Error structure and identification condition in maximum likelihood nonmetric multidimensional scaling
✍ Scribed by Makoto Abe
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 177 KB
- Volume
- 111
- Category
- Article
- ISSN
- 0377-2217
No coin nor oath required. For personal study only.
✦ Synopsis
The author addresses two previously unresolved issues in maximum likelihood estimation (MLE) for multidimensional scaling (MDS). First, a theoretically consistent error model for nonmetric MLDMS is proposed. In particular, theoretical arguments are given that the disturbance should be multiplicative with distance when a stochastic choice model is used on rank-ordered similarity data. This assumption implies that the systematic component of similarity in the rank order is a logarithmic function of distances between stimuli. Second, a problem with identi®cation condition of the maximum likelihood estimators is raised. The author provides a set of constraints that guarantees the identi®cation in MLE, and produces more desirable asymptotic con®dence regions that are parameter independent. An example using perception of business schools illustrates these ideas and demonstrates the computational tractability of the MLE approach to MDS.