By recognizing the resonance effects from ground vias, one can let the tool apply a random variance to the via pattern to avoid having all via-formed cavities resonating at the same frequency.

FIGURE 2 shows a contour stitching and a surface via pepper with random variance applied.

To produce the combined curve, we regressed these estimates against indicator variables for each level, using inverse variance weighting and allowing for a random variance component to capture heterogeneity in the association across cities.

ij] is the estimated variance in city i at level j, and [delta] is the estimated random variance component.

26) to obtain a maximum likelihood estimate of the random variance component.

To combine results across cities, we used inverse variance weighted averages including a random variance component to incorporate heterogeneity.

Where heterogeneity remained, as assessed by a chi-square test, we fitted the regression including a random variance component, estimated using a maximum likelihood approach, following the method of Berkey et al.

We extended their method to incorporate random variance components.

To allow for this, we estimated a random variance component using the method of moments.

These estimated the overall effect as a weighted average, with weights equal to the inverse of the sum of the square of the standard error plus a

random variance component.