It is common in the social sciences to collect data in the form of graded responses and then to combine adjacent categories. The joining assumptions of Jansen and Roskam (1986) and the use of the Rasch model for graded responses are explored. Implications of model choice are discussed. (SLD)

The Jansen and Roskam (1986) approach to joining categories of graded responses presents valid arguments that are subject to empirical test. The multiplicative Poisson (MPM) model of D. Andrich can be seen as an approximation to the continuous response model of Muller (1987). An extension of the MPM is suggested. (SLD)

These further remarks on the nondichotomization of graded responses attempt to clarify the differences in perspective between the two previous articles. The special case of the multiplicative Poisson model reveals why the joining assumption and dichotomization are not, in general, properties of the unidimensional Rasch model. (SLD)

A new direct and short proof is offered for the monotone likelihood ratio for the sum of independent Bernoulli random variables through use of an inequality by Marcus and Lopes (1957) on elementary symmetric functions. (SLD)

When a simple random sample of size n is employed to establish a classification rule for prediction of a polytomous variable by an independent variable, the best achievable rate of misclassification is higher than the corresponding best achievable rate if the conditional probability distribution is known for the predicted variable given the…

It is shown that common factors are not subject to indeterminancy to the extent that has been claimed (Guttman, 1955), because the measure of indeterminancy that has been adopted is ill-founded. (Author/RC)

The small-world problem revolves around the tracing of a line of acquaintances linking any two persons chosen at random. Statistical analysis of data from two experimental studies of the problem and estimation of parameters in two previously proposed models is discussed along with the models' goodness of fit. (Author/RC)

Multidimensional scaling has recently been enhanced so that data defined at only the nominal level of measurement can be analyzed. The efficacy of ALSCAL, an individual differences multidimensional scaling program which can analyze nominal, ordinal, interval and ratio data is presented. (Author/JKS)

Statistical procedures based on Bayesian estimation for obtaining estimates of a propensity (which would include estimates of proportions or relative frequencies) are described for the special case where the observer can only note whether the propensity exceeds or does not exceed a constant between 0 and 1. (JKS)

A component method is presented for maximizing estimates of a statistical procedure called redundancy analysis. Relationships of redundancy analysis to multiple correlation and principal component analysis are pointed out. An elaborate example comparing canonical correlation analysis and redundancy analysis on artificial data is presented.…

Critical examination is made of the recent controversy over the value of Monte Carlo techniques in nonmetric multidimensional scaling procedures. The case is presented that the major relevance of Monte Carlo studies is not for the local minima problem but for the meaningfulness of the obtained solutions. (Author)

A method of introducing a controlled degree of skew and kurtosis for Monte Carlo studies was derived. The form of such a transformation on normal deviates is given. Analytic and empirical validation of the method is demonstrated. (Author/JKS)