ACCOUNTING FOR NON-COMPLIANCE IN THE ANALYSIS OF RANDOMIZED RESPONSE DATA

The randomized response model is a misclassification design that is used to protect the privacy of respondents with respect to sensitive questions. Conditional misclassification probabilities are specified by the researcher and are therefore considered to be known. It is to be expected that some of the respondents do not comply with respect to the misclassification design. These respondents induce extra perturbation, which is not accounted for in the standard randomized response model. An extension of the randomized response model is presented that takes into account assumptions with respect to non-compliance under simple random sampling. The extended model is investigated using Bayesian inference. The research is motivated by randomized response data concerning violations of regulations for social benefit.     

NONPARAMETRIC STATISTICAL ANALYSIS OF DISCRETE-TIME QUEUES,WITH APPLICATIONS TO ATM TELETRAFFIC DATA

In this paper nonparametric statistical analysis of a discrete-time queueing system is considered. Estimation of performance measures of the system is studied. The attention is first focused on the estimation of the waiting time probability distribution, as well as of functionals of interest (mean waiting time, variance of the waiting time, etc.). The approach is based on the estimation of the corresponding generating function. Attention is paid to the estimation of the probability of a “long delay”, in view of its importance for applications. Results for possibly unstable models are also obtained. Finally, an application to ATM teletraffic data is provided.     

ANALYSIS OF DOUBLY CENSORED DATA AND THE HIV INCUBATION PERIOD DISTRIBUTION IN WESTERN AUSTRALIA

The paper analyses the distribution of times from HIV seroconversion to the first AIDS defining illness for a subcohort of the Western Australian HIV Cohort Study for whom the seroconversion date is known to fall within a calendar time window. The analysis is based on a generalised gamma model for the incubation times and a piecewise constant distribution for the conditional times of seroconversion given the seroconversion windows. This allows flexible hazard shapes and also allows comparison of goodness of fit of the gamma and Weibull distributions which are often used for modelling incubation times. Computational issues are discussed. In these data, neither age at seroconversion, nor calendar time of seroconversion, nor the identification of a seroconversion illness appears to afFect incubation distributions. The Weibull distribution appears to provide a reasonable fit. The distribution of times from seroconversion to an HIV-related death is also briefly considered.     

THE ANALYSIS OF MULTISTRATA DESIGNED EXPERIMENTS WITH INCOMPLETE DATA

Building upon early work of E. A. Cornish we show that G. N. Wilkinson's version of Yates' approach to the analysis of designed experiments with a single error stratum carries over completely to designs with an arbitrary non-singular covariance matrix, initially assumed known. We show that the equations, corrections, adjustments and algorithms all have their more general analogues and that these can be solved, computed or executed quite readily if the design has orthogonal block structure and satisfies Nelder's condition of general balance. The results are illustrated with a split-plot and a simple (square) lattice design.     

RAO'S SCORE TESTS IN SURVIVAL ANALYSIS: EXAMPLES AND BARTLETT TYPE ADJUSTMENTS

Score method in hypothesis testing is one of Professor C. R. Rao's great contributions to statistics. It provides a simple and unified way to test some simple and composite hypotheses in many statistical problems. Some popular tests in statistical practice derived with the help of intuitions can be shown as score tests under some statistical models. The subject-years test and log-rank test in survival analysis are two of the examples. In this paper, we first introduce these two examples. After formulating these two tests as score tests, we then review some recent results on the Bartlett type adjustments for these tests.     

NEIGHBOUR ANALYSIS OF UNIFORMITY DATA

The neighbour model of Williams (1986) is studied using barley uniformity data. Particular attention is paid to the validity of the model. This is done by comparing the variety and residual mean squares in the intra-N analysis.     

FACTORIAL ANALYSIS OF RECIDIVIST DATA

This paper presents a method of fitting factorial models to recidivism data consisting of the (possibly censored) time to ‘fail’ of individuals, in order to test for differences between groups. Here ‘failure’ means rearrest, reconviction or reincarceration, etc. A proportion P of the sample is assumed to be ‘susceptible’ to failure, i.e. to fail eventually, while the remaining 1-P are ‘immune’, and never fail. Thus failure may be described in two ways: by the probability P that an individual ever fails again (‘probability of recidivism’), and by the rate of failure Λ for the susceptibles. Related analyses have been proposed previously: this paper argues that a factorial approach, as opposed to regression approaches advocated previously, offers simplified analysis and interpretation of these kinds of data. The methods proposed, which are also applicable in medical statistics and reliability analyses, are demonstrated on data sets in which the factors are Parole Type (released to freedom or on parole), Age group (≤ 20 years, 20–40 years, > 40 years), and Marital Status. The outcome (failure) is a return to prison following first or second release.     

ON THE ROBUST ANALYSIS OF VARIANCE COMPONENTS MODELS FOR PEDIGREE DATA

Quantitative traits measured over pedigrees of individuals may be analysed using maximum likelihood estimation, assuming that the trait has a multivariate normal distribution. This approach is often used in the analysis of mixed linear models. In this paper a robust version of the log likelihood for multivariate normal data is used to construct M-estimators which are resistant to contamination by outliers. The robust estimators are found using a minimisation routine which retains the flexible parameterisations of the multivariate normal approach. Asymptotic properties of the estimators are derived, computation of the estimates and their use in outlier detection tests are discussed, and a small simulation study is conducted.     

A SEMIPARAMETRIC MIXTURE MODEL FOR THE ANALYSIS OF COMPETING RISKS DATA

This paper deals with the regression analysis of failure time data when there are censoring and multiple types of failures. We propose a semiparametric generalization of a parametric mixture model of Larson & Dinse (1985), for which the marginal probabilities of the various failure types are logistic functions of the covariates. Given the type of failure, the conditional distribution of the time to failure follows a proportional hazards model. A marginal like lihood approach to estimating regression parameters is suggested, whereby the baseline hazard functions are eliminated as nuisance parameters. The Monte Carlo method is used to approximate the marginal likelihood; the resulting function is maximized easily using existing software. Some guidelines for choosing the number of Monte Carlo replications are given. Fixing the regression parameters at their estimated values, the full likelihood is maximized via an EM algorithm to estimate the baseline survivor functions. The methods suggested are illustrated using the Stanford heart transplant data.     

THE REDUCED-RANK GROWTH CURVE MODEL FOR DISCRIMINANT ANALYSIS OF LONGITUDINAL DATA

This paper presents a method of discriminant analysis especially suited to longitudinal data. The approach is in the spirit of canonical variate analysis (CVA) and is similarly intended to reduce the dimensionality of multivariate data while retaining information about group differences. A drawback of CVA is that it does not take advantage of special structures that may be anticipated in certain types of data. For longitudinal data, it is often appropriate to specify a growth curve structure (as given, for example, in the model of Potthoff & Roy, 1964). The present paper focuses on this growth curve structure, utilizing it in a model-based approach to discriminant analysis. For this purpose the paper presents an extension of the reduced-rank regression model, referred to as the reduced-rank growth curve (RRGC) model. It estimates discriminant functions via maximum likelihood and gives a procedure for determining dimensionality. This methodology is exploratory only, and is illustrated by a well-known dataset from Grizzle & Allen (1969).     

ANALYSIS OF VECTOR AUTOREGRESSIONS IN THE PRESENCE OF SHIFTS IN MEAN

This paper considers the implications of mean shifts in a multivariate setting. It is shown that under the additive outlier type mean shift specification, the intercept in each equation of the vector autoregression (VAR) will be subject to multiple shifts when the break dates of the mean shifts to the univariate series do not coincide. Conversely, under the innovative outlier type mean shift specification, both the univariate and the multivariate time series are subject to multiple shifts when mean shifts to the innovation processes occur at different dates. We consider two procedures, the first removes the shifts series by series before forming the VAR, and the second removes intercept shifts in the VAR directly. The pros and cons of both methods are discussed.     

ANALYSIS OF MASKED DATA IN A DEPENDENT COMPETING RISKS MODEL UNDER UNKNOWN ENVIRONMENT

ABSTRACT

System failure data is often analyzed to estimate component reliabilities. Due to cost and time constraints, the exact component causing the failure of the system cannot be identified in some cases. This phenomenon is called masking. Further, it is sometimes necessary for us to take account of the influence of the operating environment. Here we consider a series system, operating under unknown environment, of two components whose failure times follow the Marshall-Olkin bivariate exponential distribution. We present a maximum likelihood approach for obtaining estimators from the masked data for this system. From a simulation study, we found that the relative errors of the estimates are almost well behaved even for small or moderate expected number of systems whose cause of failure is identified.     

THE COVARIANCE ANALYSIS OF SOME CENSORED SURVIVAL DATA FROM A LARGE SCALE STUDY OF MELANOMA

Regression models of the proportional hazard type are applied to investigate the effect of certain covariates on the survival function of some cancer patients. The censored survival data for these patients were taken from a survey conducted by the Queensland Melanoma Project through which there are available histories of all malignant melanoma cases in Queensland for the period 1963–1969; follow-up data on these cases were considered up to mid-1976. One of the results of the survival analysis shows that the well-known empirical observation that women have a better prognosis than men can be explained by the existence of a significant interaction between sex and the anatomical site of the lesion.     

ASYMPTOTIC PROPERTIES OF AN OPTIMAL ESTIMATING FUNCTION APPROACH TO THE ANALYSIS OF MARK RECAPTURE DATA

ABSTRACT

A drawback of non parametric estimators of the size of a closed population in the presence of heterogeneous capture probabilities has been their lack of analytic tractability. Here we show that the martingale estimating function/sample coverage approach to estimating the size of a closed population with heterogeneous capture probabilities is mathematically tractable and develop its large sample properties.     

MULTIVARLYTE ANALYSIS OF CLUSTERED SURVEY DATA: TESTING EQUALITY OF COVARLANCE MATRICES

The problem of testing the hypothesis of equality of covariance matrices in the presence of two-stage sampling is considered. Asymptotic test procedures based on linearization, grouping and jackknifing with or without transformation are proposed. The finite sample properties of these procedures are investigated in sampling experiments both from simulated known distributions and from a natural population.     

GLOBAL LOG-CONCAVITY OF THE LIKELIHOOD IN MODELS WITH GROUPED DISCRETE DATA

The paper considers the property of global log-concavity of the likelihood function in discrete data models in which the data are observed in ‘grouped’ form, meaning that for some observations, while the actual value is unknown, the realisation of the discrete random variable is known to fall within a certain range of values. A typical likelihood contribution in this type of model is a sum of probabilities over a range of realisations. An important issue is whether the property of log-concavity in the ungrouped case carries over to the grouped counterpart; the paper finds, by way of a simple but relevant counter-example, that this is not always the case. However, in two cases of practical interest, namely the Poisson and geometric models, the property of log-concavity is preserved under grouping.     

ANALYSIS OF DATA FROM A SINGLE EPIDEMIC1

A model with nonrandom latent and infectious periods is suggested for epidemics in a large community. This permits a relatively complete statistical analysis of data from the spread of a single epidemic. An attractive feature of such models is the possibility of exploring how the rate of spread of the disease depends on the number of susceptibles and infectives. An application to smallpox data is included.     

APPLICATION OF SEMIPARAMETRIC REGRESSION MODELS IN THE ANALYSIS OF CAPTURE-RECAPTURE EXPERIMENTS

If the capture probabilities in a capture‐recapture experiment depend on covariates, parametric models may be fitted and the population size may then be estimated. Here a semiparametric model for the capture probabilities that allows both continuous and categorical covariates is developed. Kernel smoothing and profile estimating equations are used to estimate the nonparametric and parametric components. Analytic forms of the standard errors are derived, which allows an empirical bias bandwidth selection procedure to be used to estimate the bandwidth. The method is evaluated in simulations and is applied to a real data set concerning captures of Prinia flaviventris, which is a common bird species in Southeast Asia.     

MULTILEVEL DISCRETE‐TIME EVENT HISTORY MODELS WITH APPLICATIONS TO THE ANALYSIS OF RECURRENT EMPLOYMENT TRANSITIONS

Data on the timing of events such as births, residential moves and changes in employment status are collected in many longitudinal surveys. These data often have a highly complex structure, with events of several types occurring repeatedly over time to an individual and interdependences between different event processes (e.g. births and employment transitions). The aim of this paper is to review a general class of multilevel discrete‐time event history models for handling recurrent events and transitions between multiple states. It is also shown how standard methods can be extended to allow for time‐varying covariates that are outcomes of an event process that is jointly determined with the process of interest. The considerable potential of these methods for studying transitions through the life course is illustrated in analyses of the effect of the presence and age of children on women's employment transitions, using data from the British Household Panel Survey.