Elrod and Keane 1995 - Factor-Analytic Probit Market Structure - Overview
Summary
Elrod & Keane propose a multinomial probit with a factor-analytic covariance (common factors for market structure plus equal unique variance) estimated from household panel data by simulated moments. On a laundry-detergent data set it beats the structureless Dirichlet-multinomial and equisimilar probit, Choice Map, SCULPTRE and Chintagunta’s latent-class map on predictive log-likelihood and face validity, supporting the claim that it alone recovered real market structure. Market structure means: brands compete more closely when they load similarly on a few common attributes, which a structureless (IIA) model cannot represent.
Overview
Citation. Elrod, T. and Keane, M. P. (1995), A factor-analytic probit model for representing the market structure in panel data, Journal of Marketing Research 32(1): 1-16. Scanned copy via MPRA (Paper No. 52434).
Problem. Internal market structure analysis infers brand attributes and consumer preferences from choice data. Existing methods (Table 1 in the paper) either require aggregate data, ignore marketing variables, or restrict consumer heterogeneity (linear in observed covariates, discrete latent classes, or reduced-rank).
Contribution. (1) A probit model with factor structure for household brand-preference deviations; (2) estimation for panel data (up to 24 purchases) using Keane’s (1990) simulated-moments method with the Geweke-Hajivassiliou-Keane (GHK) simulator; (3) an equisimilar probit () as the structureless benchmark in the same model family; (4) an empirical comparison on 100 households and 8 detergent brands.
Motivating PyMC examples
See https://redam94.github.io/pymc-challenges/examples.html: E84 (Market structure analysis: who competes with whom? - Allenby & Rossi (1991) margarine scanner panel; switching matrices, IIA, nested logit hierarchies, factor-structured hierarchical logit as a choice map) and E85 (Market structure from purchase incidence: panel, activity and demographics; Bernoulli-logit factor ladder). The probit factor model here is the classical precursor of those factor-structured choice maps; the Bayesian logit-factor versions are in the concept note Market Structure Analysis - IIA, Nested Logit and Choice Maps (Concept Note). Substitution note: Allenby & Rossi (1991) has no legal open copy; this MPRA paper is the closest open source on the same method family.
Source Map
| Paper section | Pages | Covered in |
|---|---|---|
| Abstract; Introduction; Models for internal market structure analysis (Table 1) | 1-4 | Elrod and Keane 1995 - Models for Internal Market Structure Analysis |
| A new factor-analytic probit model for panel data | 4-5 | Elrod and Keane 1995 - Factor-Analytic Probit Model Specification |
| Fitting probit models to panel data | 5 | Elrod and Keane 1995 - Simulated Moments and Panel Estimation |
| Model specification: factor-analytic probit (Eqs. 1-6); equisimilar probit and IIA (Eqs. 7-8) | 5-7 | Elrod and Keane 1995 - Factor-Analytic Probit Model Specification |
| Empirical assessment: data, models compared, estimation notes | 7-8 | Elrod and Keane 1995 - Empirical Assessment on Detergent Panel Data |
| Probit estimates (Table 2, Fig. 1) | 8-9 | Elrod and Keane 1995 - Empirical Assessment on Detergent Panel Data |
| Predictive validity, goodness of fit (Eqs. 9-17, Table 3), face validity, conclusions | 9-13 | Elrod and Keane 1995 - Empirical Assessment on Detergent Panel Data |
| Technical appendix (Eqs. A1-A7): MOM, MSM, panel MSM, GHK | 13-15 | Elrod and Keane 1995 - Simulated Moments and Panel Estimation |
| References | 15-16 | this note |
Main Content
Table 1 of the paper compares nine families by data type, whether they explain market shares, handle non-product variables, model structure and heterogeneity:
| Model | Data | Shares | Marketing vars | Structure | Heterogeneity |
|---|---|---|---|---|---|
| DEFENDER | market shares | yes | price | spatial | uniform/beta |
| Competitive maps | market shares | no | price | spatial | implicit |
| Grover-Srinivasan; Jain-Bass-Chen | switching | no | no | cluster | latent class |
| DeSarbo-Hoffman | pick-any/n | yes | no | spatial | idiosyncratic or explained |
| SCULPTRE | purchase frequencies | yes | no | ultrametric tree | latent class |
| Choice Map | purchase frequencies | yes | no | spatial | reduced-rank normal |
| Chintagunta (1994) | disaggregate panel | yes | any | spatial | reduced-rank latent class |
| Factor-analytic probit | disaggregate panel | yes | any | spatial | full-rank multivariate normal |
Examples
Table 2 and Table 3 results: Elrod and Keane 1995 - Empirical Assessment on Detergent Panel Data.
Relevance to marketing measurement
Market structure determines cross-elasticities: who a brand’s promotions steal from. A structureless model (IIA) predicts proportional substitution and so misprices cannibalisation and competitive response in MMM-adjacent demand modelling; factor-structured choice models capture asymmetric competition in a low-dimensional map. See Discrete Choice Models and Random Coefficients Logit Model (BLP-style demand) for continuous heterogeneity alternatives.
Connections
- Probit vs logit: the probit covariance structure relaxes IIA; mixed logit does it via random coefficients (Random Coefficients Logit Model).
- Factor structure: Factor Analysis and PPCA.
See Also
Elrod and Keane 1995 - Models for Internal Market Structure Analysis