevalence, and relative risk from misclassified data: A review. Journal of Clinical Epidemiology, 41, 923–937.
34.
Wassertheil-Smoller, S. (1990). Biostatistics and epidemiology: A primer for health professionals. New York: Springer-Verlag.
35.
Ysseldyke, E. J. (1987). Classification of handicapped students. In M. C. Wang, M. C. Reynolds, & H. J. Walberg (Eds.), Handbook of special education: Research and practice (Vol. 1: Learner characteristics and adaptive education). Oxford, England: Pergamon Press.
