Researchers in the field of conjoint analysis know the index-of-fit values worsen as the judgmental error of evaluation increases. This simulation study provides guidelines on the goodness of fit based on distribution of index-of-fit for different conjoint analysis designs. The study design included the following factors: number of profiles, number of attributes, algorithm used and judgmental model used. Critical values are provided for deciding the statistical significance of conjoint analysis results. Using these cumulative distributions, the power of the test used to reject the null hypothesis of random ranking is calculated. The test is found to be quite powerful except for the case of very small residual degrees of freedom.

Kruskal has proposed two modifications of monotone regression that can be applied if there are ties in nonmetric scaling data. In this note we prove Kruskal's conjecture that his algorithms give the optimal least squares solution of these modified monotone regression problems. We also propose another (third) approach for dealing with ties.

A method is presented to provide estimates of parameters of specified nonlinear equations from ordinal data generated from a crossed design. The analytic method, NOPE, is an iterative method in which monotone regression and the Gauss-Newton method of least squares are applied alternatively until a measure of stress is minimized. Examples of solutions from artificial data are presented together with examples of applications of the method to experimental results.

Takane, Young, and de Leeuw proposed a procedure called FACTALS for the analysis of variables of mixed measurement levels (numerical, ordinal, or nominal). Mooijaart pointed out that their algorithm does not necessarily converge, and Nevels proposed a new algorithm for the case of nominal variables. In the present paper it is shown that Nevels' procedure is incorrect, and a new procedure for handling nominal variables is proposed. In addition, a procedure for handling ordinal variables is proposed. Using these results, a monotonically convergent algorithm is constructed for FACTALS of any mixture of variables.