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The models with a heterogeneous error structure provided a significantly better fit than those with homogeneous errors (likelihood ratio test (LRT) between homo- vs. heterogeneous models with random intercepts in Tables 3 and 4; X 2 = 73.5, d.f.
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The induced field coefficients are evaluated by the forward solver up to degree and order 5. Homogeneous error nT is assumed.
The model with heterogeneous residual error variances was significantly (α < 0.001) more appropriate than the one with homogeneous error variances in all of the trials for both fixed and random locations, according to model fitting statistics.
Scalars ρ and λ are parameters of spatial association corresponding to the objective variable and the error term ε, respectively, while μ are independent and possibly homogeneous error terms [6].
For distributed SAC-SMA, spatially homogeneous error modeling yielded updated states that are spatially much more similar to the a priori states, as quantified by Earth Mover's Distance (EMD), than spatially heterogeneous error modeling by up to ∼10 times.
Before this analysis, we tested the hypothesis of homogeneous error rates on the three PT plates.
This software does not allow fitting group-specific error variances; therefore, in our interaction model and in our across-environment analyses, we fit the models assuming homogeneous error variances across environments.
Because the number of daughters per bull was high for all bulls, the reliabilities of the dEBV were high and varied little between bulls, and a homogeneous error variance structure was assumed.
These maps clearly show low and homogeneous fitting errors, all over the spatial domain corresponding to the bacterium.
Homogeneous pseudo-error variances were assumed across breeds.
To obtain a normal distribution and homogeneous residual error, ruminal LPS, blood LPS and IL-6 data were log transformed.
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