An alternative derivation is given for a simple test model which incorporates an ability parameter for the subject and difficulty level and guessing parameters for the problem. The probability of a correct response to the problem is a projective transformation of the problem difficulty. The ability and difficulty parameters separate into additive components.

Using Carroll's external analysis, several studies have found that unfolding models account for more, although seldom significantly more, variance in preferences than Tucker's vector model. In studies of sociometric ratings and political preferences, the unfolding model again rarely outpredicted the vector model by a significant amount. Yet on cross-validation, the unfolding model consistently accounted for more variance. Results suggest that sometimes significance tests are less sensitive than cross-validation procedures to the small but consistent superiority of the unfolding model. Future researchers may wish to use significance tests and cross-validation techniques in comparing models.

This note extends and elaborates Hubert’s attempt to provide an interpretation of Freeman’s measure of association, θ. The θ measure is used in a contingency table when observations are ordered on one variable and unordered on the other. No attempt is made explore the distribution of θ.

For analyses with missing data, some popular procedures delete cases with missing values, perform analysis with “missing value” correlation or covariance matrices, or estimate missing values by sample means. There are objections to each of these procedures. Several procedures are outlined here for replacing missing values by regression values obtained in various ways, and for adjusting coefficients (such as factor score coefficients) when data are missing. None of the procedures are complex or expensive.

A recent comparison of methods for estimating missing data concluded that when there is sufficient redundancy to justify using a more elaborate method than the mean of each variable, the principal components and regression methods are equally good and superior to the other methods investigated. Principal components was preferred because of its “tremendous computational savings over the regression method.” This note proposes an alternate implementation of the regression method which should be slightly faster than the principal components method.