Centre for Statistical & Survey Methodology Working Paper Series

Multi-phase variety trials using both composite and individual replicate samples: A model-based design approach

Alison B. Smith — Sun, 19 May 2013 18:58:04 PDT

This paper provides an approach for the design and analysis of variety trials that are used to obtain quality trait data. These trials are multi-phase in nature, comprising a field phase followed by one or more laboratory phases. Typically the laboratory phases are costly relative to the field phase and this necessitates a limit on the number of samples that can be tested. Historically, this has been achieved by sacrificing field replication, either by testing a single replicate plot for each variety or a single composite sample, obtained by combining material from several field replicates. An efficient statistical analysis cannot be applied to such data so that valid inference and accurate prediction of genetic effects is precluded. In this paper we propose an approach in which some varieties are tested using individual field replicate samples and others as composite samples. Replication in the laboratory is achieved by splitting a relatively small number of field samples into sub-samples for separate processing. We show that, if necessary, some of the composite samples may be split for this purpose. We also show that, given a choice of field compositing and laboratory replication strategy, an efficient design for a laboratory phase may be obtained using model-based techniques. The methods are illustrated using two examples.

Learning Design Map (LDMap) for Mathematics Teachers in Developing Countries and the Benefit of Its Use for Curriculum Review

Maman Fathurrohman — Sun, 19 May 2013 18:32:37 PDT

In this paper, Learning Design Map (LDMap) to document and share mathematical teaching and learning experiences are proposed. These maps are intended for use by mathematics teachers in developing countries. The development of the maps is based on a survey that gathered information related to the real and perceived ICT infrastructure, facilities, and resources, in one accessible area in a developing country. These maps can be created by teachers. It is expected that the map will be shared and modified by teachers and that there will be a circulation of the mathematical teaching and learning experiences among teachers through the use of these maps. The Learning Design Map (LDMap) is based on XML technology so that the data contained in this file can be extracted across platforms. Through mapping assessments, outcomes, resources and other attributes as considered desireable in the LDMaps can be designed to facilitate curriculum review. The benefit of the use of LDMaps for curriculum review is explored.

Addressing the Needs of a Developing Nation: Electronic Maps of Mathematical Learning Resources Accessible Via the Internet

Maman Fathurrohman — Sun, 19 May 2013 18:01:38 PDT

Teaching and learning of mathematics are integral parts of societies throughout the world. The fundamental or core nature of mathematics, its compulsory acquisition, requires high quality mathematics learning experiences. Moreover it is highly desirable that the emergence of new technology positively influences learning experiences in mathematics. Since 81.5 percent of countries in the world belong to developing countries, it is important that technology-based learning experiences are implemented in these countries. Based on a survey in Bojonegara Sub District, Indonesia, a prototype of modifiable and shareable electronic maps has been developed. This product would be useful for teachers mapping mathematical learning resources in the Internet for easy access and download for use for teaching and learning. The teachers could also create, modify and share the maps with others.

Assessing barotrauma among angled snapper (Pagrus auratus) and the utility of release methods

Paul A. Butcher — Sun, 19 May 2013 17:19:56 PDT

Australian recreational and commercial fishers catch snapper (Pagrus auratus) from down to ∼120 m, often evoking barotrauma. Owing to minimum legal sizes and quotas or non-consumptive fishing practices, some afflicted fish are released, raising concerns over the potential for unaccounted fishing mortality. Two experiments were completed to quantify the (1) clinical signs of barotrauma among fish angled from 6 to 120 m (experiment 1) and (2) mortality (over 3 d) of fish with barotrauma that were released following either no treatment, venting (e.g. needle) or recompression (e.g. release weight) (experiment 2). In experiment 1, barotrauma was evident in some fish angled from 11 m and all from >20 m. Fish were considered to have barotrauma if they had a prolapsed cloaca combined with a distended coelomic cavity and/or gastric herniation into the buccal cavity. Despite similar clinical signs among fish in experiment 2, none died, however, the associated trauma raises welfare concerns. Both recompression and venting offered benefits over no treatment by returning fish to depth quickly and releasing gases, respectively. Nevertheless, the release method should be dictated by the clinical signs of barotrauma and extrinsic conditions, including the competency of the fisher (e.g. for venting), presence of predators (e.g. for recompression), and exposure to sun or warm water (e.g. no treatment). More selective gears, spatial and temporal closures, or possibly replacing minimum legal sizes with quotas in deep water only could also reduce the frequency of barotrauma among released P. auratus and therefore, negative impacts on stocks.

M-Quantile Regression for Binary Data with Application to Small Area Estimation

Ray Chambers — Sun, 19 May 2013 16:31:40 PDT

M-quantile regression models are a robust and flexible alternative to random effects models, particularly in small area estimation. However quantiles, and more generally M-quantiles, are only uniquely defined for continuous variables. In this paper we extend the M-quantile regression approach to binary data, and more generally to count data. This approach is then applied to estimation of a small area proportion, where a popular alternative approach is to use a plugin version of the Empirical Best (EB) predictor based on a generalised linear mixed model for the underlying binary variable. Results from both model-based and design-based simulations comparing the binary M-quantile and the plug-in EB predictors demonstrate the usefulness of the M-quantile approach in this case. The paper concludes with two illustrative applications. The first addresses estimation of the number of unemployed people aged 16 and above resident in the Unitary Authorities and Local Authority Districts of Great Britain. The second considers estimation of the number of poor households in each of the Local Labour Systems of the Tuscany region of Italy.

Using Social Network Information for Survey Estimation

Thomas Suesse — Sun, 19 May 2013 16:25:01 PDT

Standard model-based and model-assisted methods of survey estimation aim to improve the precision of estimators of the population total or mean. These methods are often based on a linear regression model defined in terms of auxiliary variables whose values are assumed known for all population units. Friendships and other social relationships represent another form of auxiliary information that might increase the precision of these estimators. Such relationships are typically expressed in terms of a social network. Common linear models that use social networks as an additional source of information include autocorrelation, disturbance and contextual models. In this paper we investigate how much of the population network needs to be known for estimation methods based on these models to be useful. In particular, we use simulation to compare the performance of the best linear unbiased predictor under a model that ignores the network with model-based estimators that incorporate network information. Our results show that incorporating network information via a contextual model is the best performer overall. We also show that the full population network is not required, but that the partial network linking the sampled population units to the non-sampled population units needs to be known. Finally, we illustrate the contextual model by applying it to friendship network information collected in the British Household Panel Study.

Sampling the Maori Population using Proxy Screening, the Electoral Roll and Disproportionate Sampling in the New Zealand Health Survey

Robert Graham Clark — Sun, 19 May 2013 16:19:49 PDT

This chapter describes an instructive example of a hard-to-reach subpopulation: the indigenous Māori population of New Zealand. This population shares some characteristics with others described in earlier chapters: it is relatively rare, over- surveyed, and geographically dispersed, and there is no adequate population frame. There are some unique features as well: Māori are less rare than many indigenous populations, and have a special status in the NZ electoral system, so that the Electoral Roll provides a useful partial frame. A combination of strategies to oversample Māori in the NZ Health Survey is found to work well. A novel approach to setting the large number of design parameters required by this design is described, based on numerical optimization using a training and validation dataset.

Estimating Shared Copy Number Aberrations for Array CGH Data: the Linear-Median Method

Yan-Xia Lin — Tue, 13 Nov 2012 21:03:46 PST

Motivation: Existing methods for estimating copy number variations in array comparative genomic hybridization (aCGH) data are limited to estimations of the gain/loss of chromosome regions for single sample analysis. We propose the linear-median method for estimating shared copy numbers in DNA sequences across multiple samples, demonstrate its operating characteristics through simulations and applications to real cancer data, and compare it to two existing methods. Results: Our proposed linear-median method has the power to estimate common changes that appear at isolated single probe positions or very short regions. Such changes are hard to detect by current methods. This new method shows a higher rate of true positives and a lower rate of false positives. The linear-median method is non-parametric and hence is more robust in estimating copy number. Additionally, the linear-median method is easily computable for practical aCGH data sets compared to other copy number estimation methods. Supplementary Information: Supporting materials are available at Cancer Informatics online.

Emulating the Best Technology in Teaching and Learning Mathematics: Challenges Facing Libyan Higher Education

Bothaina Bukhatowa — Tue, 13 Nov 2012 21:03:45 PST

The aim of this research is to identify ways to emulate and implement the best of western technology in developing countries given the limited infrastructure, funding and expertise available. Qualitative methodology has involved analysis of the Libyan education system from an experiential and documentary perspective and then to juxtapose this with what is possible in a mathematics department at an Australian University. Three of the most notable differences are: internet access, the use of e-Learning systems and the variety of mathematics and statistical software available. The challenge is to identify the components of these systems which can be made available to support student learning, and in particular mathematics learning, when there is little or no internet access. Possible solutions are identified through an exploration of the components and functionalities of the technologies. These include the use of open source software and of components of the internet, for example html and web browsers, which allow the reshaping of how educational materials are organised and made available to students. It is apparent that professional development will be a key part of the solution.

Can telephone surveys for the whole population provide reliable information on the health of Aboriginal and Torres Strait Islander Australians?

Margo L. Barr — Tue, 13 Nov 2012 20:25:44 PST

Objective: To compare prevalence estimates for Aboriginal and Torres Strait Islander Australians collected through a telephone survey for the general population with those collected through a face-to-face survey for Aboriginal and Torres Strait Islander Australians. Design, Setting and Participants: Information about Aboriginal and Torres Strait Islander Australians from the NSW Population Health Survey 2002-2005 and the NSW component of the 2004-05 National Aboriginal and Torres Strait Islander Health Survey— including sample frame, study design, participant selection, final sample, collection period, collection method, collection agency, weighting procedure, and questionnaires—were obtained and compared. Questions that were the same, or could provide the same information, were selected. Prevalence estimates and standard errors were calculated and compared. Results: The sampling methods and data collection differed between the two surveys, although both had known probabilities of selection, and both were weighted to the corresponding Aboriginal and Torres Strait Islander population for NSW as at 31 December 2004. The differences between prevalence estimates ranged from less than 1% for current asthma; 1-2% for recommended vegetable consumption, influenza vaccination, pneumococcal vaccination, positive self-rated health, diabetes or high blood glucose, and overweight or obesity, just over 3% for recommended fruit consumption; and around 8% for non-drinkers and current smoking. Only non-drinkers (27.1% versus 19.4%; p=0.01) and current smoking (44.6% versus 52.9%; p=0.02) were statistically significantly different. Conclusion: Prevalence estimates for Aboriginal and Torres Strait Islander Australians, collected through telephone health surveys for the general population, appear to be consistent with those collected through face-to-face surveys specifically for Aboriginal and Torres Strait Islander Australians.

Imputation of household survey data using linear mixed models

Luise P. Lago — Tue, 13 Nov 2012 20:25:43 PST

This paper investigates whether using a linear mixed model to impute missing values in household surveys leads to improvement over imputation using a linear model and other standard imputation methods. The mixed model imputes leads to clear although not large improvements in predictive accuracy and the estimation of means, standard deviations and deciles, particularly when non-response is informative.

Inclusion of mobile phone numbers into an ongoing population health survey in Australia using an overlapping dual frame: description of methods, call outcomes and acceptance by staff and respondents

Margo Barr — Tue, 13 Nov 2012 20:25:42 PST

In Australia telephone surveys has been the method of choice for ongoing population health surveys. Although it was estimated in 2011 that 20% of the population were mobile phone only persons the inclusion of mobile only phone users into these existing landline population health surveys has not occurred. This paper is part of a project that is looking in detail at the inclusion of mobile phone numbers into an ongoing population health survey in Australia. This paper describes the methods used, the call outcomes and acceptance by the population, supervisors and interviewing staff.

Statistical learning in sample design

Robert Graham Clark — Tue, 13 Nov 2012 20:01:55 PST

A well-designed sampling plan can greatly enhance the information that can be produced from a survey. Once a broad sample design is identified, specific design parameters such as sample sizes and selection probabilities need to be chosen. This is typically achieved using an optimal sample design, which minimises the variance of a key statistic or statistics, expressed as a function of design parameters and population characteristics, subject to a cost constraint. In practice, only imprecise estimates of population characteristics are available, but the effects of this variability are usually ignored. A general approach to sample allocation allowing for imprecise design data is proposed and evaluated. The approach is based on the availability of two sets of design data which can act as a check on each other. One application is to stratified sampling, where estimated stratum variances may be highly variable. Pooling strata into groups may reduce this variability, at the possible cost of some inefficiency. Proportional allocation, ignoring differences between stratum variances, could also be used. The new approach enables a data- driven compromise between all three. Simulation results based on real data show useful gains in a hypothetical farm survey, business survey and household survey of a subpopulation.

Continuous analogues of Cochran-Mantel-Haenszel statistics

J C. Rayner — Tue, 13 Nov 2012 20:01:54 PST

Cochran-Mantel-Haenszel (CMH) statistics are reviewed and continuous analogues of the CMH general association and mean score statistics are given. CMH generalised correlation statistics are defined and analogues given.

Testing equality of variances for multiple univariate normal populations

David Allingham — Tue, 13 Nov 2012 20:01:53 PST

To test for equality of variances in independent random samples from multiple univariate normal populations, the test of first choice would usually be the likelihood ratio test, the Bartlett test. This test is known to be powerful when normality can be assumed. Here two Wald tests of equality of variances are derived. The first test compares every variance with every other variance and was announced in Mather and Rayner (2002), but no proof was given there. The second test is derived from a quite different model using orthogonal contrasts, but is identical to the first. This second test statistic is similar to one given in Rippon and Rayner (2010), for which no empirical assessment has been given. These tests are compared with the Bartlett test in size and power. The Bartlett test is known to be non-robust to the normality assumption, as is the orthogonal contrasts test. To deal with this difficulty an analogue of the new test is given. An indicative empirical assessment shows that it is more robust that the Bartlett test and competitive with the Levene test in its robustness to fat-tailed distributions. Moreover it is a Wald test and has good power properties in large samples. Advice is given on how to implement the new test.

Unbiased regression estimation for multi-linked data in the presence of correlated linkage error

G. Kim — Tue, 13 Nov 2012 19:37:20 PST

Linkage errors can occur when probability-based methods are used to link records from two or more distinct data sets corresponding to the same target population. Recent research on methods for modifying standard methods of regression analysis to allow for these errors assumes that when more than two linked data sets are used to generate the data for this analysis, the linkage errors in these different data sets are independent. In this paper we extend these results to accommodate the more realistic scenario of dependent linkage errors. Our simulation results show that an incorrect assumption of independent linkage errors can lead to insufficient linkage error bias correction, while an approach that allows for correlated linkage errors appears to fully correct this bias.

Potential gains from sample design using unit level cost information

David Steel — Tue, 13 Nov 2012 19:37:19 PST

In developing the sample design for a survey we usually attempt to produce a good design for the funds available. Information on costs can be used to develop sample designs that minimise the sampling variance of an estimator of total for fixed costs. Improvements in survey management systems mean that it is now possible to estimate the cost of including each unit in the sample. This paper develops relatively simple approaches to determine whether the potential gains arising from using this unit level cost information are likely to be of practical use. It is shown that the key factor is coefficient of variation of the costs relative to the coefficient of variation of the relative error on the estimated cost coefficients.

Multiple membership models for social network and group dependencies

Mark Tranmer — Tue, 13 Nov 2012 19:37:18 PST

Multilevel models have been developed and applied for individuals in groups, such as schools or areas, but these models tend to not consider the networks of an individual’s connections within and between groups; the social network has largely been ignored as an additional source of dependence in multilevel modelling that is carried out in social statistics. Typical models for network dependencies in the social networks literature, such as network autocorrelation models, have largely ignored other sources of dependence, such as the school or area in which an individual lives. To bridge this divide, a multiple membership modelling approach for jointly investigating social network and group dependencies is presented that allows social network and group dependencies on individual responses to be investigated and compared, and which can be analysed using MCMC estimation in standard statistical software for multilevel modelling. This approach is used to analyse a subsample of the Adolescent Health dataset from the US, where the two response variables of interest are individual level educational attainment and self-assessed health status, and the three individual level covariates are sex, ethnic group and age. Individual, network, school and area levels are included in the analysis. The network level can be represented with various configurations. The results suggest that the network should not be ignored from a statistical perspective when studying variations in educational attainment, as ignoring this level impacts on the estimates of variation at the other levels (school, area, individual), as well as having some impact on the point estimates and standard errors of the estimates of regression coefficients for covariates in the fixed part of the model. From a substantive perspective, this approach provides a flexible and practical way of investigating the network level, and comparing its relative importance to other group levels such as areas or schools.

Evaluating the volatility forecasting performance of best fitting GARCH models in emerging asian stock markets

Chaiwat Kosapattarapim — Tue, 13 Nov 2012 17:03:14 PST

Problem statement : While modeling the volatility of returns is essential for many areas of finance, it is well known that financial return series exhibit many non-normal characteristics that cannot be captured by the standard GARCH model with a normal error distribution. But which GARCH model and which error distribution to use is still open to question, especially where the model that best fits the in-sample data may not give the most effective out-of-sample volatility forecasting ability which we use as the criterion for the selection of the most effective model from among the alternatives. Approach: In this study, six simulated studies in GARCH (p,q) with six different error distributions (normal, skewed normal, student-t, skewed student-t, generalized error distribution and skewed generalized error distribution) are carried out. In each case, we determine the best fitting GARCH model based on the AIC criterion and then evaluate its out-of-sample volatility forecasting performance against that of other models. The analysis is then carried out using the daily closing price data from Thailand (SET), Malaysia (KLCI) and Singapore (STI) stock exchanges. Results : Our simulations show that although the best fitting model does not always provide the best future volatility estimates the differences are so insignificant that the estimates of the best fitting model can be used with confidence. The empirical application to stock markets also indicates that a non normal error distribution tends to improves the volatility forecast of returns in the presence of heavy-tailed, leptokurtic and skewness. Conclusion : The volatility forecast estimates of the best fitted model can be reliably used for volatility forecasting. Moreover, the empirical studies demonstrate that a skewed error distribution outperforms other error distributions in terms of out-of-sample volatility forecasting.

The algorithm of equal acceptance region for detecting copy number alterations: applications to next-generation sequencing data

Yan-Xia Lin — Tue, 13 Nov 2012 17:03:13 PST

The information of copy number alterations (gains and losses) in tumour genomes can be used to discovery cancer-causing genes. The estimate of copy number can be obtained from the estimate copy number ratio. The higher the depth of underlying sequencing data, the more accurate the estimate of copy number ratio. At the same time, the higher depth of a sequencing data used in copy number analysis, the more cost of data analysis. To develop a method for identifying a necessary depth of sequencing data for copy number analysis before test data are produced is of interest. In this paper, we proposed an algorithm of equal acceptance regions for detecting copy number ratios. This algorithm can be used to determine the depth of sequencing data required for copy number analysis.