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  • Articles and reports: 12-001-X200800110606
    Description:

    Data from election polls in the US are typically presented in two-way categorical tables, and there are many polls before the actual election in November. For example, in the Buckeye State Poll in 1998 for governor there are three polls, January, April and October; the first category represents the candidates (e.g., Fisher, Taft and other) and the second category represents the current status of the voters (likely to vote and not likely to vote for governor of Ohio). There is a substantial number of undecided voters for one or both categories in all three polls, and we use a Bayesian method to allocate the undecided voters to the three candidates. This method permits modeling different patterns of missingness under ignorable and nonignorable assumptions, and a multinomial-Dirichlet model is used to estimate the cell probabilities which can help to predict the winner. We propose a time-dependent nonignorable nonresponse model for the three tables. Here, a nonignorable nonresponse model is centered on an ignorable nonresponse model to induce some flexibility and uncertainty about ignorabilty or nonignorability. As competitors we also consider two other models, an ignorable and a nonignorable nonresponse model. These latter two models assume a common stochastic process to borrow strength over time. Markov chain Monte Carlo methods are used to fit the models. We also construct a parameter that can potentially be used to predict the winner among the candidates in the November election.

    Release date: 2008-06-26

  • Articles and reports: 11-522-X200600110392
    Description:

    We use a robust Bayesian method to analyze data with possibly nonignorable nonresponse and selection bias. A robust logistic regression model is used to relate the response indicators (Bernoulli random variable) to the covariates, which are available for everyone in the finite population. This relationship can adequately explain the difference between respondents and nonrespondents for the sample. This robust model is obtained by expanding the standard logistic regression model to a mixture of Student's distributions, thereby providing propensity scores (selection probability) which are used to construct adjustment cells. The nonrespondents' values are filled in by drawing a random sample from a kernel density estimator, formed from the respondents' values within the adjustment cells. Prediction uses a linear spline rank-based regression of the response variable on the covariates by areas, sampling the errors from another kernel density estimator; thereby further robustifying our method. We use Markov chain Monte Carlo (MCMC) methods to fit our model. The posterior distribution of a quantile of the response variable is obtained within each sub-area using the order statistic over all the individuals (sampled and nonsampled). We compare our robust method with recent parametric methods

    Release date: 2008-03-17

  • Articles and reports: 11-522-X200600110398
    Description:

    The study of longitudinal data is vital in terms of accurately observing changes in responses of interest for individuals, communities, and larger populations over time. Linear mixed effects models (for continuous responses observed over time) and generalized linear mixed effects models and generalized estimating equations (for more general responses such as binary or count data observed over time) are the most popular techniques used for analyzing longitudinal data from health studies, though, as with all modeling techniques, these approaches have limitations, partly due to their underlying assumptions. In this review paper, we will discuss some advances, including curve-based techniques, which make modeling longitudinal data more flexible. Three examples will be presented from the health literature utilizing these more flexible procedures, with the goal of demonstrating that some otherwise difficult questions can be reasonably answered when analyzing complex longitudinal data in population health studies.

    Release date: 2008-03-17

  • Articles and reports: 11-522-X200600110419
    Description:

    Health services research generally relies on observational data to compare outcomes of patients receiving different therapies. Comparisons of patient groups in observational studies may be biased, in that outcomes differ due to both the effects of treatment and the effects of patient prognosis. In some cases, especially when data are collected on detailed clinical risk factors, these differences can be controlled for using statistical or epidemiological methods. In other cases, when unmeasured characteristics of the patient population affect both the decision to provide therapy and the outcome, these differences cannot be removed using standard techniques. Use of health administrative data requires particular cautions in undertaking observational studies since important clinical information does not exist. We discuss several statistical and epidemiological approaches to remove overt (measurable) and hidden (unmeasurable) bias in observational studies. These include regression model-based case-mix adjustment, propensity-based matching, redefining the exposure variable of interest, and the econometric technique of instrumental variable (IV) analysis. These methods are illustrated using examples from the medical literature including prediction of one-year mortality following heart attack; the return to health care spending in higher spending U.S. regions in terms of clinical and financial benefits; and the long-term survival benefits of invasive cardiac management of heart attack patients. It is possible to use health administrative data for observational studies provided careful attention is paid to addressing issues of reverse causation and unmeasured confounding.

    Release date: 2008-03-17

  • Articles and reports: 92F0138M2008002
    Description:

    On November 26 2006, the Organization for Economic Co-operation and Development (OECD) held an international workshop on defining and measuring metropolitan regions. The reasons the OECD organized this workshop are listed below.

    1. Metropolitan Regions have become a crucial economic actor in today's highly integrated world. Not only do they play their traditional role of growth poles in their countries but they function as essential nodes of the global economy.2. Policy makers, international organisations and research networks are increasingly called to compare the economic and social performances of Metropolitan Regions across countries. Examples of this work undertaken in international organisation and networks include the UN-Habitat, the EU Urban Audit, ESPON and the OECD Competitive Cities.3. The scope of what we can learn from these international comparisons, however, is limited by the lack of a comparable definition of Metropolitan Regions. Although most countries have their own definitions, these vary significantly from one country to another. Furthermore, in search for higher cross-country comparability, international initiatives have - somehow paradoxically - generated an even larger number of definitions.4. In principle, there is no clear reason to prefer one definition to another. As each definition has been elaborated for a specific analytical purpose, it captures some features of a Metropolitan Region while it tends to overlook others. The issue, rather, is that we do not know the pros and the cons of different definitions nor, most important, the analytical implications of using one definition rather than another. 5. In order to respond to these questions, the OECD hosted an international workshop on 'Defining and Measuring Metropolitan Regions'. The workshop brought together major international organisations (the UN, Eurostat, the World Bank, and the OECD), National Statistical Offices and researchers from this field. The aim of the workshop was to develop some 'guiding principles', which could be agreed upon among the participants and would eventually provide the basis for some form of 'International Guidance' for comparing Metropolitan Regions across countries.

    This working paper was presented at this workshop. It provides the conceptual and methodological basis for the definition of metropolitan areas in Canada and provides a detailed comparison of Canada's methodology to that of the USA. The intent was to encourage discussion regarding Canada's approach to defining metropolitan areas in the effort to identify the 'guiding principles'. It is being made available as a working paper to continue this discussion and to provide background to the user community to encourage dialogue and commentary from the user community regarding Canada's metropolitan area methodology.

    Release date: 2008-02-20

  • Articles and reports: 92F0138M2007001
    Description:

    Statistics Canada creates files that provide the link between postal codes and the geographic areas by which it disseminates statistical data. By linking postal codes to the Statistics Canada geographic areas, Statistics Canada facilitates the extraction and subsequent aggregation of data for selected geographic areas from files available to users. Users can then take data from Statistics Canada for their areas and tabulate this with other data for these same areas to create a combined statistical profile for these areas.

    An issue has been the methodology used by Statistics Canada to establish the linkage of postal codes to geographic areas. In order to address this issue, Statistics Canada decided to create a conceptual framework on which to base the rules for linking postal codes and Statistics Canada's geographic areas. This working paper presents the conceptual framework and the geocoding rules. The methodology described in this paper will be the basis for linking postal codes to the 2006 Census geographic areas. This paper is presented for feedback from users of Statistics Canada's postal codes related products.

    Release date: 2007-02-12

  • Articles and reports: 12-001-X20060019257
    Description:

    In the presence of item nonreponse, two approaches have been traditionally used to make inference on parameters of interest. The first approach assumes uniform response within imputation cells whereas the second approach assumes ignorable response but make use of a model on the variable of interest as the basis for inference. In this paper, we propose a third appoach that assumes a specified ignorable response mechanism without having to specify a model on the variable of interest. In this case, we show how to obtain imputed values which lead to estimators of a total that are approximately unbiased under the proposed approach as well as the second approach. Variance estimators of the imputed estimators that are approximately unbiased are also obtained using an approach of Fay (1991) in which the order of sampling and response is reversed. Finally, simulation studies are conducted to investigate the finite sample performance of the methods in terms of bias and mean square error.

    Release date: 2006-07-20

  • Articles and reports: 11F0024M20050008805
    Description:

    This paper reports on the potential development of sub-annual indicators for selected service industries using Goods and Services Tax (GST) data. The services sector is now of central importance to advanced economies; however, our knowledge of this sector remains incomplete, partly due to a lack of data. The Voorburg Group on Service Statistics has been meeting for almost twenty years to develop and incorporate better measures for the services sector. Despite this effort, many sub-annual economic measures continue to rely on output data for the goods-producing sector and, with the exception of distributive trades, on employment data for service industries.

    The development of sub-annual indicators for service industries raises two questions regarding the national statistical program. First, is there a need for service output indicators to supplement existing sub-annual measures? And second, what service industries are the most promising for development? The paper begins by reviewing the importance of service industries and how they behave during economic downturns. Next, it examines considerations in determining which service industries to select as GST-based, sub-annual indicators. A case study of the accommodation services industry serves to illustrate improving timeliness and accuracy. We conclude by discussing the opportunities for, and limitations of, these indicators.

    Release date: 2005-10-20

  • Articles and reports: 12-002-X20050018030
    Description:

    People often wish to use survey micro-data to study whether the rate of occurrence of a particular condition in a subpopulation is the same as the rate of occurrence in the full population. This paper describes some alternatives for making inferences about such a rate difference and shows whether and how these alternatives may be implemented in three different survey software packages. The software packages illustrated - SUDAAN, WesVar and Bootvar - all can make use of bootstrap weights provided by the analyst to carry out variance estimation.

    Release date: 2005-06-23

  • Articles and reports: 12-001-X20040027753
    Description:

    Samplers often distrust model-based approaches to survey inference because of concerns about misspecification when models are applied to large samples from complex populations. We suggest that the model-based paradigm can work very successfully in survey settings, provided models are chosen that take into account the sample design and avoid strong parametric assumptions. The Horvitz-Thompson (HT) estimator is a simple design-unbiased estimator of the finite population total. From a modeling perspective, the HT estimator performs well when the ratios of the outcome values and the inclusion probabilities are exchangeable. When this assumption is not met, the HT estimator can be very inefficient. In Zheng and Little (2003, 2004) we used penalized splines (p-splines) to model smoothly - varying relationships between the outcome and the inclusion probabilities in one-stage probability proportional to size (PPS) samples. We showed that p spline model-based estimators are in general more efficient than the HT estimator, and can provide narrower confidence intervals with close to nominal confidence coverage. In this article, we extend this approach to two-stage sampling designs. We use a p-spline based mixed model that fits a nonparametric relationship between the primary sampling unit (PSU) means and a measure of PSU size, and incorporates random effects to model clustering. For variance estimation we consider the empirical Bayes model-based variance, the jackknife and balanced repeated replication (BRR) methods. Simulation studies on simulated data and samples drawn from public use microdata in the 1990 census demonstrate gains for the model-based p-spline estimator over the HT estimator and linear model-assisted estimators. Simulations also show the variance estimation methods yield confidence intervals with satisfactory confidence coverage. Interestingly, these gains can be seen for a common equal-probability design, where the first stage selection is PPS and the second stage selection probabilities are proportional to the inverse of the first stage inclusion probabilities, and the HT estimator leads to the unweighted mean. In situations that most favor the HT estimator, the model-based estimators have comparable efficiency.

    Release date: 2005-02-03
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Analysis (69)

Analysis (69) (60 to 70 of 69 results)

  • Articles and reports: 12-001-X199200214487
    Description:

    This paper reviews the idea of robustness for randomisation and model-based inference for descriptive and analytic surveys. The lack of robustness for model-based procedures can be partially overcome by careful design. In this paper a robust model-based approach to analysis is proposed based on smoothing methods.

    Release date: 1992-12-15

  • Articles and reports: 12-001-X199200214488
    Description:

    In many finite population sampling problems the design that is optimal in the sense of minimizing the variance of the best linear unbiased estimator under a particular working model is bad in the sense of robustness - it leaves the estimator extremely vulnerable to bias if the working model is incorrect. However there are some important models under which one design provides both efficiency and robustness. We present a theorem that identifies such models and their optimal designs.

    Release date: 1992-12-15

  • Articles and reports: 12-001-X199100214504
    Description:

    Simple or marginal quota surveys are analyzed using two methods: (1) behaviour modelling (superpopulation model) and prediction estimation, and (2) sample modelling (simple restricted random sampling) and estimation derived from the sample distribution. In both cases the limitations of the theory used to establish the variance formulas and estimates when measuring totals are described. An extension of the quota method (non-proportional quotas) is also briefly described and analyzed. In some cases, this may provide a very significant improvement in survey precision. The advantages of the quota method are compared with those of random sampling. The latter remains indispensable in the case of large scale surveys within the framework of Official Statistics.

    Release date: 1991-12-16

  • Articles and reports: 12-001-X199100114521
    Description:

    Marginal and approximate conditional likelihoods are given for the correlation parameters in a normal linear regression model with correlated errors. This general likelihood approach is applied to obtain marginal and approximate conditional likelihoods for the correlation parameters in sampling on successive occasions under both simple random sampling on each occasion and more complex surveys.

    Release date: 1991-06-14

  • Articles and reports: 12-001-X199000114560
    Description:

    Early developments in sampling theory and methods largely concentrated on efficient sampling designs and associated estimation techniques for population totals or means. More recently, the theoretical foundations of survey based estimation have also been critically examined, and formal frameworks for inference on totals or means have emerged. During the past 10 years or so, rapid progress has also been made in the development of methods for the analysis of survey data that take account of the complexity of the sampling design. The scope of this paper is restricted to an overview and appraisal of some of these developments.

    Release date: 1990-06-15

  • Articles and reports: 12-001-X198900214568
    Description:

    The paper describes a Monte Carlo study of simultaneous confidence interval procedures for k > 2 proportions, under a model of two-stage cluster sampling. The procedures investigated include: (i) standard multinomial intervals; (ii) Scheffé intervals based on sample estimates of the variances of cell proportions; (iii) Quesenberry-Hurst intervals adapted for clustered data using Rao and Scott’s first and second order adjustments to X^2; (iv) simple Bonferroni intervals; (v) Bonferroni intervals based on transformations of the estimated proportions; (vi) Bonferroni intervals computed using the critical points of Student’s t. In several realistic situations, actual coverage rates of the multinomial procedures were found to be seriously depressed compared to the nominal rate. The best performing intervals, from the point of view of coverage rates and coverage symmetry (an extension of an idea due to Jennings), were the t-based Bonferroni intervals derived using log and logit transformations. Of the Scheffé-like procedures, the best performance was provided by Quesenberry-Hurst intervals in combination with first-order Rao-Scott adjustments.

    Release date: 1989-12-15

  • Articles and reports: 12-001-X198500114364
    Description:

    Conventional methods of inference in survey sampling are critically examined. The need for conditioning the inference on recognizable subsets of the population is emphasized. A number of real examples involving random sample sizes are presented to illustrate inferences conditional on the realized sample configuration and associated difficulties. The examples include the following: estimation of (a) population mean under simple random sampling; (b) population mean in the presence of outliers; (c) domain total and domain mean; (d) population mean with two-way stratification; (e) population mean in the presence of non-responses; (f) population mean under general designs. The conditional bias and the conditional variance of estimators of a population mean (or a domain mean or total), and the associated confidence intervals, are examined.

    Release date: 1985-06-14

  • Articles and reports: 12-001-X198400114351
    Description:

    Most sample surveys conducted by organizations such as Statistics Canada or the U.S. Bureau of the Census employ complex designs. The design-based approach to statistical inference, typically the institutional standard of inference for simple population statistics such as means and totals, may be extended to parameters of analytic models as well. Most of this paper focuses on application of design-based inferences to such models, but rationales are offered for use of model-based alternatives in some instances, by way of explanation for the author’s observation that both modes of inference are used in practice at his own institution.

    Within the design-based approach to inference, the paper briefly describes experience with linear regression analysis. Recently, variance computations for a number of surveys of the Census Bureau have been implemented through “replicate weighting”; the principal application has been for variances of simple statistics, but this technique also facilitates variance computation for virtually any complex analytic model. Finally, approaches and experience with log-linear models are reported.

    Release date: 1984-06-15

  • Articles and reports: 12-001-X198100214319
    Description:

    The problems associated with making analytical inferences from data based on complex sample designs are reviewed. A basic issue is the definition of the parameter of interest and whether it is a superpopulation model parameter or a finite population parameter. General methods based on a generalized Wald Statistics and its modification or on modifications of classical test statistics are discussed. More detail is given on specific methods-on linear models and regression and on categorical data analysis.

    Release date: 1981-12-15
Reference (3)

Reference (3) ((3 results))

  • Surveys and statistical programs – Documentation: 12-001-X19970013101
    Description:

    In the main body of statistics, sampling is often disposed of by assuming a sampling process that selects random variables such that they are independent and identically distributed (IID). Important techniques, like regression and contingency table analysis, were developed largely in the IID world; hence, adjustments are needed to use them in complex survey settings. Rather than adjust the analysis, however, what is new in the present formulation is to draw a second sample from the original sample. In this second sample, the first set of selections are inverted, so as to yield at the end a simple random sample. Of course, to employ this two-step process to draw a single simple random sample from the usually much larger complex survey would be inefficient, so multiple simple random samples are drawn and a way to base inferences on them developed. Not all original samples can be inverted; but many practical special cases are discussed which cover a wide range of practices.

    Release date: 1997-08-18

  • Surveys and statistical programs – Documentation: 12-001-X19970013102
    Description:

    The selection of auxiliary variables is considered for regression estimation in finite populations under a simple random sampling design. This problem is a basic one for model-based and model-assisted survey sampling approaches and is of practical importance when the number of variables available is large. An approach is developed in which a mean squared error estimator is minimised. This approach is compared to alternative approaches using a fixed set of auxiliary variables, a conventional significance test criterion, a condition number reduction approach and a ridge regression approach. The proposed approach is found to perform well in terms of efficiency. It is noted that the variable selection approach affects the properties of standard variance estimators and thus leads to a problem of variance estimation.

    Release date: 1997-08-18

  • Surveys and statistical programs – Documentation: 12-001-X19960022980
    Description:

    In this paper, we study a confidence interval estimation method for a finite population average when some auxiliairy information is available. As demonstrated by Royall and Cumberland in a series of empirical studies, naive use of existing methods to construct confidence intervals for population averages may result in very poor conditional coverage probabilities, conditional on the sample mean of the covariate. When this happens, we propose to transform the data to improve the precision of the normal approximation. The transformed data are then used to make inference on the original population average, and the auxiliary information is incorporated into the inference directly, or by calibration with empirical likelihood. Our approach is design-based. We apply our approach to six real populations and find that when transformation is needed, our approach performs well compared to the usual regression method.

    Release date: 1997-01-30
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