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  • Articles and reports: 11-522-X20020016745

    The attractiveness of the Regression Discontinuity Design (RDD) rests on its close similarity to a normal experimental design. On the other hand, it is of limited applicability since it is not often the case that units are assigned to the treatment group on the basis of an observable (to the analyst) pre-program measure. Besides, it only allows identification of the mean impact on a very specific subpopulation. In this technical paper, we show that the RDD straightforwardly generalizes to the instances in which the units' eligibility is established on an observable pre-program measure with eligible units allowed to freely self-select into the program. This set-up also proves to be very convenient for building a specification test on conventional non-experimental estimators of the program mean impact. The data requirements are clearly described.

    Release date: 2004-09-13

  • Articles and reports: 11-522-X20020016750

    Analyses of data from social and economic surveys sometimes use generalized variance function models to approximate the design variance of point estimators of population means and proportions. Analysts may use the resulting standard error estimates to compute associated confidence intervals or test statistics for the means and proportions of interest. In comparison with design-based variance estimators computed directly from survey microdata, generalized variance function models have several potential advantages, as will be discussed in this paper, including operational simplicity; increased stability of standard errors; and, for cases involving public-use datasets, reduction of disclosure limitation problems arising from the public release of stratum and cluster indicators.

    These potential advantages, however, may be offset in part by several inferential issues. First, the properties of inferential statistics based on generalized variance functions (e.g., confidence interval coverage rates and widths) depend heavily on the relative empirical magnitudes of the components of variability associated, respectively, with:

    (a) the random selection of a subset of items used in estimation of the generalized variance function model(b) the selection of sample units under a complex sample design (c) the lack of fit of the generalized variance function model (d) the generation of a finite population under a superpopulation model.

    Second, under conditions, one may link each of components (a) through (d) with different empirical measures of the predictive adequacy of a generalized variance function model. Consequently, these measures of predictive adequacy can offer us some insight into the extent to which a given generalized variance function model may be appropriate for inferential use in specific applications.

    Some of the proposed diagnostics are applied to data from the US Survey of Doctoral Recipients and the US Current Employment Survey. For the Survey of Doctoral Recipients, components (a), (c) and (d) are of principal concern. For the Current Employment Survey, components (b), (c) and (d) receive principal attention, and the availability of population microdata allow the development of especially detailed models for components (b) and (c).

    Release date: 2004-09-13

  • Articles and reports: 12-001-X20030026785

    To avoid disclosures, one approach is to release partially synthetic, public use microdata sets. These comprise the units originally surveyed, but some collected values, for example sensitive values at high risk of disclosure or values of key identifiers, are replaced with multiple imputations. Although partially synthetic approaches are currently used to protect public use data, valid methods of inference have not been developed for them. This article presents such methods. They are based on the concepts of multiple imputation for missing data but use different rules for combining point and variance estimates. The combining rules also differ from those for fully synthetic data sets developed by Raghunathan, Reiter and Rubin (2003). The validity of these new rules is illustrated in simulation studies.

    Release date: 2004-01-27

  • Articles and reports: 12-001-X20030016610

    In the presence of item nonreponse, unweighted imputation methods are often used in practice but they generally lead to biased estimators under uniform response within imputation classes. Following Skinner and Rao (2002), we propose a bias-adjusted estimator of a population mean under unweighted ratio imputation and random hot-deck imputation and derive linearization variance estimators. A small simulation study is conducted to study the performance of the methods in terms of bias and mean square error. Relative bias and relative stability of the variance estimators are also studied.

    Release date: 2003-07-31

  • Articles and reports: 92F0138M2003002

    This working paper describes the preliminary 2006 census metropolitan areas and census agglomerations and is presented for user feedback. The paper briefly describes the factors that have resulted in changes to some of the census metropolitan areas and census agglomerations and includes tables and maps that list and illustrate these changes to their limits and to the component census subdivisions.

    Release date: 2003-07-11

  • Articles and reports: 92F0138M2003001

    The goal of this working paper is to assess how well Canada's current method of delineating Census Metropolitan Areas (CMAs) and Census Agglomerations (CAs) reflects the metropolitan nature of these geographic areas according to the facilities and services they provide. The effectiveness of Canada's delineation methodology can be evaluated by applying a functional model to Statistics Canada's CMAs and CAs.

    As a consequence of the research undertaken for this working paper, Statistics Canada has proposed lowering the urban core population threshold it uses to define CMAs: a CA will be promoted to a CMA if it has a total population of at least 100,000, of which 50,000 or more live in the urban core. User consultation on this proposal took place in the fall of 2002 as part of the 2006 Census content determination process.

    Release date: 2003-03-31

  • Articles and reports: 11F0019M2003199
    Geography: Canada

    Using a nationally representative sample of establishments, we have examined whether selected alternative work practices (AWPs) tend to reduce quit rates. Overall, our analysis provides strong evidence of a negative association between these AWPs and quit rates among establishments of more than 10 employees operating in high-skill services. We also found some evidence of a negative association in low-skill services. However, the magnitude of this negative association was reduced substantially when we added an indicator of whether the workplace has a formal policy of information sharing. There was very little evidence of a negative association in manufacturing. While establishments with self-directed workgroups have lower quit rates than others, none of the bundles of work practices considered yielded a negative and statistically significant effect. We surmise that key AWPs might be more successful in reducing labour turnover in technologically complex environments than in low-skill ones.

    Release date: 2003-03-17

  • Articles and reports: 12-001-X20020026428

    The analysis of survey data from different geographical areas where the data from each area are polychotomous can be easily performed using hierarchical Bayesian models, even if there are small cell counts in some of these areas. However, there are difficulties when the survey data have missing information in the form of non-response, especially when the characteristics of the respondents differ from the non-respondents. We use the selection approach for estimation when there are non-respondents because it permits inference for all the parameters. Specifically, we describe a hierarchical Bayesian model to analyse multinomial non-ignorable non-response data from different geographical areas; some of them can be small. For the model, we use a Dirichlet prior density for the multinomial probabilities and a beta prior density for the response probabilities. This permits a 'borrowing of strength' of the data from larger areas to improve the reliability in the estimates of the model parameters corresponding to the smaller areas. Because the joint posterior density of all the parameters is complex, inference is sampling-based and Markov chain Monte Carlo methods are used. We apply our method to provide an analysis of body mass index (BMI) data from the third National Health and Nutrition Examination Survey (NHANES III). For simplicity, the BMI is categorized into 3 natural levels, and this is done for each of 8 age-race-sex domains and 34 counties. We assess the performance of our model using the NHANES III data and simulated examples, which show our model works reasonably well.

    Release date: 2003-01-29

  • Articles and reports: 11-522-X20010016277

    This paper discusses in detail issues dealing with the technical aspects of designing and conducting surveys. It is intended for an audience of survey methodologists.

    The advent of computerized record-linkage methodology has facilitated the conduct of cohort mortality studies in which exposure data in one database are electronically linked with mortality data from another database. In this article, the impact of linkage errors on estimates of epidemiological indicators of risk, such as standardized mortality ratios and relative risk regression model parameters, is explored. It is shown that these indicators can be subject to bias and additional variability in the presence of linkage errors, with false links and non-links leading to positive and negative bias, respectively, in estimates of the standardized mortality ratio. Although linkage errors always increase the uncertainty in the estimates, bias can be effectively eliminated in the special case in which the false positive rate equals the false negative rate within homogeneous states defined by cross-classification of the covariates of interest.

    Release date: 2002-09-12

  • Articles and reports: 89-552-M2000007
    Geography: Canada

    This paper addresses the problem of statistical inference with ordinal variates and examines the robustness to alternative literacy measurement and scaling choices of rankings of average literacy and of estimates of the impact of literacy on individual earnings.

    Release date: 2000-06-02
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  • Articles and reports: 12-001-X199200214487

    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

    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

    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

    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

    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

    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

    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

    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

    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

    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

    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

    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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