Sentence examples for trend function from inspiring English sources
The validation was conducted for the model including no spatial trend function (Eq. 8.3), the model with a spatial trend function of low dimension (Eq. 8.4) and the model with a trend function of optimal dimension concerning AIC (Eq. 8.51).
The results of the investigation were presented as the trend function.
Additionally the dimension of the spatial trend function was decreased slightly (edf = 93.38).
By increasing the dimension of the 2-dimensional spatial trend function, the model was improved significantly.
An optimum value was reached at approximately 120 degrees of freedom (edf) for the spatial trend function (Eq. 8.5).
The test is based on the separation between an empirical version of the relative trend function and its greatest convex minorant.
Several approaches are proposed, one of them enforcing orthogonality between the trend functions and the complementary random field.
where f(t) and g(t) represent the polynomial time trend functions, ε dt and ε st are the error terms.
The residuals for the models with more complex spatial trend functions (Eq. 8.51 and Eq. 8.51 Duchon) showed no spatial dependencies anymore (Figure 9C and 9D).
Therefore simple empirical semi-variograms of the randomized quantile residuals were calculated for various models with spatial trend functions of different complexity.
Figure 9 Empirical semi-variograms for the randomized quantile residuals of four negative binomial regression models (Eqs. 8.3, A; 8.4, B 8.51, C 8.51Duchon, D) with spatial trend functions of different complexity (solid black dots).
