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Constancy of the variance of a measure over the levels of the factor under study.
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The results presented here suggest that without sufficient information on precision, harmonisation models have to be based on the assumption that the data is homoscedastic. Consequently, an MLFR approach will not have its full advantage over using OLR.
In particular, we extend the classical homoscedastic model by assuming that variation in the error term is an exponential function of an intercept term, the day-ahead forecast of total demand and its square (i.e., FQ, [FQ.sup.2]), that are included in the model in order to capture possible demand-size effects, and a vector of days-of-the-week dummies (DAY).
The verisimilitude ratio test shows the hypothesis that [lambda] = 0is rejected, which high lights that the heteroscedastic model is more appropriate than the homoscedastic one.
The OLR model most frequently used for instrumental calibrations (x-axis concentration and y-axis response; GRM concentration and X-ray intensity, respectively, in XRF spectrometry) requires the following assumptions to be fulfilled [4, 7,10,12-18]: (i) all errors are in the y-axis; (ii) x-axis is either error-free or has at most 10% error of the y-axis errors; (iii) errors in both axes are normally distributed; and (iv) errors in the y-axis are homoscedastic. Some or all of these assumptions are violated in most instrumental calibrations through the OLR model.
The errors are homoscedastic, indicating that our approach is acceptable in practice.
The first scenario is normal homoscedastic scenario with balanced design where all of the methods theoretically identify the same true cut-point.
The homoscedastic model shown in Equation 6 assumed a single residual error term.
If data from all individuals are not in a steady state but can be transformed to have a homoscedastic trend, adjustment for the trend is achievable by use of a suitable ANOVA model (analysis of covariance or generalized linear models) or by transforming data or adjusting the interpretation of the results (5, 6).
As shown in (16) we can separate the heteroscedastic variance into its homoscedastic component ([mathematical expression not reproducible]) and the element related to investments.