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- Articles and reports: 11F0019M2004234Geography: CanadaDescription:
This article analyses the relationship between the quality of education that immigrants received in their home country, as measured by international test scores, and their success in the Canadian labour market.
Release date: 2004-12-15 - Articles and reports: 11-522-X20020016430Description:
Linearization (or Taylor series) methods are widely used to estimate standard errors for the co-efficients of linear regression models fit to multi-stage samples. When the number of primary sampling units (PSUs) is large, linearization can produce accurate standard errors under quite general conditions. However, when the number of PSUs is small or a co-efficient depends primarily on data from a small number of PSUs, linearization estimators can have large negative bias.
In this paper, we characterize features of the design matrix that produce large bias in linearization standard errors for linear regression co-efficients. We then propose a new method, bias reduced linearization (BRL), based on residuals adjusted to better approximate the covariance of the true errors. When the errors are independent and identically distributed (i.i.d.), the BRL estimator is unbiased for the variance. Furthermore, a simulation study shows that BRL can greatly reduce the bias, even if the errors are not i.i.d. We also propose using a Satterthwaite approximation to determine the degrees of freedom of the reference distribution for tests and confidence intervals about linear combinations of co-efficients based on the BRL estimator. We demonstrate that the jackknife estimator also tends to be biased in situations where linearization is biased. However, the jackknife's bias tends to be positive. Our bias-reduced linearization estimator can be viewed as a compromise between the traditional linearization and jackknife estimators.
Release date: 2004-09-13 - Articles and reports: 11-522-X20020016717Description:
In the United States, the National Health and Nutrition Examination Survey (NHANES) is linked to the National Health Interview Survey (NHIS) at the primary sampling unit level (the same counties, but not necessarily the same persons, are in both surveys). The NHANES examines about 5,000 persons per year, while the NHIS samples about 100,000 persons per year. In this paper, we present and develop properties of models that allow NHIS and administrative data to be used as auxiliary information for estimating quantities of interest in the NHANES. The methodology, related to Fay-Herriot (1979) small-area models and to calibration estimators in Deville and Sarndal (1992), accounts for the survey designs in the error structure.
Release date: 2004-09-13 - Articles and reports: 11-522-X20020016723Description:
Categorical outcomes, such as binary, ordinal and nominal responses, occur often in survey research. Logistic regression investigates the relationship between such categorical responses variables and a set of explanatory variables. The LOGISTIC procedure can be used to perform a logistic analysis on data from a random sample. However, this approach is not valid if the data come from other sample designs, such as complex survey designs with stratification, clustering and/or unequal weighting. In these cases, specialized techniques must be applied in order to produce the appropriate estimates and standard errors.
The SURVEYLOGISTIC procedure, experimental in Version 9, brings logistic regression for survey data to the SAS System and delivers much of the functionality of the LOGISTIC procedure. This paper describes the methodological approach and applications for this new software.
Release date: 2004-09-13 - Articles and reports: 11-522-X20020016725Description:
In 1997, the US Office of Management and Budget issued revised standards for the collection of race information within the federal statistical system. One revision allows individuals to choose more than one race group when responding to federal surveys and other federal data collections. This change presents challenges for analyses that involve data collected under both the old and new race-reporting systems, since the data on race are not comparable. The following paper discusses the problems encountered by these changes and methods developed to overcome them.
Since most people under both systems report only a single race, a common proposed solution is to try to bridge the transition by assigning a single-race category to each multiple-race reporter under the new system, and to conduct analyses using just the observed and assigned single-race categories. Thus, the problem can be viewed as a missing-data problem, in which single-race responses are missing for multiple-race reporters and needing to be imputed.
The US Office of Management and Budget suggested several simple bridging methods to handle this missing-data problem. Schenker and Parker (Statistics in Medicine, forthcoming) analysed data from the National Health Interview Survey of the US National Center for Health Statistics, which allows multiple-race reporting but also asks multiple-race reporters to specify a primary race, and found that improved bridging methods could result from incorporating individual-level and contextual covariates into the bridging models.
While Schenker and Parker discussed only three large multiple-race groups, the current application requires predicting single-race categories for several small multiple-race groups as well. Thus, problems of sparse data arise in fitting the bridging models. We address these problems by building combined models for several multiple-race groups, thus borrowing strength across them. These and other methodological issues are discussed.
Release date: 2004-09-13 - Articles and reports: 11-522-X20020016729Description:
For most survey samples, if not all, we have to deal with the problem of missing values. Missing values are usually caused by nonresponse (such as refusal of participant or interviewer was unable to contact respondent) but can also be produced at the editing step of the survey in an attempt to resolve problems of inconsistent or suspect responses. The presence of missing values (nonresponse) generally leads to bias and uncertainty in the estimates. To treat this problem, the appropriate use of all available auxiliary information permits the maximum reduction of nonresponse bias and variance. During this presentation, we will define the problem, describe the methodology that SEVANI is based on and discuss potential uses of the system. We will end the discussion by presenting some examples based on real data to illustrate the theory in practice.
In practice, it is very difficult to estimate the nonresponse bias. However, it is possible to estimate the nonresponse variance by assuming that the bias is negligible. In the last decade, many methods were indeed proposed to estimate this variance, and some of these have been implemented in the System for Estimation of Variance due to Nonresponse and Imputation (SEVANI).
The methodology used to develop SEVANI is based on the theory of two-phase sampling where we assume that the second phase of selection is nonresponse. However, contrary to two-phase sampling, an imputation or nonresponse model is required for variance estimation. SEVANI also assumes that nonresponse is treated by reweighting respondent units or by imputing their missing values. Three imputation methods are considered: the imputation of an auxiliary variable, regression imputation (deterministic or random) and nearest-neighbour imputation.
Release date: 2004-09-13 - Articles and reports: 11-522-X20020016731Description:
Behavioural researchers use a variety of techniques to predict respondent scores on constructs that are not directly observable. Examples of such constructs include job satisfaction, work stress, aptitude for graduate study, children's mathematical ability, etc. The techniques commonly used for modelling and predicting scores on such constructs include factor analysis, classical psychometric scaling and item response theory (IRT), and for each technique there are often several different strategies that can be used to generate individual scores. However, researchers are seldom satisfied with simply measuring these constructs. They typically use the derived scores in multiple regression, analysis of variance and numerous multivariate procedures. Though using predicted scores in this way can result in biased estimates of model parameters, not all researchers are aware of this difficulty. The paper will review the literature on this issue, with particular emphasis on IRT methods. Problems will be illustrated, some remedies suggested, and areas for further research will be identified.
Release date: 2004-09-13 - Articles and reports: 11-522-X20020016735Description:
In the 2001 Canadian Census of Population, calibration or regression estimation was used to calculate a single set of household level weights to be used for all census estimates based on a one in five national sample of more than two million households. Because many auxiliary variables were available, only a subset of them could be used. Otherwise, some of the weights would have been smaller than the number one or even negative. In this technical paper, a forward selection procedure was used to discard auxiliary variables that caused weights to be smaller than one or that caused a large condition number for the calibration weight matrix being inverted. Also, two calibration adjustments were done to achieve close agreement between auxiliary population counts and estimates for small areas. Prior to 2001, the projection generalized regression (GREG) estimator was used and the weights were required to be greater than zero. For the 2001 Census, a switch was made to a pseudo-optimal regression estimator that kept more auxiliary variables and, at the same time, required that the weights be one or more.
Release date: 2004-09-13 - Articles and reports: 11-522-X20020016745Description:
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-X20020016749Description:
Survey sampling is a statistical domain that has been slow to take advantage of flexible regression methods. In this technical paper, two approaches are discussed that could be used to make these regression methods accessible: adapt the techniques to the complex survey design that has been used or sample the survey data so that the standard techniques are applicable.
In following the former route, we introduce techniques that account for the complex survey structure of the data for scatterplot smoothing and additive models. The use of penalized least squares in the sampling context is studied as a tool for the analysis of a general trend in a finite population. We focus on smooth regression with a normal error model. Ties in covariates abound for large scale surveys resulting in the application of scatterplot smoothers to means. The estimation of smooths (for example, smoothing splines) depends on the sampling design only via the sampling weights, meaning that standard software can be used for estimation. Inference for these curves is more challenging, as a result of correlations induced by the sampling design. We propose and illustrate tests that account for the sampling design. Illustrative examples are given using the Ontario health survey, including scatterplot smoothing, additive models and model diagnostics. In an attempt to resolve the problem by appropriate sampling of the survey data file, we discuss some of the hurdles that are faced when using this approach.
Release date: 2004-09-13
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Analysis (15)
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- Articles and reports: 11F0019M2004234Geography: CanadaDescription:
This article analyses the relationship between the quality of education that immigrants received in their home country, as measured by international test scores, and their success in the Canadian labour market.
Release date: 2004-12-15 - Articles and reports: 11-522-X20020016430Description:
Linearization (or Taylor series) methods are widely used to estimate standard errors for the co-efficients of linear regression models fit to multi-stage samples. When the number of primary sampling units (PSUs) is large, linearization can produce accurate standard errors under quite general conditions. However, when the number of PSUs is small or a co-efficient depends primarily on data from a small number of PSUs, linearization estimators can have large negative bias.
In this paper, we characterize features of the design matrix that produce large bias in linearization standard errors for linear regression co-efficients. We then propose a new method, bias reduced linearization (BRL), based on residuals adjusted to better approximate the covariance of the true errors. When the errors are independent and identically distributed (i.i.d.), the BRL estimator is unbiased for the variance. Furthermore, a simulation study shows that BRL can greatly reduce the bias, even if the errors are not i.i.d. We also propose using a Satterthwaite approximation to determine the degrees of freedom of the reference distribution for tests and confidence intervals about linear combinations of co-efficients based on the BRL estimator. We demonstrate that the jackknife estimator also tends to be biased in situations where linearization is biased. However, the jackknife's bias tends to be positive. Our bias-reduced linearization estimator can be viewed as a compromise between the traditional linearization and jackknife estimators.
Release date: 2004-09-13 - Articles and reports: 11-522-X20020016717Description:
In the United States, the National Health and Nutrition Examination Survey (NHANES) is linked to the National Health Interview Survey (NHIS) at the primary sampling unit level (the same counties, but not necessarily the same persons, are in both surveys). The NHANES examines about 5,000 persons per year, while the NHIS samples about 100,000 persons per year. In this paper, we present and develop properties of models that allow NHIS and administrative data to be used as auxiliary information for estimating quantities of interest in the NHANES. The methodology, related to Fay-Herriot (1979) small-area models and to calibration estimators in Deville and Sarndal (1992), accounts for the survey designs in the error structure.
Release date: 2004-09-13 - Articles and reports: 11-522-X20020016723Description:
Categorical outcomes, such as binary, ordinal and nominal responses, occur often in survey research. Logistic regression investigates the relationship between such categorical responses variables and a set of explanatory variables. The LOGISTIC procedure can be used to perform a logistic analysis on data from a random sample. However, this approach is not valid if the data come from other sample designs, such as complex survey designs with stratification, clustering and/or unequal weighting. In these cases, specialized techniques must be applied in order to produce the appropriate estimates and standard errors.
The SURVEYLOGISTIC procedure, experimental in Version 9, brings logistic regression for survey data to the SAS System and delivers much of the functionality of the LOGISTIC procedure. This paper describes the methodological approach and applications for this new software.
Release date: 2004-09-13 - Articles and reports: 11-522-X20020016725Description:
In 1997, the US Office of Management and Budget issued revised standards for the collection of race information within the federal statistical system. One revision allows individuals to choose more than one race group when responding to federal surveys and other federal data collections. This change presents challenges for analyses that involve data collected under both the old and new race-reporting systems, since the data on race are not comparable. The following paper discusses the problems encountered by these changes and methods developed to overcome them.
Since most people under both systems report only a single race, a common proposed solution is to try to bridge the transition by assigning a single-race category to each multiple-race reporter under the new system, and to conduct analyses using just the observed and assigned single-race categories. Thus, the problem can be viewed as a missing-data problem, in which single-race responses are missing for multiple-race reporters and needing to be imputed.
The US Office of Management and Budget suggested several simple bridging methods to handle this missing-data problem. Schenker and Parker (Statistics in Medicine, forthcoming) analysed data from the National Health Interview Survey of the US National Center for Health Statistics, which allows multiple-race reporting but also asks multiple-race reporters to specify a primary race, and found that improved bridging methods could result from incorporating individual-level and contextual covariates into the bridging models.
While Schenker and Parker discussed only three large multiple-race groups, the current application requires predicting single-race categories for several small multiple-race groups as well. Thus, problems of sparse data arise in fitting the bridging models. We address these problems by building combined models for several multiple-race groups, thus borrowing strength across them. These and other methodological issues are discussed.
Release date: 2004-09-13 - Articles and reports: 11-522-X20020016729Description:
For most survey samples, if not all, we have to deal with the problem of missing values. Missing values are usually caused by nonresponse (such as refusal of participant or interviewer was unable to contact respondent) but can also be produced at the editing step of the survey in an attempt to resolve problems of inconsistent or suspect responses. The presence of missing values (nonresponse) generally leads to bias and uncertainty in the estimates. To treat this problem, the appropriate use of all available auxiliary information permits the maximum reduction of nonresponse bias and variance. During this presentation, we will define the problem, describe the methodology that SEVANI is based on and discuss potential uses of the system. We will end the discussion by presenting some examples based on real data to illustrate the theory in practice.
In practice, it is very difficult to estimate the nonresponse bias. However, it is possible to estimate the nonresponse variance by assuming that the bias is negligible. In the last decade, many methods were indeed proposed to estimate this variance, and some of these have been implemented in the System for Estimation of Variance due to Nonresponse and Imputation (SEVANI).
The methodology used to develop SEVANI is based on the theory of two-phase sampling where we assume that the second phase of selection is nonresponse. However, contrary to two-phase sampling, an imputation or nonresponse model is required for variance estimation. SEVANI also assumes that nonresponse is treated by reweighting respondent units or by imputing their missing values. Three imputation methods are considered: the imputation of an auxiliary variable, regression imputation (deterministic or random) and nearest-neighbour imputation.
Release date: 2004-09-13 - Articles and reports: 11-522-X20020016731Description:
Behavioural researchers use a variety of techniques to predict respondent scores on constructs that are not directly observable. Examples of such constructs include job satisfaction, work stress, aptitude for graduate study, children's mathematical ability, etc. The techniques commonly used for modelling and predicting scores on such constructs include factor analysis, classical psychometric scaling and item response theory (IRT), and for each technique there are often several different strategies that can be used to generate individual scores. However, researchers are seldom satisfied with simply measuring these constructs. They typically use the derived scores in multiple regression, analysis of variance and numerous multivariate procedures. Though using predicted scores in this way can result in biased estimates of model parameters, not all researchers are aware of this difficulty. The paper will review the literature on this issue, with particular emphasis on IRT methods. Problems will be illustrated, some remedies suggested, and areas for further research will be identified.
Release date: 2004-09-13 - Articles and reports: 11-522-X20020016735Description:
In the 2001 Canadian Census of Population, calibration or regression estimation was used to calculate a single set of household level weights to be used for all census estimates based on a one in five national sample of more than two million households. Because many auxiliary variables were available, only a subset of them could be used. Otherwise, some of the weights would have been smaller than the number one or even negative. In this technical paper, a forward selection procedure was used to discard auxiliary variables that caused weights to be smaller than one or that caused a large condition number for the calibration weight matrix being inverted. Also, two calibration adjustments were done to achieve close agreement between auxiliary population counts and estimates for small areas. Prior to 2001, the projection generalized regression (GREG) estimator was used and the weights were required to be greater than zero. For the 2001 Census, a switch was made to a pseudo-optimal regression estimator that kept more auxiliary variables and, at the same time, required that the weights be one or more.
Release date: 2004-09-13 - Articles and reports: 11-522-X20020016745Description:
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-X20020016749Description:
Survey sampling is a statistical domain that has been slow to take advantage of flexible regression methods. In this technical paper, two approaches are discussed that could be used to make these regression methods accessible: adapt the techniques to the complex survey design that has been used or sample the survey data so that the standard techniques are applicable.
In following the former route, we introduce techniques that account for the complex survey structure of the data for scatterplot smoothing and additive models. The use of penalized least squares in the sampling context is studied as a tool for the analysis of a general trend in a finite population. We focus on smooth regression with a normal error model. Ties in covariates abound for large scale surveys resulting in the application of scatterplot smoothers to means. The estimation of smooths (for example, smoothing splines) depends on the sampling design only via the sampling weights, meaning that standard software can be used for estimation. Inference for these curves is more challenging, as a result of correlations induced by the sampling design. We propose and illustrate tests that account for the sampling design. Illustrative examples are given using the Ontario health survey, including scatterplot smoothing, additive models and model diagnostics. In an attempt to resolve the problem by appropriate sampling of the survey data file, we discuss some of the hurdles that are faced when using this approach.
Release date: 2004-09-13
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