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Estimation of the Correlation Coefficient Based on Selected Data

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  • Gösta Hägglund
  • Rolf Larsson

Abstract

In psychometrics, it is often the case that one encounters data that may not be considered random but selected in a systematic way according to some explanatory variable. In this article, maximum likelihood estimation is considered when data are supposed to arise from a bivariate normal distribution that is truncated in an extreme way. Two methods are presented and compared, one of them being purely numerical, while the other is based on an approximation. Both methods are tried on both simulated and on real data. The purely numerical method is shown to be the most reliable over all, but in some cases, the computationally less burdensome approximate method turns out to work almost as well.

Suggested Citation

  • Gösta Hägglund & Rolf Larsson, 2006. "Estimation of the Correlation Coefficient Based on Selected Data," Journal of Educational and Behavioral Statistics, , vol. 31(4), pages 377-411, December.
    • Handle: RePEc:sae:jedbes:v:31:y:2006:i:4:p:377-411
    DOI: 10.3102/10769986031004377
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