A Multivariate Extension of the Dynamic Logit Model for Longitudinal Data Based on a Latent Markov Heterogeneity Structure

For the analysis of multivariate categorical longitudinal data, we propose an extension of the dynamic logit model. The resulting model is based on a marginal parameterization of the conditional distribution of each vector of response variables given the covariates, the lagged response variables, and a set of subject-specific parameters for the unobserved heterogeneity. The latter ones are assumed to follow a first-order Markov chain. For the maximum likelihood estimation of the model parameters, we outline an EM algorithm. The data analysis approach based on the proposed model is illustrated by a simulation study and an application to a dataset, which derives from the Panel Study on Income Dynamics and concerns fertility and female participation to the labor market.

[1]  Andrew J. Viterbi,et al.  Error bounds for convolutional codes and an asymptotically optimum decoding algorithm , 1967, IEEE Trans. Inf. Theory.

[2]  Lee Manning Wiggins,et al.  Panel analysis : Latent probability models for attitude and behavior processes , 1974 .

[3]  Otis Dudley Duncan,et al.  Panel Analysis: Latent Probability Models for Attitude and Behavior Processes. , 1975 .

[4]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[5]  P. McCullagh.  Regression Models for Ordinal Data , 1980 .

[6]  J. Heckman.  Heterogeneity and State Dependence , 1981 .

[7]  J. Heckman,et al.  A Method for Minimizing the Impact of Distributional Assumptions in Econometric Models for Duration Data , 1984 .

[8]  J. Kadane.  Structural Analysis of Discrete Data with Econometric Applications , 1984 .

[9]  Cheng Hsiao,et al.  Analysis of Panel Data , 1987 .

[10]  A. Shapiro.  Towards a unified theory of inequality constrained testing in multivariate analysis , 1988 .

[11]  B. Lindsay,et al.  Semiparametric Estimation in the Rasch Model and Related Exponential Response Models, Including a Simple Latent Class Model for Item Analysis , 1991 .

[12]  Biing-Hwang Juang,et al.  Hidden Markov Models for Speech Recognition , 1991 .

[13]  G. Molenberghs,et al.  Marginal Modeling of Correlated Ordinal Data Using a Multivariate Plackett Distribution , 1994 .

[14]  A. Agresti,et al.  Simultaneously Modeling Joint and Marginal Distributions of Multivariate Categorical Responses , 1994 .

[15]  J. Vermunt,et al.  Discrete-Time Discrete-State Latent Markov Models with Time-Constant and Time-Varying Covariates , 1999 .

[16]  G. Glonek.  A class of regression models for multivariate categorical responses , 1996 .

[17]  Lain L. MacDonald,et al.  Hidden Markov and Other Models for Discrete- valued Time Series , 1997 .

[18]  A. Forcina,et al.  A Unified Approach to Likelihood Inference on Stochastic Orderings in a Nonparametric Context , 1998 .

[19]  Raquel Carrasco,et al.  Binary Choice with Binary Endogenous Regressors in Panel Data: Estimating the Effect of Fertility on Female Labor Participation , 1998 .

[20]  D. Hyslop,et al.  State dependence, serial correlation and heterogeneity in intertemporal labor force , 1999 .

[21]  T R Ten Have,et al.  Mixed Effects Models with Bivariate and Univariate Association Parameters for Longitudinal Bivariate Binary Response Data , 1999, Biometrics.

[22]  Geoffrey J. McLachlan,et al.  Finite Mixture Models , 2019, Annual Review of Statistics and Its Application.

[23]  Raquel Carrasco,et al.  Binary Choice With Binary Endogenous Regressors in Panel Data , 2001 .

[24]  A. Forcina,et al.  Marginal regression models for the analysis of positive association of ordinal response variables , 2001 .

[25]  Geert Verbeke,et al.  MEANINGFUL STATISTICAL MODEL FORMULATIONS FOR REPEATED MEASURES , 2004 .

[26]  F. Bartolucci.  Likelihood inference for a class of latent Markov models under linear hypotheses on the transition probabilities , 2006 .

[27]  B. Qaqish,et al.  Multivariate logistic models , 2006 .

[28]  Athanasios C. Micheas,et al.  Constrained Statistical Inference: Inequality, Order, and Shape Restrictions , 2006 .

[29]  F. Scholz.  Maximum Likelihood Estimation , 2006 .

[30]  Francesco Bartolucci,et al.  Maximum Likelihood Estimation of an Extended Latent Markov Model for Clustered Binary Panel Data , 2007, Comput. Stat. Data Anal..

[31]  Emmanuel Lesaffre,et al.  Latent‐variable models for longitudinal data with bivariate ordinal outcomes , 2007, Statistics in medicine.

[32]  Francesco Bartolucci,et al.  A latent Markov model for detecting patterns of criminal activity , 2007 .

[33]  Francesco Bartolucci,et al.  An extended class of marginal link functions for modelling contingency tables by equality and inequality constraints , 2007 .