Including spatial correlation in structural equation

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Including spatial correlation in structural equation

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Apr 7, 2018 - 0.56 0.07. 0.0000. 0.54 0.08. 0.0000. Clay.Ar. â¼. EVISD. 0.23 0.09. 0.0072. 0.21 0.11. 0.0415. Clay.Ar. â¼. LSTM. â0.02 0.09. 0.7827. 0.09 0.11.

Supplementary material for manuscript “Including spatial correlation in structural equation modelling of soil properties”, submitted to Spatial Statistics

1. Tables Table I: Model estimates (Est) with standard errors (SE) and p-values for standard SEM and spatial SEM. Var is variables and Op is operator. Operator ∼ refers to “is regressed on”, operator ∼∼ refers to “is correlated with”.

Relations

Standard SEM

Var

Op

Var

Est

SE

p-value

CEC.Ar CEC.Ar CEC.Ar CEC.Br CEC.Br CEC.Br CEC.Br CEC.Cr CEC.Cr Clay.Ar Clay.Ar Clay.Ar Clay.Ar Clay.Ar Clay.Br Clay.Br Clay.Br Clay.Br Clay.Br Clay.Br Clay.Br Clay.Cr Clay.Cr Clay.Cr

∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼

OC.Ar Clay.Ar DEM Clay.Br DEM LON EVISD Clay.Cr EVISD Clay.Cr EVISD LSTM NDWI.B TWI Clay.Ar Clay.Cr VDCHN TWI NDWI.B LON LSTM DEM VDCHN LON

0.23 0.97 0.22 0.92 0.60 0.47 0.12 0.72 0.33 0.56 0.23 –0.02 0.20 –0.20 0.40 0.36 –0.11 –0.01 –0.02 0.26 0.06 0.80 –0.03 1.47

0.03 0.03 0.03 0.04 0.11 0.12 0.04 0.05 0.06 0.07 0.09 0.09 0.07 0.06 0.07 0.07 0.05 0.06 0.05 0.08 0.07 0.33 0.07 0.37

0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0018 0.0000 0.0000 0.0000 0.0072 0.7827 0.0026 0.0012 0.0000 0.0000 0.0362 0.7991 0.7670 0.0008 0.3881 0.0170 0.6275 0.0001

Preprint submitted to Spatial Statistics

Spatial SEM Est

SE

p-value

0.25 0.03 0.0000 0.97 0.03 0.0000 0.22 0.04 0.0000 0.96 0.04 0.0000 0.84 0.13 0.0000 0.69 0.13 0.0000 0.08 0.04 0.0638 0.76 0.05 0.0000 0.19 0.06 0.0006 0.54 0.08 0.0000 0.21 0.11 0.0415 0.09 0.11 0.3758 0.29 0.08 0.0006 –0.20 0.08 0.0074 0.40 0.06 0.0000 0.44 0.07 0.0000 0.04 0.06 0.4585 0.03 0.06 0.5823 0.02 0.06 0.7769 0.35 0.08 0.0000 0.15 0.08 0.0664 0.90 0.35 0.0100 –0.09 0.07 0.2000 1.57 0.39 0.0001 Continued on next page

April 7, 2018

Table I: Continued from previous page

Relations

Standard SEM

Var

Op

Var

Est

SE

p-value

Clay.Cr OC.Ar OC.Ar OC.Ar OC.Ar OC.Ar OC.Ar OC.Br OC.Br OC.Br OC.Br OC.Br OC.Br OC.Br OC.Cr OC.Cr CEC.Ar CEC.Ar CEC.Ar CEC.Br CEC.Br CEC.Cr Clay.Ar Clay.Br Clay.Cr OC.Ar OC.Br OC.Br OC.Cr OC.Cr

∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼∼ ∼∼ ∼∼ ∼∼ ∼∼ ∼∼ ∼∼ ∼∼ ∼∼ ∼∼ ∼∼ ∼∼ ∼∼ ∼∼

LSTM Clay.Ar EVISD LSTM NDWI.B NDWI.A Clay.Br OC.Ar Clay.Br EVISD LSTM NDWI.A VDCHN DEM OC.Br DEM CEC.Br Clay.Br CEC.Ar CEC.Cr CEC.Br CEC.Cr Clay.Ar Clay.Br Clay.Cr OC.Ar Clay.Ar OC.Br Clay.Cr OC.Cr

0.33 0.02 0.04 –0.33 –0.28 –0.42 0.45 0.26 0.64 –0.15 0.03 –0.06 0.03 0.38 0.52 0.16 0.08 –0.06 0.08 0.20 0.19 0.41 0.51 0.28 0.68 0.62 –0.17 0.59 0.22 0.58

0.11 0.11 0.15 0.10 0.08 0.17 0.11 0.08 0.10 0.15 0.12 0.16 0.07 0.09 0.07 0.07 0.01 0.02 0.02 0.03 0.02 0.05 0.07 0.04 0.08 0.08 0.06 0.08 0.06 0.08

0.0020 0.8444 0.8116 0.0012 0.0007 0.0144 0.0000 0.0017 0.0000 0.2945 0.7910 0.7131 0.7131 0.0000 0.0000 0.0153 0.0000 0.0006 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0021 0.0000 0.0004 0.0000

2

Spatial SEM Est

SE

p-value

0.27 –0.08 0.04 –0.17 –0.16 –0.28 0.45 0.18 0.67 –0.16 0.01 0.02 0.03 0.27 0.42 0.00 0.11 –0.05 0.12 0.20 0.24 0.40 0.76 0.34 0.75 0.91 –0.17 0.82 0.29 0.87

0.11 0.11 0.18 0.12 0.10 0.21 0.11 0.08 0.10 0.17 0.14 0.18 0.08 0.11 0.08 0.08 0.02 0.02 0.02 0.03 0.03 0.05 0.10 0.05 0.09 0.11 0.08 0.10 0.08 0.11

0.0138 0.4783 0.8165 0.1669 0.1249 0.1777 0.0001 0.0298 0.0000 0.3614 0.9292 0.9173 0.6800 0.0144 0.0000 0.9900 0.0000 0.0069 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0282 0.0000 0.0003 0.0000

2. Figures

Figure I: Pearson correlations between soil properties and covariates.

3

Figure II: Difference maps between spatial SEM and standard SEM predictions. Cation exchange capacity (CEC) (cmolc kg–1 ), organic carbon (OC) (mass %), and Clay (mass %) for the A, B and C horizons.

4