Australian & New Zealand Journal of Statistics最新文献

This paper is concerned with the formulation of $��N�$-mixture models for estimating the abundance and probability of detection of a species from binary response, count and time-to-detection data. A modelling framework, which encompasses time-to-first-detection within the context of detection/non-detection and time-to-each-detection and time-to-first-detection within the context of count data, is introduced. Two observation processes which depend on whether or not double counting is assumed to occur are also considered. The main focus of the paper is on the derivation of explicit forms for the likelihoods associated with each of the proposed models. Closed-form expressions for the likelihoods associated with time-to-detection data are new and are developed from the theory of order statistics. A key finding of the study is that, based on the assumption of no double counting, the likelihoods associated with times-to-detection together with count data are the product of the likelihood for the counts alone and a term which depends on the detection probability parameter. This result demonstrates that, in this case, recording times-to-detection could well improve precision in estimation over recording counts alone. In contrast, for the double counting protocol with exponential arrival times, no information was found to be gained by recording times-to-detection in addition to the count data. An R package and an accompanying vignette are also introduced in order to complement the algebraic results and to demonstrate the use of the models in practice.

The performance, in terms of coverage and expected length, of the model averaged tail area (MATA) confidence interval, proposed by Turek & Fletcher (2012, Computational Statistics & Data Analysis, 56, 2809–2815), depends greatly on the data-based model weights used in its construction. We generalise the computationally convenient exact formulae due to Kabaila, Welsh & Abeysekera (2016, Scandinavian Journal of Statistics, 43, 35–48) for the coverage and expected length of this confidence interval for two nested linear regression models to the case of two or more nested linear regression models. This permits the numerical assessment of the performance, in terms of coverage probability and scaled expected length, of the MATA confidence interval for any given data-based model weights in the context of three or more nested linear regression models. We illustrate this numerical assessment of performance of the MATA confidence interval, for model weights based on any given Generalised Information Criterion, in the context of three nested linear regression models using the real life ‘Cholesterol’ data. This provides a very informative further exploration of the influence of these model weights on the performance of this confidence interval.

We consider the problem of evaluating designs for a two-arm randomised experiment with an incidence (binary) outcome under a non-parametric general response model. Our two main results are that the a priori pair matching design is (1) the optimal design as measured by mean squared error among all block designs which includes complete randomisation. And (2), this pair-matching design is minimax, that is, it provides the lowest mean squared error under an adversarial response model. Theoretical results are supported by simulations and clinical trial data where we demonstrate the superior performance of pairwise matching designs under realistic conditions.

Regression models that ignore measurement error in predictors may produce highly biased estimates leading to erroneous inferences. It is well known that it is extremely difficult to take measurement error into account in Gaussian non-parametric regression. This problem becomes even more difficult when considering other families such as binary, Poisson and negative binomial regression. We present a novel method aiming to correct for measurement error when estimating regression functions. Our approach is sufficiently flexible to cover virtually all distributions and link functions regularly considered in generalised linear models. This approach depends on approximating the first and the second moment of the response after integrating out the true unobserved predictors in any semi-parametric generalised regression model. By the latter is meant a model with both linear and non-parametric effects that are connected to the mean response by a link function and with a response distribution in an exponential family or quasi-likelihood model. Unlike previous methods, the method we now propose is not restricted to truncated splines and can utilise various basis functions. Moreover, it can operate without making any distributional assumption about the unobserved predictor. Through extensive simulation studies, we study the performance of our method under many scenarios.

High levels of prenatal alcohol exposure (PAE) result in significant cognitive deficits in children, but the exact nature of the dose-response relationship is less well understood. To investigate this relationship, data were assembled from six longitudinal birth cohort studies examining the effects of PAE on cognitive outcomes from early school age through adolescence. Structural equation models (SEMs) are a natural approach to consider, because of the way they conceptualise multiple observed outcomes as relating to an underlying latent variable of interest, which can then be modelled as a function of exposure and other predictors of interest. However, conventional SEMs could not be fitted in this context because slightly different outcome measures were used in the six studies. In this paper we propose a multi-group Bayesian SEM that maps the unobserved cognition variable to a broad range of observed outcomes. The relation between these variables and PAE is then examined while controlling for potential confounders via propensity score adjustment. By examining different possible dose-response functions, the proposed framework is used to investigate whether there is a threshold PAE level that results in minimal cognitive deficit.

Multivariate zero-inflated Poisson (ZIP) distributions are important tools for modelling and analysing correlated count data with extra zeros. Unfortunately, existing multivariate ZIP distributions consider only the overall zero-inflation while the component zero-inflation is not well addressed. This paper proposes a flexible multivariate ZIP distribution, called the multivariate component ZIP distribution, in which both the overall and component zero-inflations are taken into account. Likelihood-based inference procedures including the calculation of maximum likelihood estimates of parameters in the model without and with covariates are provided. Simulation studies indicate that the performance of the proposed methods on the multivariate component ZIP model is satisfactory. The Australia health care utilisation data set is analysed to demonstrate that the new distribution is more appropriate than the existing multivariate ZIP distributions.

In this paper a semi-parametric approach is developed to model non-linear relationships in time series data using polynomial splines. Polynomial splines require very little assumption about the functional form of the underlying relationship, so they are very flexible and can be used to model highly non-linear relationships. Polynomial splines are also computationally very efficient. The serial correlation in the data is accounted for by modelling the noise as an autoregressive integrated moving average (ARIMA) process, by doing so, the efficiency in nonparametric estimation is improved and correct inferences can be obtained. The explicit structure of the ARIMA model allows the correlation information to be used to improve forecasting performance. An algorithm is developed to automatically select and estimate the polynomial spline model and the ARIMA model through backfitting. This method is applied on a real-life data set to forecast hourly electricity usage. The non-linear effect of temperature on hourly electricity usage is allowed to be different at different hours of the day and days of the week. The forecasting performance of the developed method is evaluated in post-sample forecasting and compared with several well-accepted models. The results show the performance of the proposed model is comparable with a long short-term memory deep learning model.