Skip to main content
SpringerLink
Log in

The simultaneous assessment of normality and homoscedasticity in linear fixed effects models

  • Published:
Journal of Statistical Theory and Practice Aims and scope Submit manuscript

Abstract

This article investigates the problem of simultaneously testing the normality and homoscedasticity assumptions in a linear fixed effects model when we have grouped data. This has been facilitated by the assumption of a smooth alternative to the normal distribution. The smooth alternative is specified using Legendre polynomials, and the score statistic is derived under two scenarios: a common smooth alternative across the different groups, or different smooth alternatives across the different groups. A data-driven approach available in the literature is used for determining the order of the polynomials. For the null distribution of the score statistic, the accuracy of the asymptotic chi-squared distribution is numerically investigated under a one-way fixed effects model with balanced and unbalanced data. The results are illustrated with an example.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Andrews, D. Ε., and Α. Μ. Herzberg. 1985. Data: A collection of problems from many fields for students and research workers. New York, NY: Springer-Verlag.

    Book  Google Scholar 

  • Bogdan, M. 1996. Data driven smooth tests for bivariate normality. Preprint IM PWr 42/96, Technical University of Wroclaw, Wroclaw, Poland.

  • Bogdan, M. 1999. Data driven smooth tests for bivariate normality. Journal of Multivariate Analysis 68:26–53.

    Article  MathSciNet  Google Scholar 

  • Chang, C.-H., N. Pal, and J.-J. Lin. 2016. A revisit to test the equality of variances of several populations. Communications in Statistics—Simulation and Computation, to appear. https://doi.org/10.1080/03610918.2016.1202277

    Article  MathSciNet  Google Scholar 

  • Inglot, T., and T. Ledwina. 1996. Asymptotic optimality of data-driven Neymans tests for uniformity. Annals of Statistics 24:1982–2019.

    Article  MathSciNet  Google Scholar 

  • Inglot, T., W. Kallenberg, and T. Ledwina. 1997. Data driven smooth tests for composite hypotheses. Annals of Statistics 25:1222–1250.

    Article  MathSciNet  Google Scholar 

  • Janic, Α., and T. Ledwina. 2009. Data-driven smooth tests for a location-scale family revisited. Journal of Statistical Theory and Practice 3:645–664.

    Article  MathSciNet  Google Scholar 

  • Kallenberg, W., and T. Ledwina. 1995. Consistency and Monte Carlo simulation of a data driven version of smooth goodness-of-fit tests. Annals of Statistics 23:1594–1608.

    Article  MathSciNet  Google Scholar 

  • Kallenberg, W., and T. Ledwina. 1997a. Data-driven smooth tests for composite hypotheses: Comparison of powers. Journal of Statistical Computation and Simulation 59:101–121.

    Article  MathSciNet  Google Scholar 

  • Kallenberg, W., and T. Ledwina. 1997b. Data-driven smooth tests when the hypothesis is composite. Journal of the American Statistical Association 92:1094–1104.

    Article  MathSciNet  Google Scholar 

  • Kallenberg, W., T. Ledwina, and E. Rafajlowicz. 1997. Testing bivariate independence and normality. Sankhyã, Series A 59:42–59.

    MathSciNet  MATH  Google Scholar 

  • Ledwina, T. 1994. Data-driven version of Neymans smooth test of fit. Journal of the American Statistical Association 89:1000–1005.

    Article  MathSciNet  Google Scholar 

  • Mardia, K. V., and J. T. Kent. 1991. Rao score tests for goodness of fit and independence. Biometrika 78:355–363.

    Article  MathSciNet  Google Scholar 

  • Montgomery, D. C. 2012. Design and analysis of experiments, 8th Ed. New York, NY: John Wiley.

    Google Scholar 

  • Neyman, J. 1937. Smooth test for goodness of fit. Skandinaviska Aktuarietidskrift 20:149–199.

    MATH  Google Scholar 

  • Peña, Ε. Α., and Ε. Η. Slate. 2006. Global validation of linear model assumptions. Journal of the American Statistical Association 101:341–354.

    Article  MathSciNet  Google Scholar 

  • Rayner, J. C. W., O. Thas, and D. J. Best. 2009. Smooth tests of goodness of fit: Using R. New York, NY: John Wiley.

    Book  Google Scholar 

  • Reaven, G. M., and R G. Miller. 1979. An attempt to define the nature of chemical diabetes using a multidimensional analysis. Diabetologia 16:17–24.

    Article  Google Scholar 

  • Yang, Y. 2016. The simultaneous assessment of normality and homoscedasticity in some linear models. Doctoral dissertation submitted to the University of Maryland Baltimore County, Baltimore, MD.

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Maryland Baltimore County, 1000 Hilltop Circle, 21250, Baltimore, Maryland, USA

    Ye Yang & Thomas Mathew

Authors
  1. Ye Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Thomas Mathew
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Thomas Mathew.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, Y., Mathew, T. The simultaneous assessment of normality and homoscedasticity in linear fixed effects models. J Stat Theory Pract 12, 66–81 (2018). https://doi.org/10.1080/15598608.2017.1320243

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1080/15598608.2017.1320243

Keywords

AMS Subject Classification

Search

Navigation