Handling non-ignorable dropouts in longitudinal data: A conditional model based on a latent Markov heterogeneity structure

We illustrate a class of conditional models for the analysis of longitudinal data suffering attrition in random effects models framework, where the subject-specific random effects are assumed to be discrete and to follow a time-dependent latent process. The latent process accounts for unobserved heterogeneity and correlation between individuals in a dynamic fashion, and for dependence between the observed process and the missing data mechanism. Of particular interest is the case where the missing mechanism is non-ignorable. To deal with the topic we introduce a conditional to dropout model. A shape change in the random effects distribution is considered by directly modeling the effect of the missing data process on the evolution of the latent structure. To estimate the resulting model, we rely on the conditional maximum likelihood approach and for this aim we outline an EM algorithm. The proposal is illustrated via simulations and then applied on a dataset concerning skin cancers. Comparisons with other well-established methods are provided as well

A latent class selection model for nonignorably missing data

When we have data with missing values, the assumption that data are missing at random is very convenient. It is, however, sometimes questionable because some of the missing values could be strongly related to the underlying true values. We introduce methods for nonignorable multivariate missing data, which assume that missingness is related to the variables in question, and to the additional covariates, through a latent variable measured by the missingness indicators. The methodology developed here is useful for investigating the sensitivity of one's estimates to untestable assumptions about the missing-data mechanism. A simulation study and data analysis are conducted to evaluate the performance of the proposed method and to compare to that of MAR-based alternatives.Nonignorable missing Multiple imputation Latent class model

La imputación múltiple y su aplicación a series temporales financieras

Cuando una base de datos presenta valores no disponibles (NA ó missings), su análisis es imposible hasta que no se decida lo que hacer con ellos. A tal efecto, la literatura ha desarrollado distintos enfoques para enfrentarse a este problema. Los primero métodos fueron los basados en regresión (Yates [1933]), y posteriormente se utilizaron algoritmos basados en la función de verosimilitud (algoritmo EM). Rubin [1987] estudia el problema de los NA y pone de manifiesto que los algoritmos mencionados son de imputación única y, entre sus inconvenientes más importantes, destaca la omisión de la incertidumbre que causa la presencia de los missings en el ulterior análisis. Para tal fin, Rubin [1987] propone la imputación múltiple, cuyo objetivo es la medición de la incertidumbre omitida por los métodos de imputación única, lo que se consigue mediante dos herramientas: algoritmos MCMC y la inferencia de Rubin. La imputación múltiple se ha utilizado únicamente en el campo de los datos de sección cruzada, y esta Tesis pretende extender su aplicación al campo de la series temporales financieras. Para tal fin, se estudian las técnicas que sobre las que se fundamentan los métodos MCMC, la inferencia de Rubin y los modelos heteroscedásticos condicionados. El resultado es la imputación mediante separación, que consigue adaptar la técnica de imputación múltiple a las series temporales financieras mediante la combinación de un filtro asimétrico, un método Bootstrap y el conocido algoritmo GibbsSampling. La Tesis se extiende con un librería programada en lenguaje R, de próxima incorporación en el cuerpo de librerías contribuidas en el portal oficial del citado lenguaje, que implementa el método propuesto.When a database contains missing values, the forthcoming analysis becomes impossible until one decides how to deal with them. That is the reason why the literature has developed different ways to solve problems associated with NA values. The first methods of this specific literature were regression-based (Yates [1933]), but later more sophisticated algorithms were available (EM algorithm). Rubin [1987] makes a deep analysis on the topic and develops Multiple Imputation, a Monte Carlo technique in which the missing values are replaced by m>1 simulated versions, where m is typically small (e.g. 3-10). In Rubin's method for `repeated imputation' inference, each of the simulated complete datasets is analyzed by standard methods, and the results are combined to produce estimates and confidence intervals that incorporate missing-data uncertainty. Multiple Imputation has been widely used in cross section studies but not in time series. This doctoral thesis aims to extend Multiple Imputation to longitudinal studies, specifically to financial time series. To do so, we propose a method based on an asymmetric filter which splits the original time series in conditional variance and innovations. This procedure allows us to generate plausible values combining the algorithms Gibbs Sampling and Approximate Bayesian Bootstrap. The validity of the proposed method is discussed through extensive tests on different financial time series (firms and market indices). The analysis of empirical tests displays that, after imputing the data, they maintain its individual characteristics. Furthermore, results exhibit high precision in the shape parameter of the conditional distribution of returns, and densities of both conditional variance and innovations