Jennifer S. K. Chan

Maximum Likelihood Estimation for Probit-Linear Mixed Models with Correlated Random Effects

The probit-normal model for binary data (McCulloch, 1994, Journal of the American Statistical Association 89, 330-335) is extended to allow correlated random effects. To obtain maximum likelihood estimates, we use the EM algorithm with its M-step greatly simplified under the assumption of a probit link and its E-step made feasible by Gibbs sampling. Standard errors are calculated by inverting a Monte Carlo approximation of the information matrix rather than via the SEM algorithm. A method is also suggested that accounts for the Monte Carlo variation explicitly. As an illustration, we present a new analysis of the famous salamander mating data. Unlike previous analyses, we find it necessary to introduce different variance components for different species of animals. Finally, we consider models with correlated errors as well as correlated random effects.

Methadone maintenance and drug-related crime

Using data from an evaluation of methadone maintenance treatment, this study investigated factors associated with continued involvement in crime during treatment, and in particular whether there appeared to be differences in effectiveness of treatment between different methadone clinics. The methodology was an observational study, in which 304 patients attending three low-intervention, private methadone clinics in Sydney were interviewed on three occasions over a twelve month period. Outcome measures were self-reported criminal activity and police department records of convictions. By self-report, crime dropped promptly and substantially on entry to treatment, to a level of acquisitive crime about one-eighth that reported during the last addiction period. Analysis of official records indicated that rates of acquisitive convictions were significantly lower in the in-treatment period compared to prior to entry to treatment, corroborating the changes suggested by self-report. Persisting involvement in crime in treatment was predicted by two factors: the cost of persisting use of illicit drugs, particularly cannabis, and ASPD symptom count. Treatment factors also were independently predictive of continued involvement in crime. By both self-report and official records, and adjusting for subject factors, treatment at one clinic was associated with greater involvement in crime. This clinic operated in a chaotic and poorly organized way. It is concluded that crime during methadone treatment is substantially lower than during street addiction, although the extent of reduction depends on the quality of treatment being delivered.

A comparison of estimators for regression models with change points

We consider two problems concerning locating change points in a linear regression model. One involves jump discontinuities (change-point) in a regression model and the other involves regression lines connected at unknown points. We compare four methods for estimating single or multiple change points in a regression model, when both the error variance and regression coefficients change simultaneously at the unknown point(s): Bayesian, Julious, grid search, and the segmented methods. The proposed methods are evaluated via a simulation study and compared via some standard measures of estimation bias and precision. Finally, the methods are illustrated and compared using three real data sets. The simulation and empirical results overall favor both the segmented and Bayesian methods of estimation, which simultaneously estimate the change point and the other model parameters, though only the Bayesian method is able to handle both continuous and dis-continuous change point problems successfully. If it is known that regression lines are continuous then the segmented method ranked first among methods.

Stochastic volatility models with leverage and heavy-tailed distributions: A Bayesian approach using scale mixtures

This paper studies a heavy-tailed stochastic volatility (SV) model with leverage effect, where a bivariate Student-t distribution is used to model the error innovations of the return and volatility equations. Choy et al. (2008) studied this model by expressing the bivariate Student-t distribution as a scale mixture of bivariate normal distributions. We propose an alternative formulation by first deriving a conditional Student-t distribution for the return and a marginal Student-t distribution for the log-volatility and then express these two Student-t distributions as a scale mixture of normal (SMN) distributions. Our approach separates the sources of outliers and allows for distinguishing between outliers generated by the return process or by the volatility process, and hence is an improvement over the approach of Choy et al. (2008). In addition, it allows an efficient model implementation using the WinBUGS software. A simulation study is conducted to assess the performance of the proposed approach and its comparison with the approach by Choy et al. (2008). In the empirical study, daily exchange rate returns of the Australian dollar to various currencies and daily stock market index returns of various international stock markets are analysed. Model comparison relies on the Deviance Information Criterion and convergence diagnostic is monitored by Gewekes convergence test.

Predicting potential drop‐out and future commitment for first‐time donors based on first 1·5‐year donation patterns: the case in Hong Kong Chinese donors

Background and Objectives  Adequate blood supply is crucial to the health‐care system. To maintain a stable donor pool, donation‐promotion strategies should not only be targeted in recruitment but also focus on retaining donors to give blood regularly. A study using statistical modelling is conducted to understand the first 4‐year donation patterns for drop‐out and committed first‐time blood donors and to build model for the donor‐type identification based on their first 1·5‐year donation patterns.

Modelling stochastic volatility using generalized t distribution

In modelling financial return time series and time-varying volatility, the Gaussian and the Student-t distributions are widely used in stochastic volatility (SV) models. However, other distributions such as the Laplace distribution and generalized error distribution (GED) are also common in SV modelling. Therefore, this paper proposes the use of the generalized t (GT) distribution whose special cases are the Gaussian distribution, Student-t distribution, Laplace distribution and GED. Since the GT distribution is a member of the scale mixture of uniform (SMU) family of distribution, we handle the GT distribution via its SMU representation. We show this SMU form can substantially simplify the Gibbs sampler for Bayesian simulation-based computation and can provide a mean of identifying outliers. In an empirical study, we adopt a GT–SV model to fit the daily return of the exchange rate of Australian dollar to three other currencies and use the exchange rate to US dollar as a covariate. Model implementation relies on Bayesian Markov chain Monte Carlo algorithms using the WinBUGS package.

The Analysis of Methadone Clinic Data Using Marginal and Conditional Logistic Models with Mixture or Random Effects

Summary The paper develops methods for the statistical analysis of outcomes of methadone maintenance treatment (MMT). Subjects for this study were a cohort of patients entering MMT in Sydney in 1986. Urine drug tests on these subjects were performed weekly during MMT, and were reported as either positive or negative for morphine, the marker of recent heroin use. To allow correlation between the repeated binary measurements, a marginal logistic model was fitted using the generalized estimating equation (GEE) approach and the alternating logistic regression approach. Conditional logistic models are also considered. Results of separate fitting to each patient and score tests suggest that there is substantial between-patient variation in response to MMT. To account for the population heterogeneity and to facilitate subject-specific inference, the conditional logistic model is extended by introducing random intercepts. The two, three and four group mixture models are also investigated. The model of best fit is a three group mixture model, in which about a quarter of the subjects have a poor response to MMT, with continued heroin use independent of daily dose of methadone; about a quarter of the subjects have a very good response, with little or no heroin use, again independent of dose; and about half the subjects responded in a dose-dependent fashion, with reduced heroin use while receiving higher doses of methadone. These findings are consistent with clinical experience. There is also an association between reduced drug use and increased duration in treatment. The mixture model is recommended since it is quite tractable in terms of estimation and model selection as well as being supported by clinical experience.

A new approach for handling longitudinal count data with zero-inflation and overdispersion: poisson geometric process model.

For time series of count data, correlated measurements, clustering as well as excessive zeros occur simultaneously in biomedical applications. Ignoring such effects might contribute to misleading treatment outcomes. A generalized mixture Poisson geometric process (GMPGP) model and a zero-altered mixture Poisson geometric process (ZMPGP) model are developed from the geometric process model, which was originally developed for modelling positive continuous data and was extended to handle count data. These models are motivated by evaluating the trend development of new tumour counts for bladder cancer patients as well as by identifying useful covariates which affect the count level. The models are implemented using Bayesian method with Markov chain Monte Carlo (MCMC) algorithms and are assessed using deviance information criterion (DIC).

A Bayesian conditional autoregressive geometric process model for range data

Extreme value theories indicate that the range is an efficient estimator of local volatility in financial time series. A geometric process (GP) framework that incorporates the conditional autoregressive range (CARR)-type mean function is presented for range data. The proposed model, called the conditional autoregressive geometric process range (CARGPR) model, allows for flexible trend patterns, threshold effects, leverage effects, and long-memory dynamics in financial time series. For robustness considerations, a log-t distribution is adopted. Model implementation can be easily done using the WinBUGS package. A simulation study shows that model parameters are estimated with high accuracy. In the empirical study on the range data of an Australian stock market index, the CARGPR model outperforms the CARR model in both in-sample estimation and out-of-sample forecast.

Bayesian analysis of robust Poisson geometric process model using heavy-tailed distributions

Abstract We propose a robust Poisson geometric process model with heavy-tailed distributions to cope with the problem of outliers as it may lead to an overestimation of mean and variance resulting in inaccurate interpretations of the situations. Two heavy-tailed distributions namely Student’s t and exponential power distributions with different tailednesses and kurtoses are used and they are represented in scale mixture of normal and scale mixture of uniform respectively. The proposed model is capable of describing the trend and meanwhile the mixing parameters in the scale mixture representations can detect the outlying observations. Simulations and real data analysis are performed to investigate the properties of the models.