Nonresponses and missing data are common in observational studies. Ignoring or inadequately handling missing data may lead to biased parameter estimation, incorrect standard errors and, as a consequence, incorrect statistical inference and conclusions. We present a strategy for modelling non-ignorable missingness where the probability of nonresponse depends on the outcome. Using a simple case of logistic regression, we quantify the bias in regression estimates and show the observed likelihood is non-identifiable under non-ignorable missing data mechanism. We then adopt a selection model factorisation of the joint distribution as the basis for a sensitivity analysis to study changes in estimated parameters and the robustness of study conclusions against different assumptions. A Bayesian framework for model estimation is used as it provides a flexible approach for incorporating different missing data assumptions and conducting sensitivity analysis. Using simulated data, we explore the performance of the Bayesian selection model in correcting for bias in a logistic regression. We then implement our strategy using survey data from the 45 and Up Study to investigate factors associated with worsening health from the baseline to follow-up survey. Our findings have practical implications for the use of the 45 and Up Study data to answer important research questions relating to health and quality-of-life. Copyright © 2017 John Wiley & Sons, Ltd.
Wang, J.J.J., Bartlett, M. & Ryan, L. 2017, 'On the impact of nonresponse in logistic regression: application to the 45 and Up study.', BMC medical research methodology, vol. 17, no. 1, p. 80.View/Download from: Publisher's site
In longitudinal studies, nonresponse to follow-up surveys poses a major threat to validity, interpretability and generalisation of results. The problem of nonresponse is further complicated by the possibility that nonresponse may depend on the outcome of interest. We identified sociodemographic, general health and wellbeing characteristics associated with nonresponse to the follow-up questionnaire and assessed the extent and effect of nonresponse on statistical inference in a large-scale population cohort study.We obtained the data from the baseline and first wave of the follow-up survey of the 45 and Up Study. Of those who were invited to participate in the follow-up survey, 65.2% responded. Logistic regression model was used to identify baseline characteristics associated with follow-up response. A Bayesian selection model approach with sensitivity analysis was implemented to model nonignorable nonresponse.Characteristics associated with a higher likelihood of responding to the follow-up survey include female gender, age categories 55-74, high educational qualification, married/de facto, worked part or partially or fully retired and higher household income. Parameter estimates and conclusions are generally consistent across different assumptions on the missing data mechanism. However, we observed some sensitivity for variables that are strong predictors for both the outcome and nonresponse.Results indicated in the context of the binary outcome under study, nonresponse did not result in substantial bias and did not alter the interpretation of results in general. Conclusions were still largely robust under nonignorable missing data mechanism. Use of a Bayesian selection model is recommended as a useful strategy for assessing potential sensitivity of results to missing data.
Wichitaksorn, N., Wang, J.J.J., Choy, S.T.B. & Gerlach, R. 2015, 'Analyzing return asymmetry and quantiles through stochastic volatility models using asymmetric Laplace error via uniform scale mixtures', Applied Stochastic Models in Business and Industry, vol. 31, no. 5, pp. 584-608.View/Download from: UTS OPUS or Publisher's site
Copyright © 2014 John Wiley & Sons, Ltd. Copyright © 2014 John Wiley & Sons, Ltd. This paper proposes a new approach to analyze stock return asymmetry and quantiles. We also present a new scale mixture of uniform (SMU) representation for the asymmetric Laplace distribution (ALD). The use of the SMU for a probability distribution is a data augmentation technique that simplifies the Gibbs sampler of the Bayesian Markov chain Monte Carlo algorithms. We consider a stochastic volatility (SV) model with an ALD error distribution. With the SMU representation, the full conditional distribution for some parameters is shown to have closed form. It is also known that the ALD can be used to obtain the coefficients of quantile regression models. This paper also considers a quantile SV model by fixing the skew parameter of the ALD at specific quantile level. Simulation study shows that the proposed methodology works well in both SV and quantile SV models using Bayesian approach. In the empirical study, we analyze index returns of the stock markets in Australia, Japan, Hong Kong, Thailand, and the UK and study the effect of S & P 500 on these returns. The results show the significant return asymmetry in some markets and the influence by S & P 500 in all markets at all quantile levels.
Fung, T., Wang, J.J.J. & Seneta, E. 2014, 'The deviance information criterion in comparison of normal mixing models', International Statistical Review, vol. 82, no. 3, pp. 411-421.View/Download from: UTS OPUS or Publisher's site
© 2014 International Statistical Institute. Model selection from several non-nested models by using the deviance information criterion within Bayesian inference Using Gibbs Sampling (BUGS) software needs to be treated with caution. This is particularly important if one can specify a model in various mixing representations, as for the normal variance-mean mixing distribution occurring in financial contexts. We propose a procedure to compare goodness of fit of several non-nested models, which uses BUGS software in part.
Olivier, J., Wang, J. & Grzebieta, R. 2014, 'A systematic review of methods used to assess mandatory bicycle helmet legislation in New Zealand', Journal of the Australasian College of Road Safety, vol. 25, no. 4, pp. 24-31.View/Download from: UTS OPUS
Background: Mandatory helmet legislation (MHL)
for cyclists became effective in New Zealand (NZ) on
1 January 1994. Assessments of the NZ MHL have led
to conflicting conclusions regarding its effectiveness at
reducing cycling head injury and risk of fatality. These
studies also differ in their use of analytic approaches and
Objectives: The aim of this paper is to systematically
review all studies that assess the NZ MHL in accordance
with quality criteria for assessing population-based
Data Sources: A search of Medline, Scopus and Web
of Science for peer-reviewed articles from 1994 to 9
September 2014 was conducted.
Study Selection: Documents were independently extracted
by two reviewers and limited to original articles in peerreviewed
journals that assessed the NZ MHL in terms of
cycling head injury.
Results: The results from three of the four included studies
indicated a positive effect of MHL for increasing helmet
wearing and reducing head injuries. However, the findings
of these studies must be interpreted within the context of
Conclusion: We believe more high quality evaluations are
needed to provide evidence for an objective assessment of
MHL in NZ.
Olivier, J., Wang, J., Walter, S. & Grzebieta, R. 2014, 'Anti-Helmet Arguments: Lies, Damned Lies and Flawed Statistics', Journal of the Australasian College of Road Safety, vol. 25, no. 4, pp. 10-23.View/Download from: UTS OPUS
Bicycle helmets are designed to mitigate head injury during
a collision. In the early 1990's, Australia and New Zealand
mandated helmet wearing for cyclists in an effort to
increase helmet usage. Since that time, helmets and helmet
laws have been portrayed as a failure in the peer-reviewed
literature, by the media and various advocacy groups. Many
of these criticisms claim helmets are ineffective, helmet
laws deter cycling, helmet wearing increases the risk of an
accident, no evidence helmet laws reduce head injuries at
a population level, and helmet laws result in a net health
reduction. This paper reviews the data and methods used
to support these arguments and shows they are statistically
flawed. When the majority of evidence against helmets or
mandatory helmet legislation (MHL) is carefully scrutinised
it appears overstated, misleading or invalid. Moreover,
much of the statistical analysis has been conducted by
people with known affiliations with anti-helmet or antiMHL
Wang, J., Olivier, J. & Grzebieta, R. 2014, 'Response to 'Evaluation of New Zealand's bicycle helmet law' article.', The New Zealand Medical Journal, vol. 127, no. 1389, pp. 106-108.
The Generalised Normal Variance-Mean (GNVM) model in which the mixing random variable is Gamma distributed is considered. This model generalises the popular Variance-Gamma (VG) distribution. This GNVM model can be interpreted as the addition of noise to a (skew) VG base. The discussion is based on goodness of fit criteria and on parameter estimation. The conclusion is that the shape of the VG distribution can be adjusted in a favourable way by adding noise. © 2013 Elsevier B.V. All rights reserved.
Wang, J.J.J., Choy, S.T.B. & Chan, J.S.K. 2013, 'Modelling stochastic volatility using generalized t distribution', Journal of Statistical Computation and Simulation, vol. 83, no. 2, pp. 340-354.View/Download from: UTS OPUS or Publisher's site
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. © 2013 Copyright Taylor and Francis Group, LLC.
In stochastic volatility (SV) models, asset returns conditional on the latent volatility are usually assumed to have a normal, Student-t or exponential power (EP) distribution. An earlier study uses a generalised t (GT) distribution for the conditional returns and the results indicate that the GT distribution provides a better model fit to the Australian Dollar/Japanese Yen daily exchange rate than the Student-t distribution. In fact, the GT family nests a number of well-known distributions including the commonly used normal, Student-t and EP distributions. This paper extends the SV model with a GT distribution by incorporating general volatility asymmetry. We compare the empirical performance of nested distributions of the GT distribution as well as different volatility asymmetry specifications. The new asymmetric GT SV models are estimated using the Bayesian Markov chain Monte Carlo (MCMC) method to obtain parameter and log-volatility estimates. By using daily returns from the Standard and Poors (S & P) 500 index, we investigate the effects of the specification of error distributions as well as volatility asymmetry on parameter and volatility estimates. Results show that the choice of error distributions has a major influence on volatility estimation only when volatility asymmetry is not accounted for. © 2012 IMACS. Published by Elsevier B.V. All rights reserved.
Wang, J.J.J., Chan, J.S.K. & Choy, S.T.B. 2011, 'Stochastic volatility models with leverage and heavy-tailed distributions: A Bayesian approach using scale mixtures', Computational Statistics and Data Analysis, vol. 55, no. 1, pp. 852-862.View/Download from: UTS OPUS or Publisher's site
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 Geweke's convergence test. © 2010 Elsevier B.V. All rights reserved.
Wang, J., Bartlett, M. & Ryan, L. 2016, 'Housing transition and aging: 45 and Up Study', Joint Statistical Meetings, Chicago.
Wang, J., Olivier, J., Patummasut, M. & Techakamolsuk, P. 1970, 'The effect of the 100% Motorcycle Helmet Use Campaign on motorcyclist head injuries in Thailand.', Australasian Road Safety Conference Proceedings, Australasian Road Safety Conference.
Wang, J., Grzebieta, R., Walter, S. & Olivier, J. 2013, 'An evaluation of the methods used to assess the effectiveness of mandatory bicycle helmet legislation in New Zealand', Australasian College of RoadSafety Conference, Adelaide.
Wang, J., Olivier, J., Grzebieta, R. & Walter, S. 2013, 'Onthe use of Empirical Bayes for Comparative Interrupted Time Series with an Application to Mandatory Helmet Legislation', Road Safety Research, Policing and Education Conference, Brisbane.
Wang, J., Walter, S., Grzebieta, R. & Olivier, J. 2013, 'A Comparison of Statistical Methods in Interrupted Time Series Analysis to Estimate an Intervention Effect', Australasian Road Safety Research, Policing and Education Conference, Brisbane.View/Download from: UTS OPUS
Since the introduction of mandatory helmet legislation (MHL) in Australia, debate on the effect of MHL on cyclist head injuries has been ongoing. The debate sometimes revolves around the statistical methodology used to assess intervention effectiveness. Supporters of rescinding the MHL thereby encouraging cyclists to ride without helmets, regularly dismiss statistical evaluations as being flawed for various reasons. In a more general context, researchers want to estimate whether and how a policy intervention changed an outcome of interest. Quasi-experimental interrupted time series (ITS) is the most appropriate design to evaluate the longitudinal effects of policy interventions and segmented regression analysis is often used as a powerful statistical method for ITS. Recent research has employed a log-linear regression model for the hospital admission counts of head and limb injuries from New South Wales, Australia, from a 36 month period centred at the time of legislation. Estimation of the model was done using a frequentist approach. In this paper, we re-analyse this data using empirical Bayes and full Bayesian methods, since the use of these methods has become popular in road safety studies. In particular, we show how a full Bayesian method can be readily implemented in WinBUGS software. We discuss the advantages and disadvantages of each method and describe and compare the different estimation methods in terms of parameter estimates. The results show that all three estimation methods give consistent conclusions regarding the positive effect of compulsory helmet wearing on cyclist head injuries in New South Wales.