%0 Journal Article
%J Econometric Reviews
%D 2018
%T Testing for state dependence in binary panel data with individual covariates by a modified quadratic exponential model
%A Francesco Bartolucci
%A Nigro, Valentina
%A Pigini, Claudia
%K Survey Methodology
%X We propose a test for state dependence in binary panel data with individual covariates. For this aim, we rely on a quadratic exponential model in which the association between the response variables is accounted for in a different way with respect to more standard formulations. The level of association is measured by a single parameter that may be estimated by a Conditional Maximum Likelihood (CML) approach. Under the dynamic logit model, the conditional estimator of this parameter converges to zero when the hypothesis of absence of state dependence is true. Therefore, it is possible to implement a t-test for this hypothesis which may be very simply performed and attains the nominal significance level under several structures of the individual covariates. Through an extensive simulation study, we find that our test has good finite sample properties and it is more robust to the presence of (autocorrelated) covariates in the model specification in comparison with other existing testing procedures for state dependence. The proposed approach is illustrated by two empirical applications: the first is based on data coming from the Panel Study of Income Dynamics and concerns employment and fertility; the second is based on the Health and Retirement Study and concerns the self reported health status.
%B Econometric Reviews
%V 37
%P 61-88
%G eng
%U https://www.tandfonline.com/doi/full/10.1080/07474938.2015.1060039https://www.tandfonline.com/doi/pdf/10.1080/07474938.2015.1060039
%N 1
%! Econometric Reviews
%R 10.1080/07474938.2015.1060039
%0 Journal Article
%J Computational Economics
%D 2017
%T Adaptive Quadrature for Maximum Likelihood Estimation of a Class of Dynamic Latent Variable Models
%A Cagnone, Silvia
%A Francesco Bartolucci
%K Older Adults
%K Survey Methodology
%X Maximum likelihood estimation of models based on continuous latent variables generally requires to solve integrals that are not analytically tractable. Numerical approximations represent a possible solution to this problem. We propose to use the adaptive Gaussianâ€“Hermite (AGH) numerical quadrature approximation for a particular class of continuous latent variable models for time-series and longitudinal data. These dynamic models are based on time-varying latent variables that follow an autoregressive process of order 1, AR(1). Two examples are the stochastic volatility models for the analysis of financial time series and the limited dependent variable models for the analysis of panel data. A comparison between the performance of AGH methods and alternative approximation methods proposed in the literature is carried out by simulation. Empirical examples are also used to illustrate the proposed approach.
%B Computational Economics
%V 49
%P 599 - 622
%8 Jan-04-2017
%G eng
%N 4
%! Comput Econ
%R 10.1007/s10614-016-9573-4
%0 Journal Article
%J Econometric Reviews
%D 2015
%T Testing for State Dependence in Binary Panel Data with Individual Covariates by a Modified Quadratic Exponential Model
%A Francesco Bartolucci
%A Nigro, Valentina
%A Pigini, Claudia
%K Methodology
%X AbstractWe propose a test for state dependence in binary panel data with individual covariates. For this aim, we rely on a quadratic exponential model in which the association between the response variables is accounted for in a different way with respect to more standard formulations. The level of association is measured by a single parameter that may be estimated by a Conditional Maximum Likelihood (CML) approach. Under the dynamic logit model, the conditional estimator of this parameter converges to zero when the hypothesis of absence of state dependence is true. This allows us to implement a t-test for this hypothesis which may be very simply performed and attains the nominal significance level under several structures of the individual covariates. Through an extensive simulation study, we find that our test has good finite sample properties and it is more robust to the presence of (autocorrelated) covariates in the model specification in comparison with other existing testing procedures for state dependence. The proposed approach is illustrated by two empirical applications: the first is based on data coming from the Panel Study of Income Dynamics and concerns employment and fertility; the second is based on the Health and Retirement Study and concerns the self reported health status.
%B Econometric Reviews
%P 1-37
%G eng
%U http://dx.doi.org/10.1080/07474938.2015.1060039
%4 Conditional inference/Dynamic logit model/Quadratic exponential model/t-test
%$ 999999
%R 10.1080/07474938.2015.1060039
%0 Journal Article
%J Journal of Econometrics
%D 2015
%T Testing for time-invariant unobserved heterogeneity in generalized linear models for panel data
%A Francesco Bartolucci
%A Belotti, F.
%A Peracchi, F.
%K Health Conditions and Status
%K Methodology
%X Recent literature on panel data emphasizes the importance of accounting for time-varying unobservable individual effects, which may stem from either omitted individual characteristics or macro-level shocks that affect each individual unit differently. In this paper, we propose a simple specification test of the null hypothesis that the individual effects are time-invariant against the alternative that they are time-varying. Our test is an application of Hausman (1978) testing procedure and can be used for any generalized linear model for panel data that admits a sufficient statistic for the individual effect. This is a wide class of models which includes the Gaussian linear model and a variety of nonlinear models typically employed for discrete or categorical outcomes. The basic idea of the test is to compare two alternative estimators of the model parameters based on two different formulations of the conditional maximum likelihood method. Our approach does not require assumptions on the distribution of unobserved heterogeneity, nor it requires the latter to be independent of the regressors in the model. We investigate the finite sample properties of the test through a set of Monte Carlo experiments. Our results show that the test performs well, with small size distortions and good power properties. We use a health economics example based on data from the Health and Retirement Study to illustrate the proposed test.
%B Journal of Econometrics
%I 184
%V 184
%P 111-123
%G eng
%U http://www.scopus.com/inward/record.url?eid=2-s2.0-84913536688andpartnerID=40andmd5=72f27b89df012501a4fbcd9a41c40830
%N 1
%4 Fixed-effects/Generalized linear models/Generalized linear models/Hausman-type tests/Longitudinal data/Self-reported health
%$ 999999
%0 Journal Article
%J Journal of the Royal Statistical Society. Series C: Applied Statistics
%D 2014
%T Longitudinal analysis of self-reported health status by mixture latent auto-regressive models
%A Francesco Bartolucci
%A Bacci, S.
%A Pennoni, F.
%K Expectations
%K Methodology
%X Motivated by an application to a longitudinal data set coming from the Health and Retirement Study about self-reported health status, we propose a model for longitudinal data which is based on a latent process to account for the unobserved heterogeneity between sample units in a dynamic fashion. The latent process is modelled by a mixture of auto-regressive AR(1) processes with different means and correlation coefficients, but with equal variances. We show how to perform maximum likelihood estimation of the proposed model by the joint use of an expectation-maximization algorithm and a Newton-Raphson algorithm, implemented by means of recursions developed in the hidden Markov model literature. We also introduce a simple method to obtain standard errors for the parameter estimates and suggest a strategy to choose the number of mixture components. In the application the response variable is ordinal; however, the approach may also be applied in other settings. Moreover, the application to the self-reported health status data set allows us to show that the model proposed is more flexible than other models for longitudinal data based on a continuous latent process. The model also achieves a goodness of fit that is similar to that of models based on a discrete latent process following a Markov chain, while retaining a reduced number of parameters. The effect of different formulations of the latent structure of the model is evaluated in terms of estimates of the regression parameters for the covariates. 2013 Royal Statistical Society.
%B Journal of the Royal Statistical Society. Series C: Applied Statistics
%I 63
%V 63
%P 267-288
%G eng
%U http://www.scopus.com/inward/record.url?eid=2-s2.0-84894489600andpartnerID=40andmd5=1e6e75b146104446a60a2ac085881c27
%N 2
%4 Expectation-maximization algorithm/Hidden Markov model/Latent Markov model/Proportional odds model/Quadrature methods
%$ 999999
%R 10.1111/rssc.12030