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The asymptotic distribution of the sum of weighted squared residuals in binary choice models

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  • F.A.G. Windmeijer

Abstract

It is claimed by some authors that the distribution of the sum of weighted squared residuals, used as a goodness of fit measure in binary choice models, behaves for large n as a x2n– k–1 distribution. This claim seems to be based on a false analogy with the well–known Pearson x2 statistic for frequency tables with a fixed number of cells and cell sizes tending to infinity. We derive the asymptotic (normal) distribution and show that the approximation by the x2 distribution in general will not be valid. A new x2 test is proposed based on the asymptotic normality of the measure.

Suggested Citation

  • F.A.G. Windmeijer, 1990. "The asymptotic distribution of the sum of weighted squared residuals in binary choice models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 44(2), pages 69-78, June.
    • Handle: RePEc:bla:stanee:v:44:y:1990:i:2:p:69-78
    DOI: 10.1111/j.1467-9574.1990.tb01527.x
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    Cited by:

    1. F.A.G. Windmeijer, 1994. "A goodness-of-fit test in the multinomial legit model based on weighted squared residuals," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 48(3), pages 271-283, November.
    2. Khor, L.Y. & Zeller, M., 2018. "Storing a staple crop for own consumption: Linkages to food security," 2018 Conference, July 28-August 2, 2018, Vancouver, British Columbia 277244, International Association of Agricultural Economists.
    3. María Carmen Lea-Pereira & Laura Amaya-Pascasio & Patricia Martínez-Sánchez & María del Mar Rodríguez Salvador & José Galván-Espinosa & Luis Téllez-Ramírez & Fernando Reche-Lorite & María-José Sánchez, 2022. "Predictive Model and Mortality Risk Score during Admission for Ischaemic Stroke with Conservative Treatment," IJERPH, MDPI, vol. 19(6), pages 1-16, March.
    4. Jeroen Weesie, 2002. "On Pearson's X^2 for categorical response variables," Dutch-German Stata Users' Group Meetings 2002 7, Stata Users Group.
    5. Small, Henry, 2018. "Characterizing highly cited method and non-method papers using citation contexts: The role of uncertainty," Journal of Informetrics, Elsevier, vol. 12(2), pages 461-480.

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