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A diagnostic tool for regression analysis of complex survey data

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Abstract

Although a nonparametric regression model allows us to obtain a graphical display of the relationship between the response variable and the independent variables, the exact form of the regression function is not evident. This weakness can be overcome by a parametric model since the relationship between the dependent and the independent variables is specified mathematically. The object of this paper is to introduce a new graphical approach, called the shift function plot, with which a hypothesis test is constructed to evaluate the goodness-of-fit of a parametric regression model. Under multi-stage stratified sampling schemes, we apply the shift function plots to survey data. Asymptotic properties of the survey estimator of the shift function are established. An empirical example from the 1990 Ontario Health Survey is used to illustrate the application of the shift function.

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References

  • Bellhouse DR, Stafford JE (1999) Density estimation from complex surveys. Stat Sin 9:407–424

    MATH  MathSciNet  Google Scholar 

  • Bellhouse DR, Stafford JE (2001) Local polynomial regression in complex surveys. Surv Methodol 27:197–203

    Google Scholar 

  • Binder DA (1983) On the variance of asymptotically normal estimators from complex surveys. Int Stat Rev 51:279–292

    Article  MATH  MathSciNet  Google Scholar 

  • Doksum KA, Sievers GL (1976) Plotting with confidence: graphical comparisons of two populations. Biometrika 63:421–434

    Article  MATH  MathSciNet  Google Scholar 

  • Fuller WA (1975) Regression analysis for sample surveys. Sankhyā, Series C 37:117–132

  • Hàjek J (1960) Limiting distributions in simple random sampling from a finite population. Magyar Tudoanyos Akademia Budapest Matematikai Kutato Intezet Koelemenyei 5:361–374

  • Hart JD (1997) Nonparametric smoothing and lack-of-fit tests, Chapter 6. Springer, New York

  • Madow WG (1948) On the limiting distributions of estimates based on samples from finite universes. Ann Math Stat 19(4):535–545

    Article  MATH  MathSciNet  Google Scholar 

  • Shao J (1996) Resampling methods in sample survey. Statistics 27:203–254

    Article  MATH  MathSciNet  Google Scholar 

  • Wang Z (2004) Some nonparametric regression techniques for complex survey data. PhD. Thesis, University of Western Ontario. London, ON, pp 97–109

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Authors and Affiliations

  1. Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, Canada

    Zilin Wang

  2. Department of Statistical and Actuarial Sciences, University of Western Ontario, London, ON, Canada

    David Bellhouse

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  1. Zilin Wang
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  2. David Bellhouse
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Correspondence to Zilin Wang.

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Wang, Z., Bellhouse, D. A diagnostic tool for regression analysis of complex survey data. Stat Papers 56, 1041–1053 (2015). https://doi.org/10.1007/s00362-014-0623-5

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  • DOI: https://doi.org/10.1007/s00362-014-0623-5

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