A component method is presented maximizing Stewart and Love's redundancy index. Relationships with multiple correlation and principal component analysis are pointed out and a rotational procedure for obtaining bi-orthogonal variates is given. An elaborate example comparing canonical correlation analysis and redundancy analysis on artificial data is presented.

stochastic subject, unidimensionality, local independence, experimental independence, local homogeneity, monotonicity, subpopulation invariance, pairwise determination, nonnegative association,

unidimensionality axiom,

Simulation studies examined the effect of misspeci fication of the latent ability (θ) distribution on the ac curacy and efficiency of marginal maximum likelihood (MML) item parameter estimates and on MML statistics to test sufficiency and conditional independence. Re sults were compared to the conditional maximum like lihood (CML) approach. Results showed that if θ is as sumed to be normally distributed when its distribution is actually skewed, MML estimators lose accuracy and efficiency when compared to CML estimators. The ef fects are not large, though they increase as the skew- ness of the number-correct score distribution increases. However, statistics to test the sufficiency and condi tional independence assumptions of the Rasch model in the MML approach are very sensitive to misspecifi cation of the θ distribution. Index terms: ability dis tribution, conditional likelihood, efficiency, goodness of fit, marginal likelihood, Rasch model, robustness.

The Mokken scale is critically discussed. It is argued that Loevinger's H, adapted by Mokken and advocated as a coefficient of scalability, is sensitive to properties of the item set which are extraneous to Mokken's requirement of holomorphy of item response curves. Therefore, when defined in terms of H, the Mokken scale is ambiguous. It is furthermore argued that item-selection free statistical inferences con-ceming the latent person order appear to be insufficiently based on double monotony alone, and that the Rasch model is the only item response model fulfilling this requirement. Finally, it is contended that the Mokken scale is an unfruitful compromise between the requirements of a Guttman scale and the requirements of classical test theory. The so-called &dquo;Mokken scale analysis,&dquo; first developed by Mokken (1971), has recently become more widely used, especially in the Netherlands (e.g., Niemoeller & van Schuur, 1983; Stokman & van Schuur, 1980) and in Germany (e.g., Henning, 1976). Mokken and Lewis (1982) gave a brief account of the Mokken scale and some related issues. Although they referred to a number of recent publications, such as Henning (1976) and Molenaar (1982a,b), they ignored the fact that Henning had reported rather disappointing results, and that Jansen (1981, 1982a,b) and Jansen, Roskam, and van den Wollenberg (1982) had raised a number of critical points with respect to the use of Loevinger's II (as adapted by Mokken) to indicate &dquo;scalability.&dquo; 9 This paper reiterates the points raised by Jansen et al., and in addition, some related issues are discussed in a fairly non-technical way; for technical details, the reader is referred to Jansen (1982b,