Bayesian dynamic probit models for the analysis of longitudinal data

In this paper, we discuss the relation between liquidity and the business cycle.There are some reasons that we should link liquidity with the business cycle. The“flight to liquidity” or “flight to quality” hypothesis might be the most important one. It is more likely that an investor shifts his portfolio from those stocks with lower liquidity or higher risk when the economy is in a recession.Instead of business cycle measures, we use the NBER recession signal as the proxy of real economy. We apply dynamic and static probit model to monthly liquidity proxy, because the NBER recession is not always available in current period. Besides we use Amihud (2002) ILR as our liquidity proxy.The dynamic probit model with liquidity added does not result in a significance improvement on prediction. No matter in sample or out of sample, the pure dynamic probit model performs well with itself history only. However, as we mentioned earlier, NBER recession signal is usually announced well until the recession has happened for months, leading to an infeasibility to implement dynamic model. On the other hand, liquidity plays an important role in static probit model. We find a robust positive relation between liquidity and recession. Adding liquidity as a predictor in the static model would significantly improve the forecast accuracy in th short horizon. This observation remains robust with comparison to other financial variables ( e.g. term spread, credit spread, market volatility, and excess return). We also find the existence of “size effect” that small firm is more sensitive to future recession. Our finding above is consistent with our claims of “flight to liquidity; that is, it is more likely for market participants to shift his portfolio from those stock with lower liquidity or higher risk in advance when the economy would be in a recession. The primary contribution of this paper is that liquidity proxy, Amihud’s liquidity proxy here, does provide useful information when predicting the future recession. We find that the liquidity proxy performs well especially in a short prediction horizon. Besides, the liquidity of small firms is more informative in prediction.

Analysis of binary longitudinal data with time-varying effects

Longitudinal designs for biomarker traits are very appealing for a number of reasons. First, the collection of repeated biomarker measurements over time allows investigators to characterize both the overall and individual trajectories in these measurements. This helps investigators to understand overall effects as well as how individuals vary around these average effects. Distinguishing individual heterogeneity from average trend is impossible without longitudinal data. This distinction is important for understanding individual between-subject in its own right, as well as in developing predictors of disease outcome from longitudinal marker data. There are many statistical issues that are unique to longitudinal data analysis ranging from correctly specifying realistic models which characterize average changes over time and individual variation, accounting for observations that are taken at unequally spaced observation times which may differ between individuals, to accounting for missing data due to occasionally missed measurements or loss to follow-up. When the reason for missing data is not related to the underlying observation process, most longitudinal data analysis methods can be routinely applied. However, complex modelling is necessary when the reason for missing an observation or dropout is directly related to the underlying outcome process [1–2]. Statistical techniques that appropriately analyze continuous and discrete longitudinal data have been discussed by many authors. Diggle, et al. [3] provides a good summary of these techniques for the practitioner, while Fitzmaurice et al. [4] discusses recent advances from a more technical perspective. The three papers in this section present innovative approaches for solving important methodological problems in biomarker studies. Most standard longitudinal data analysis techniques assume that the measurement process is independent of the outcome process. However, when the outcome is related to the underlying observation process, failure to properly account for the observation process can result in bias [5]. Schildcrout et al.[6] proposed an approach for regression modelling for longitudinal binary data where the outcome is measured with probabilities determined by an auxiliary variable that is related, but not identical to the binary outcome. Modelling multivariate longitudinal biomarker data is an increasingly common issue with the advent of an increasing number of important biomarker techniques (e.g., multiple cytokines in a multiplex assay or multiple reproductive hormones that describe complex biological phenomenon). Although various authors have proposed techniques for analyzing multivariate longitudinal data [7–8 and others], little work has focused on estimating multivariate linear mixed models under known constraints in the relationship between the multivariate outcomes. Roy et al [9] proposes such an approach for analyzing multivariate reproductive hormones over the menstrual cycle, where established relationships have solid biological justification. Finally, the collection of longitudinal biomarker data as disease predictors is becoming an increasingly important design in diagnostic medicine. Pfeiffer et al. [10] proposes flexible non-parametric methodology for combining biomarkers that exploits the longitudinal structure in formulating a score that is used for predicting a binary outcome.

Parsimonious modelling of the within‐subject covariance structure while heeding its positive‐definiteness is of great importance in the analysis of longitudinal data. Using the Cholesky decomposition and the ensuing unconstrained and statistically meaningful reparameterisation, we provide a convenient and intuitive framework for developing conditionally conjugate prior distributions for covariance matrices and show their connections with generalised inverse Wishart priors. Our priors offer many advantages with regard to elicitation, positive definiteness, computations using Gibbs sampling, shrinking covariances toward a particular structure with considerable flexibility, and modelling covariances using covariates. Bayesian estimation methods are developed and the results are compared using two simulation studies. These simulations suggest simpler and more suitable priors for the covariance structure of longitudinal data.

We provide sufficient conditions for estimating from longitudinal data the causal effect of a time-dependent exposure or treatment on the marginal probability of response for a dichotomous outcome. We then show how one can estimate this effect under these conditions using the g-computation algorithm of Robins. We also derive the conditions under which some current approaches to the analysis of longitudinal data, such as the generalized estimating equations (GEE) approach of Zeger and Liang, the feedback model techniques of Liang and Zeger, and within-subject conditional methods, can provide valid tests and estimates of causal effects. We use our methods to estimate the causal effect of maternal stress on the marginal probability of a child's illness from the Mothers' Stress and Children's Morbidity data and compare our results with those previously obtained by Zeger and Liang using a GEE approach.

The analysis of longitudinal data with non-ignorable missingness remains an active area in biostatistics research. This article discusses various random effects and latent process models which have been proposed for analyzing longitudinal binary data subject to both non-ignorable intermittent missing data and dropout. These models account for non-ignorable missingness by introducing random effects or a latent process which is shared between the response model and the model for the missing-data mechanism. We discuss various random effects and latent processes approaches and compare these approaches with analyses from an opiate clinical trial data set, which had high proportion of intermittent missingness and dropout. We also compare these random effect and latent process approaches with other methods for accounting for non-ignorable missingness using this data set.

An econometric analysis of three health economic issues in China

The development of adequate models for binary time series data with covariate adjustment has been an active research area in the last years. In the case, where interest is focused on marginal and association parameters, generalized estimating equations (GEE) (see for example Lipsitz, Laird and Harrington (1991) and Liang, Zeger and Qaqish (1992)) and likelihood (see for example Fitzmaurice and Laird (1993) and Molenberghs and Lesaffre (1994)) based methods have been proposed. The number of parameters required for the full specification of these models grows exponentially with the length of the binary time series. Therefore, the analysis is often focused on marginal and first order parameters. In this case, the multivariate probit model (Ashford and Sowden (1970)) becomes an attractive alternative to the above models. The application of the multivariate probit model has been hampered by the intractability of the maximum likelihood estimator, when the length of the binary time series is large. This paper shows that this difficulty can be overcome by the use of Markov Chain Monte Carlo methods. This analysis also allows for valid point and interval estimates of the parameters in small samples. In addition, the analysis is adopted to handle the case of missing at random responses. The approach is illustrated on data involving binary responses measured at unequally spaced time points. Finally, this data analysis is compared to a GEE analysis given in Fitzmaurice and Lipsitz (1995).

The Markov process amplitude (MPA) EEG model effectively representing spontaneous brain activity of the EEG was introduced. The relationship between the electrical mechanism for EEG generation and the proposed model was also investigated. The MPA EEG model was described by the sinusoidal waves with the randomly fluctuating amplitude of the first-order Markov process. The parameters of the MPA EEG model were determined optimally based on the real EEG records. The results of model outputs in the frequency domain demonstrated an excellent fit with the power spectrum of the corresponding EEG. The simulated model signal in the time domain also showed good agreement with the EEG time series. The satisfactory results from the MPA EEG model suggest its possible applicability in clinical practice. Furthermore, from the high goodness of fit, the authors think that the neurons oscillate at fixed frequencies and are modulated by synaptic interactions in accordance with the first-order Markov process.

This article proposes a Bayesian method for estimating the dynamic panel-ordered probit model. We compare four alternative algorithms for the estimation of ordered probit models. Furthermore, this article presents the empirical results of the application of the dynamic ordered probit model to subjective well being based on the micro-level survey data extracted from the Japanese Panel Survey of Consumers. The results of the application reveal that income and savings have positive effects on life satisfaction, whereas our posterior results show that marriage and labor force participation have negative effects on the same.

Purpose The purpose of this paper is to test the existence of true persistence in the generation and adoption of product innovations in the context of a developing country. Design/methodology/approach A dynamic probit model with random effects is used to test true persistence relying on a panel data set constructed from three waves of the Colombian innovation survey (Encuesta de Desarrollo e Innvovación Tecnológica) covering the time span from 2003 to 2008. Findings This paper empirically shows the existence of true innovation persistence for two of the three types of product innovation studied: the adoption of product innovation that is new to the firm; and the adoption of product innovation that is new to the national market. However, the study could not confirm true persistence in the generation of product innovation. Originality/value To the best of our knowledge, this is the first study that systematically tests innovation persistence differentiating between the adoption of innovations that are new to the firm and innovation that is new to the national market. It is also the first study in this research area that uses a dynamic probit model with random effects according to the original specification by Wooldridge (2005).

We introduce LAMP: the Linear Additive Markov Process. Transitions in LAMP may be influenced by states visited in the distant history of the process, but unlike higher-order Markov processes, LAMP retains an efficient parameterization. LAMP also allows the specific dependence on history to be learned efficiently from data. We characterize some theoretical properties of LAMP, including its steady-state and mixing time. We then give an algorithm based on alternating minimization to learn LAMP models from data. Finally, we perform a series of real-world experiments to show that LAMP is more powerful than first-order Markov processes, and even holds its own against deep sequential models (LSTMs) with a negligible increase in parameter complexity.

Corporate fraud is not only curtailed investors’ rights and privileges but also disrupts the overall market economy. For this reason, the formulation of a model that could help detect any unusual market fluctuations would be essential for investors. Thus, we propose an early warning system for predicting fraud associated with financial statements based on the Bayesian probit model while examining historical data from 1999 to 2017 with 327 businesses in Taiwan to create a visual method to aid in decision making. In this study, we utilize a parametric estimation via the Markov Chain Monte Carlo (MCMC). The result show that it can reduce over or under-confidence within the decision-making process when standard logistic regression is utilized. In addition, the Bayesian probit model in this study is found to offer more accurate calculations and not only represent the prediction value of the responses but also possible ranges of these responses via a simple plot.

Valid inference can be drawn from a random-effects model for repeated measures that are incomplete if whether the data are missing or not, known as missingness, is independent of the missing data. Data that are missing completely at random or missing at random are two data types for which missingness is ignorable. Given ignorable missingness, statistical inference can proceed without addressing the source of the missing data in the model. If the missingness is not ignorable, however, recommendations are to fit multiple models that represent different plausible explanations of the missing data. A popular choice in methods for evaluating nonignorable missingness is a random-effects pattern-mixture model that extends a random-effects model to include one or more between-subjects variables that represent fixed patterns of missing data. Generally straightforward to implement, a fixed pattern-mixture model is one among several options for assessing nonignorable missingness, and when it is used as the sole model to address nonignorable missingness, understanding the impact of missingness is greatly limited. This paper considers alternatives to a fixed pattern-mixture model for nonignorable missingness that are generally straightforward to fit and encourage researchers to give greater attention to the possible impact of nonignorable missingness in longitudinal data analysis. Patterns of both monotonic and non-monotonic (intermittently) missing data are addressed. Empirical longitudinal psychiatric data are used to illustrate the models. A small Monte Carlo data simulation study is presented to help illustrate the utility of such methods.Supplementary InformationThe online version contains supplementary material available at 10.3758/s13428-023-02128-y.

This thesis presents a comprehensive exploration of linear mixed models that incorporate measurement errors in specific covariates for longitudinal data with non-ignorable and non-monotone missing responses. The primary objective is to estimate mean response parameters and variance components utilizing a combined methodology of Regression Calibration (RC) and Monte Carlo EM. The investigation begins with an in-depth examination of the RC method applied to linear mixed models, particularly its adaptation to longitudinal data with covariates affected by measurement errors. A thorough simulation study is conducted, involving various mean response functions, revealing that the RC method produces unbiased and efficient estimators in scenarios where the true underlying model includes covariates with measurement errors. Subsequently, linear mixed models are introduced for longitudinal data with non-ignorable missing responses. The thesis proposes a semi-parametric Monte Carlo EM algorithm for the simultaneous estimation of regression parameters and variance components in linear mixed models with non-ignorable and non-monotone missing responses, combining the Monte Carlo EM algorithm of Ibrahim et al. and the RC method. The simulation study demonstrates the effectiveness of the proposed method, even in the presence of a substantial proportion of non-ignorable missing responses. The thesis concludes with an application of the proposed RC-MCEM method to actual longitudinal data from the Canadian Community Health Survey (CCHS), focusing on individuals with alcoholism and exploring how measurement errors in certain covariates can introduce biases in parameter estimation. The complexity of the problem is further elucidated when missingness occurs in the response variable.