A Parametric Procedure for Ultrametric Tree Estimation from Conditional Rank Order Proximity Data

Psychometrika, Volume 60, Issue 1, pp 47-75

29 Pages Posted: 8 Jun 2016

See all articles by Martin R. Young

Martin R. Young

Massey University - School of Economics and Finance

Wayne S. DeSarbo

Pennsylvania State University

Date Written: March 1995

Abstract

The psychometric and classification literatures have illustrated the fact that a wide class of discrete or network models (e.g., hierarchical or ultrametric trees) for the analysis of ordinal proximity data are plagued by potential degenerate solutions if estimated using traditional nonmetric procedures (i.e., procedures which optimize a STRESS-based criteria of fit and whose solutions are invariant under a monotone transformation of the input data). This paper proposes a new parametric, maximum likelihood based procedure for estimating ultrametric trees for the analysis of conditional rank order proximity data. We present the technical aspects of the model and the estimation algorithm. Some preliminary Monte Carlo results are discussed. A consumer psychology application is provided examining the similarity of fifteen types of snack/breakfast items. Finally, some directions for future research are provided.

Keywords: hierarchical clustering, proximity data, conditional rank orders, maximum likelihood estimation, consumer psychology

Suggested Citation

Young, Martin R. and DeSarbo, Wayne S., A Parametric Procedure for Ultrametric Tree Estimation from Conditional Rank Order Proximity Data (March 1995). Psychometrika, Volume 60, Issue 1, pp 47-75. Available at SSRN: https://ssrn.com/abstract=2791039

Martin R. Young

Massey University - School of Economics and Finance ( email )

Private Bag 11222
Palmerston North, 4442
New Zealand

Wayne S. DeSarbo (Contact Author)

Pennsylvania State University ( email )

University Park
State College, PA 16802
United States

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