What Does “Explained Variance“ Explain

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Bibliographic Data

ID7971122
AuthorsChristopher H Achen (corresponding author)
Year1990
Volume2
Pages173-184
Publication date1990-01-01
Open AccessYes
TypeARTICLE
VenuePolitical Analysis (JOURNAL)
Journal identifiersISSN: 1047-1987 • E-ISSN: 1476-4989
PublisherCambridge University Press (CUP) (PUBLISHER)
DOI10.1093/pan/2.1.173
OpenAlexW2004042461
LanguageEN
Citations received15
References cited2

Two quite different statistical specifications lead to conventional regression computations. Under the first, usually called unconditional regression , the independent variables are assigned a distribution, and the sampling distributions of parameters are computed over it, not just over the variation in the disturbance. Then the multiple squared coefficient of correlation, R 2 , is a substantively meaningful quantity with a population value. In such cases, it is certainly meaningful to estimate R 2 and to use the resulting estimate for the usual descriptive and inferential purposes. The nature of most social scientific work, however, generates data poorly described by the first specification. The second specification, conditional regression , is usually more helpful, and for that reason, it overwhelmingly predominates in econometric textbooks. Under it, sampling distributions are conditioned on the observed values of the independent variables. Then, R 2 is a purely descriptive quantity with little substantive content. It is not a parameter, and it will vary meaninglessly across samples even when the underlying statistical law is unchanged. By contrast, the standard error of estimate (SEE) lacks these difficulties, and is a far better statistic for assessing goodness of fit. Lewis-Beck and Skalaban are persuasive where unconditional regression is concerned. But their argument encounters serious difficulties in the far more common situation in which conditional regression applies. Their blurring of the distinction between the two situations explains why their seemingly persuasive logic leads them astray

Argument (complex analysis · Contrast (vision · Econometrics · Economics · Goodness of fit · Linear regression · Population · Regression · Regression analysis · Sampling distribution · Statistic · Statistics · Variance (accounting · Computer Science · Mathematics · Philosophy and History of Science · Qualitative Comparative Analysis Research · Statistical Mechanics and Entropy

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