# Semivariogram interpretation

From: sudhaveturi <asremlforum_at_VSNI.CO.UK>
Date: Thu, 7 Jan 2010 16:53:17 +0000

I have a few questions pertaining to the interpretation of a semivariogram.

I fit a longitudinal mixed model in a multivariate framework with response variables DLA score1, DLA score2, DLA score3 (diseased leaf area in maize) across three time points (traits) with independent variables Trait, Cycle, Trait.Cycle (fixed effects) and Trait.Cycle.Id, Trait.Rep and Trait.Rep.Block (random effects) where:

Trait=1,2,3; Rep=1,2,3; Blocks=1,2...20 (nested in Reps).
Cycle=1,2..7 (Selection occurs over 7 different Cycles)
Id=individual entry or genotype=1,2...315( nested in Cycles).

DLA_score1 DLA_score2 DLA_score3 ~ Trait Cycle Trait.Cycle !r Trait.Cycle.Id Trait.Rep Trait.Rep.Block !f mv (in ASReml)
On the G sIde I fit Trait.Cycle.Id as:
Trait.Cycle.Id 2
Trait 0 AR1H 0.5 0.5 0.5 0.5 !GP
Cycle.Id 0 ID

I get a semivariogram for Trait.Cycle.Id with Trait on the outer displacement axis and Cycle.Id on the inner displacement axis. My questions here are:

1) While I understand that displacements in this case refer to absolute distance between Trait co-ordinates(1,2,3) on the outer displacement axis, I was wondering how the co-ordinates are ordered for the inner displacement axis. Do displacements on the inner displacement axis refer to absolute distance between 2205 co-ordinates(315x7 Cycle.Id combinations)? Is the ordering of the co-ordinates the same as it would be in the sln file for blup values of Trait.Cycle.Id?
Also since displacements only make sense in a geostatistical / spatial or longitudinal framework, would absolute distances between co-ordinates of Cycle.Id make sense here?

2) In this case, the semivariogram has 20 ridges; how that number was arrived at is not very clear to me.

3) Each point on the semivariogram is (lij1, lij2,vij(bar)).

vij =(1/2)[ai(si)-aj(sj )]2 ; i; j = 1; : : : ; n; i <> j (where ai(si)=estimated predicted values (blups) for elements of the data vector indexed by a vector of spatial/time-based coordinates si; i=1,2..n) and lij1= si1-sj1 and lij2=si2-sj2 (inner and outer displacements).

As there will be many vijâ€™s with the same displacements, I understand that ASReml calculates the mean of all vijâ€™s with the same displacement after ignoring the signs. The vij(bar)â€™s would represent the semi-variances of differences between blup values at co-ordinates with same displacements.
Does the value indicated on the top right of the variogram represent the highest such averaged squared deviation between blup values at a particular set of absolute displacements?

I can attach any files/datasets if required. Any help would be greatly appreciated.

Thank you

Sudha Veturi
Biostatistician (Researcher),
Department of Plant and Soil Sciences,
531 S College Ave, 152 Townsend Hall
University of Delaware,
Newark, DE, 19716

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