Sparse Conjoint Analysis Through Maximum Likelihood Estimation
2013 (English)In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 61, no 22, 5704-5715 p.Article in journal (Refereed) Published
Conjoint analysis (CA) is a classical tool used in preference assessment, where the objective is to estimate the utility function of an individual, or a group of individuals, based on expressed preference data. An example is choice-based CA for consumer profiling, i.e., unveiling consumer utility functions based solely on choices between products. A statistical model for choice-based CA is investigated in this paper. Unlike recent classification-based approaches, a sparsity-aware Gaussian maximum likelihood (ML) formulation is proposed to estimate the model parameters. Drawing from related robust parsimonious modeling approaches, the model uses sparsity constraints to account for outliers and to detect the salient features that influence decisions. Contributions include conditions for statistical identifiability, derivation of the pertinent Cramer-Rao Lower Bound (CRLB), and ML consistency conditions for the proposed sparse nonlinear model. The proposed ML approach lends itself naturally to l(1)-type convex relaxations which are well-suited for distributed implementation, based on the alternating direction method of multipliers (ADMM). A particular decomposition is advocated which bypasses the apparent need for outlier communication, thus maintaining scalability. The performance of the proposed ML approach is demonstrated by comparing against the associated CRLB and prior state-of-the-art using both synthetic and real data sets.
Place, publisher, year, edition, pages
2013. Vol. 61, no 22, 5704-5715 p.
Conjoint analysis, maximum likelihood, estimation, sparse, CRLB, ADMM
IdentifiersURN: urn:nbn:se:kth:diva-133963DOI: 10.1109/TSP.2013.2278529ISI: 000326102300018ScopusID: 2-s2.0-84886510290OAI: oai:DiVA.org:kth-133963DiVA: diva2:664444
FunderEU, European Research Council, 228044
QC 201311152013-11-152013-11-142013-11-15Bibliographically approved