Likelihood based procedures for general nonlinear structural equation analysis

Valid Statistical inferences in nonlinear structural equation models are of great interest recently. This dissertation aims at fitting a nonlinear structural equation model consisting of two parts; a general nonlinear measurement model relating observed variables or indicators to unobserved concepts or latent variables, and a nonlinear simultaneous structural model describing relationships among the latent variables. For model identification, we assume an explicitly solved reduced structural model exists. This dissertation is composed of two papers.;The first paper deals with the case where the latent variables in the reduced structural model are normally distributed. We developed maximum likelihood estimation by a Monte Carlo EM algorithm. The asymptotic covariance matrix of the estimator is computed by the inverse of the empirical observed information matrix. Initial values of the parameters for general and special reduced structural models are presented. For a Monte Carlo EM algorithm, we developed a new procedure both to choose the Monte Carlo sample size for computing the expectation in the E-step, and to stop the algorithm. Simulation studies for structural equation models with a variety of structural models are presented to assess the performance of our stopping rule and the estimators.;The second paper develops distribution-free statistical procedures without specifying distribution forms of the latent variables. We use the normal-mixtures as a flexible distribution family. A pseudo maximum likelihood estimation procedure is introduced by first obtaining the measurement model parameters by factor analysis, then maximizing the pseudo likelihood, the likelihood evaluated at the measurement model parameters estimates, with respect to the structural equation model parameters. The asymptotic covariance matrix of the measurement parameters estimates is computed by non-parametric bootstrap, which is combined with the empirical information matrix of all parameters for the full likelihood to produce an estimate of the asymptotic covariance of the reduced model parameters estimates. Simulation studies are presented

Bayesian Analysis of Structural Credit Risk Models with Microstructure Noises

In this paper a Markov chain Monte Carlo (MCMC) technique is developed for the Bayesian analysis of structural credit risk models with microstructure noises. The technique is based on the general Bayesian approach with posterior computations performed by Gibbs sampling. Simulations from the Markov chain, whose stationary distribution converges to the posterior distribution, enable exact finite sample inferences of model parameters. The exact inferences can easily be extended to latent state variables and any nonlinear transformation of state variables and parameters, facilitating practical credit risk applications. In addition, the comparison of alternative models can be based on devian information criterion (DIC) which is straightforwardly obtained from the MCMC output. The method is implemented on the basic structural credit risk model with pure microstructure noises and some more general specifications using daily equity data from US and emerging markets. We find empirical evidence that microstructure noises are positively correlated with the firm values in emerging markets.MCMC, Credit risk, Microstructure noise, Devian information criterion

A review of R-packages for random-intercept probit regression in small clusters

Generalized Linear Mixed Models (GLMMs) are widely used to model clustered categorical outcomes. To tackle the intractable integration over the random effects distributions, several approximation approaches have been developed for likelihood-based inference. As these seldom yield satisfactory results when analyzing binary outcomes from small clusters, estimation within the Structural Equation Modeling (SEM) framework is proposed as an alternative. We compare the performance of R-packages for random-intercept probit regression relying on: the Laplace approximation, adaptive Gaussian quadrature (AGQ), Penalized Quasi-Likelihood (PQL), an MCMC-implementation, and integrated nested Laplace approximation within the GLMM-framework, and a robust diagonally weighted least squares estimation within the SEM-framework. In terms of bias for the fixed and random effect estimators, SEM usually performs best for cluster size two, while AGQ prevails in terms of precision (mainly because of SEM's robust standard errors). As the cluster size increases, however, AGQ becomes the best choice for both bias and precision

Estimation of extended mixed models using latent classes and latent processes: the R package lcmm

The R package lcmm provides a series of functions to estimate statistical models based on linear mixed model theory. It includes the estimation of mixed models and latent class mixed models for Gaussian longitudinal outcomes (hlme), curvilinear and ordinal univariate longitudinal outcomes (lcmm) and curvilinear multivariate outcomes (multlcmm), as well as joint latent class mixed models (Jointlcmm) for a (Gaussian or curvilinear) longitudinal outcome and a time-to-event that can be possibly left-truncated right-censored and defined in a competing setting. Maximum likelihood esimators are obtained using a modified Marquardt algorithm with strict convergence criteria based on the parameters and likelihood stability, and on the negativity of the second derivatives. The package also provides various post-fit functions including goodness-of-fit analyses, classification, plots, predicted trajectories, individual dynamic prediction of the event and predictive accuracy assessment. This paper constitutes a companion paper to the package by introducing each family of models, the estimation technique, some implementation details and giving examples through a dataset on cognitive aging

Sequential Monte Carlo Methods for Estimating Dynamic Microeconomic Models

This paper develops methods for estimating dynamic structural microeconomic models with serially correlated latent state variables. The proposed estimators are based on sequential Monte Carlo methods, or particle filters, and simultaneously estimate both the structural parameters and the trajectory of the unobserved state variables for each observational unit in the dataset. We focus two important special cases: single agent dynamic discrete choice models and dynamic games of incomplete information. The methods are applicable to both discrete and continuous state space models. We first develop a broad nonlinear state space framework which includes as special cases many dynamic structural models commonly used in applied microeconomics. Next, we discuss the nonlinear filtering problem that arises due to the presence of a latent state variable and show how it can be solved using sequential Monte Carlo methods. We then turn to estimation of the structural parameters and consider two approaches: an extension of the standard full-solution maximum likelihood procedure (Rust, 1987) and an extension of the two-step estimation method of Bajari, Benkard, and Levin (2007), in which the structural parameters are estimated using revealed preference conditions. Finally, we introduce an extension of the classic bus engine replacement model of Rust (1987) and use it both to carry out a series of Monte Carlo experiments and to provide empirical results using the original data.dynamic discrete choice, latent state variables, serial correlation, sequential Monte Carlo methods, particle filtering

Testing Measurement Invariance with Ordinal Missing Data: A Comparison of Estimators and Missing Data Techniques

Ordinal missing data are common in measurement equivalence/invariance (ME/I) testing studies. However, there is a lack of guidance on the appropriate method to deal with ordinal missing data in ME/I testing. Five methods may be used to deal with ordinal missing data in ME/I testing, including the continuous full information maximum likelihood estimation method (FIML), continuous robust FIML (rFIML), FIML with probit links (pFIML), FIML with logit links (lFIML), and mean and variance adjusted weight least squared estimation method combined with pairwise deletion (WLSMV_PD). The current study evaluates the relative performance of these methods in producing valid chi-square difference tests (Δχ2) and accurate parameter estimates. The result suggests that all methods except for WLSMV_PD can reasonably control the type I error rates of (Δχ2) tests and maintain sufficient power to detect noninvariance in most conditions. Only pFIML and lFIML yield accurate factor loading estimates and standard errors across all the conditions. Recommendations are provided to researchers based on the results

Simulation-based Estimation Methods for Financial Time Series Models

This chapter overviews some recent advances on simulation-based methods of estimating financial time series models that are widely used in financial economics. The simulation-based methods have proven to be particularly useful when the likelihood function and moments do not have tractable forms, and hence, the maximum likelihood (ML) method and the generalized method of moments (GMM) are diffcult to use. They are also capable of improving the finite sample performance of the traditional methods. Both frequentist's and Bayesian simulation-based methods are reviewed. Frequentist's simulation-based methods cover various forms of simulated maximum likelihood (SML) methods, the simulated generalized method of moments (SGMM), the efficient method of moments (EMM), and the indirect inference (II) method. Bayesian simulation-based methods cover various MCMC algorithms. Each simulation-based method is discussed in the context of a specific financial time series model as a motivating example. Empirical applications, based on real exchange rates, interest rates and equity data, illustrate how the simulation-based methods are implemented. In particular, SML is applied to a discrete time stochastic volatility model, EMM to estimate a continuous time stochastic volatility model, MCMC to a credit risk model, the II method to a term structure model.Generalized method of moments, Maximum likelihood, MCMC, Indirect Inference, Credit risk, Stock price, Exchange rate, Interest rate..

A general multivariate latent growth model with applications in student careers Data warehouses

The evaluation of the formative process in the University system has been assuming an ever increasing importance in the European countries. Within this context the analysis of student performance and capabilities plays a fundamental role. In this work we propose a multivariate latent growth model for studying the performances of a cohort of students of the University of Bologna. The model proposed is innovative since it is composed by: (1) multivariate growth models that allow to capture the different dynamics of student performance indicators over time and (2) a factor model that allows to measure the general latent student capability. The flexibility of the model proposed allows its applications in several fields such as socio-economic settings in which personal behaviours are studied by using panel data.Comment: 20 page