Exploratory Tobit Factor Analysis for Multivariate Censored Data

We propose Multivariate Tobit models with a factor structure on the covariance matrix. Such models are particularly useful in the exploratory analysis of multivariate censored data and the identification of latent variables from behavioral data. The factor structure provides a parsimonious representation of the censored data and reduces the dimensionality of the integration required in evaluating the likelihood. In addition, the factor model parameters lend themselves to substantive interpretation and graphical display. The models are estimated with simulated maximum likelihood. Applications to the prescription of pharmaceutical products and the analysis of multi-category buying behavior are provided.

[1]  D. Lawley.  VI.—The Estimation of Factor Loadings by the Method of Maximum Likelihood , 1940 .

[2]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[3]  K. Sher,et al.  Alcohol outcome expectancies and alcohol use: a latent variable cross-lagged panel study. , 1996, Journal of abnormal psychology.

[4]  Stan Lipovetsky,et al.  Latent Variable Models and Factor Analysis , 2001, Technometrics.

[5]  Peter E. Rossi,et al.  Similarities in Choice Behavior Across Product Categories , 1998 .

[6]  Bengt Muthén,et al.  Tobit factor analysis , 1989 .

[7]  R. Olsen,et al.  Note on the Uniqueness of the Maximum Likelihood Estimator for the Tobit Model , 1978 .

[8]  Gary J. Russell,et al.  Modeling Multiple Category Brand Preference with Household Basket Data , 1997 .

[9]  D. J. Bartholomew,et al.  Factor Analysis for Categorical Data , 1980 .

[10]  T. Amemiya.  Generalized Least Squares with an Estimated Autocovariance Matrix , 1973 .

[11]  Ulrich Küsters,et al.  Latent Trait Models with Indicators of Mixed Measurement Level , 1988 .

[12]  H. Kaiser.  The varimax criterion for analytic rotation in factor analysis , 1958 .

[13]  Michael Keane,et al.  Simulation estimation for panel data models with limited dependent variables , 1993 .

[14]  N. L. Johnson,et al.  Continuous Univariate Distributions. , 1995 .

[15]  T. Wales,et al.  Sample Selectivity and the Estimation of Labor Supply Functions , 1980 .

[16]  Nanny Wermuth,et al.  Response models for mixed binary and quantitative variables , 1992 .

[17]  J. Tobin.  Estimation of Relationships for Limited Dependent Variables , 1958 .

[18]  Herman Rubin,et al.  Statistical Inference in Factor Analysis , 1956 .

[19]  L. Ryan,et al.  Latent Variable Models for Mixed Discrete and Continuous Outcomes , 1997 .

[20]  J. Heckman.  The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models , 1976 .

[21]  W. Greene.  ON THE ASYMPTOTIC BIAS OF THE ORDINARY LEAST SQUARES ESTIMATOR OF THE TOBIT MODEL , 1981 .

[22]  C. Orme.  A Note on the Uniqueness of the Maximum Likelihood Estimator in the Truncated Regression Model , 1989 .

[23]  M. Bhaskara Rao,et al.  Model Selection and Inference , 2000, Technometrics.

[24]  R. Rust,et al.  Model selection criteria: an investigation of relative accuracy, posterior probabilities, and combinations of criteria , 1995 .

[25]  Andrew M. Jones,et al.  Charitable donations by UK households: evidence from the Family Expenditure Survey , 1991 .

[26]  B. Dansky,et al.  Combat exposure and adult psychosocial adjustment among U.S. Army veterans serving in Vietnam, 1965-1971. , 1996, Journal of abnormal psychology.

[27]  Nan M. Laird,et al.  Regression Models for a Bivariate Discrete and Continuous Outcome with Clustering , 1995 .

[28]  J. Donovan,et al.  Young adult drinking-driving: behavioral and psychosocial correlates. , 1993, Journal of studies on alcohol.

[29]  Niels G. Waller,et al.  Genetic tobit factor analysis: Quantitative genetic modeling with censored data , 1992, Behavior genetics.

[30]  L. Ryan,et al.  Latent variable models with fixed effects. , 1996, Biometrics.

[31]  Michael P. Keane,et al.  A model of health plan choice:: Inferring preferences and perceptions from a combination of revealed preference and attitudinal data , 1998 .

[32]  John P. Burkett,et al.  Bureaucratic behavior modeled by reduced-rank regression: The case of expenditures from the Soviet state budget , 1998 .

[33]  Tom Wansbeek,et al.  Identification, Equivalent Models, and Computer Algebra , 1994 .

[34]  Christian Gourieroux,et al.  Simulation-based econometric methods , 1996 .

[35]  H. Akaike.  Factor analysis and AIC , 1987 .

[36]  H. O. Lancaster.  Traces and Cumulants of Quadratic Forms in Normal Variables , 1954 .

[37]  S. Chib.  Bayes inference in the Tobit censored regression model , 1992 .

[38]  M D Maraun,et al.  Metaphor Taken as Math: Indeterminancy in the Factor Analysis Model. , 1996, Multivariate behavioral research.

[39]  Wayne S. DeSarbo,et al.  A Latent Structure Double Hurdle Regression Model for Exploring Heterogeneity in Consumer Search Patterns , 1998 .

[40]  Lung-fei Lee,et al.  Asymptotic Bias in Simulated Maximum Likelihood Estimation of Discrete Choice Models , 1995, Econometric Theory.

[41]  Hettie A. Richardson,et al.  The Impact of High Involvement Work Processes on Organizational Effectiveness , 1999 .

[42]  M. Lu,et al.  Separating the True Effect from Gaming in Incentive‐Based Contracts in Health Care , 1999 .

[43]  Lung-fei Lee,et al.  Simulated Maximum Likelihood Estimation of Dynamic Discrete Choice Statistical Models Some Monte Carlo Results , 1997 .

[44]  Pradeep K. Chintagunta,et al.  Investigating Household State Dependence Effects across Categories , 1999 .

[45]  H. Bozdogan.  Model selection and Akaike's Information Criterion (AIC): The general theory and its analytical extensions , 1987 .

[46]  S. Mulaik,et al.  Limited Information Parameter Estimates for Latent or Mixed Manifest and Latent Variable Models. , 1988, Multivariate behavioral research.