RACIAL DIFFERENCES IN MEASUREMENT ERROR IN EDUCATIONAL ACHIEVEMENT MODELS

Autor: Dianne Robertshaw, Lee M. Wolfle
Rok vydání: 1983
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Zdroj: Journal of Educational Measurement. 20:39-49
ISSN: 1745-3984
0022-0655
DOI: 10.1111/j.1745-3984.1983.tb00188.x
Popis: Reliable and theoretically meaningful measurement is a prerequisite for good educational research; yet it has not always assumed the prominence it deserves. The linear statistical model is probably the most commonly used analytic tool in educational research, but using the linear statistical model carries with it a clear, but often overlooked, assumption about measurement error. As Blalock (1964, p. 49) noted, one assumes that "there may be errors of measurement with respect to the dependent variable Y, but that all of the independent variables have been measured without error." Such an assumption is obviously unrealistic for most social data, and has a well-known effect upon least-squares estimators-they are biased (Walker and Lev, 1953, p. 306). Until recently, there was little that an educational researcher could do about least-squares indicators biased by measurement error. There were basically only three alternatives. By far the most common was to naively assume that the variables were measured without error, and wistfully hope the resulting estimates were robust. A second alternative was to correct correlation coefficients for attenuation, and use the corrected estimates as inputs to a regression analysis. This procedure, however, in the absence of multiple measurements required a priori knowledge of the reliability coefficients for the variables; furthermore, one had to assume the reliabilities were invariant from one population, subpopulation, or sample to the one at hand. These restrictions severely limit the use of regression analyses based on correlations corrected for attenuation. Yet a third alternative was to measure implied coefficients between latent variables for which one had multiple manifest indicators. Siegel and Hodge (1968), for example, explicated several such models in their paper directed to sociologists; furthermore, they noted that correlations corrected for attenuation were merely special cases of their multiple indicator models. The problem with this alternative, as noted by both Hauser and Goldberger (1971) and Long (1976), is its casual approach toward statistical estimation and hypothesis testing. The problem results from overidentified models, which yield multiple estimates of the associations among latent variables. In response, some authors have chosen to ignore one or more of the identifying equations (e.g., Blalock, 1970; Land, 1970); others have averaged the estimates from the several equations (e.g., Hauser, 1970). A better alternative would be to obtain estimates of overidentified parameters by maximum likelihood estimation (MLE). These procedures grew out of the work of Lawley (1943), but the immense computational load required for the iterative estimation of maximum-likelihood estimates prevented their application in practice. Thus, the application of more adequate statistical procedures languished until Joreskog (1966, 1967, 1969) discovered an efficient MLE computational procedure, soon to be followed
Databáze: OpenAIRE
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