1992 **Abstract:** The optimization of multivariate measurement designs when limited resources are available is not a simple task. This paper presents a method for determining the optimal number of conditions to use in measurement designs when resource constraints are imposed.

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“…Several authors have studied how one can optimize generalizability coefficients, reliability coefficients, or validity coefficients, or how one can minimize decision error rates. In many cases this was studied in the context of a budget constraint (e.g., Allison et al, 1997 ; Ellis, 2013 ; Liu, 2003 ; Marcoulides, 1993 , 1995 , 1997 ; Marcoulides & Goldstein, 1990a , 1990b , 1992 ; Meyer et al, 2013 ; Sanders, 1992 ; Sanders et al, 1991 ) or fixed total testing time (e.g., Ebel, 1953 ; Hambleton, 1987 ; Horst, 1949 , 1951 ). Alternatively, one may minimize the costs of measurement given constraints on the generalizability coefficient or error variance (e.g., Peng et al, 2012 ; Sanders et al, 1989 ), which is a similar problem.…”

confidence: 99%

“…Several authors have studied how one can optimize generalizability coefficients, reliability coefficients, or validity coefficients, or how one can minimize decision error rates. In many cases this was studied in the context of a budget constraint (e.g., Allison et al, 1997 ; Ellis, 2013 ; Liu, 2003 ; Marcoulides, 1993 , 1995 , 1997 ; Marcoulides & Goldstein, 1990a , 1990b , 1992 ; Meyer et al, 2013 ; Sanders, 1992 ; Sanders et al, 1991 ) or fixed total testing time (e.g., Ebel, 1953 ; Hambleton, 1987 ; Horst, 1949 , 1951 ). Alternatively, one may minimize the costs of measurement given constraints on the generalizability coefficient or error variance (e.g., Peng et al, 2012 ; Sanders et al, 1989 ), which is a similar problem.…”

confidence: 99%

“…However, they cannot apply the Lagrange multiplier to some more complicated designs (i.e., the mixed design and multivariate conceptual design and etc. ), which is deficient Goldstein, 1991, 1992;Macrolides, 1994Macrolides, , 1995 [27][28][29][30].…”

confidence: 99%

“…Approaches have been proposed to maximize reliability within a budget constraint. Woodward and Joe (1973) derived equations for their constrained optimization; Saunders et al (1989) deployed discrete optimization, which was further updated by Saunders (1992) with the Cauchy–Schwartz inequity approach; Marcoulides (1993, 1995) as well as Marcoulides and Goldstein (1990, 1991, 1992) had developed the LaGrange multiplier approach and other related variants to handle the optimization within both univariate and multivariate G-theory. Meyer et al (2014) extended the LaGrange multiplier approaches to G-theory with nested designs.…”

confidence: 99%