Dear All,
I intend to fit spatial covariance structure to yield data using the
geostatistical model
z(s) = u(s) +e(s).
where z(s) denotes the yield measures at location,s, geo-referenced with
longitude and latitude coordinates. u(s) denotes deterministic component or
large-scale trend and e(s) stands for stochastic component or local-scale
structure.

Do I need to carry out trend surface analysis before fitting
several covariance structures- Guassian, spherical, exponential, power,
linear and linear log? I wish to identify the best structure that defined
the spatial pattern of the yield in the field.

I did trend analysis by regressing yield as function of spatial coordinates
i.e
yield ~easting + northing


lm(formula = yield ~ easting + northing, data = canocrop1)

Coefficients:

(Intercept)      easting     northing

 -1.930e+04    7.787e-03    2.945e-03

 Call:

lm(formula = yield ~ easting + northing, data = canocrop1)

Residuals:

   Min     1Q Median     3Q    Max

-39.87  -4.98   1.73   6.61 346.93

Coefficients:

              Estimate Std. Error t value Pr(>|t|)

(Intercept) -1.930e+04  3.920e+03  -4.924 8.58e-07 ***

easting      7.787e-03  6.389e-04  12.189  < 2e-16 ***

northing     2.945e-03  6.983e-04   4.217 2.49e-05 ***

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 15.49 on 13243 degrees of freedom

Multiple R-squared:  0.0169,   Adjusted R-squared:  0.01675

F-statistic: 113.8 on 2 and 13243 DF,  p-value: < 2.2e-16

The outcome revealed that the parameter estimate of easting and northing
are significantly different from zero. Does it mean there is trend or not?
I am yet to know the appropriate interpretation of the output of trend
surface analysis. I wish anyone could explain better to me.

If there is a trend? What is the next thing before proceeding with the
analysis?

Sometimes, interaction of easting and northing is included in the model.
When is it right to do this? i.e.
yield ~ easting + northing easting*northing

 Please I would like to know the reason for this trend surface analysis
before  proceed with fitting of spatial covariance structure.

Thanks while looking forward to reading your response.

Best regards
Moshood

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