sj-zip-2-smm-10.1177_09622802221122403 - Supplemental material for Bayesian analysis of longitudinal binary responses based on the multivariate probit model: A comparison of five methods

Supplemental material, sj-zip-2-smm-10.1177_09622802221122403 for Bayesian analysis of longitudinal binary responses based on the multivariate probit model: A comparison of five methods by Kaifeng Lu and Fang Chen in Statistical Methods in Medical Research</p

Evaluating Status Change of Soil Potassium from Path Model

<div><p>The purpose of this study is to determine critical environmental parameters of soil K availability and to quantify those contributors by using a proposed path model. In this study, plot experiments were designed into different treatments, and soil samples were collected and further analyzed in laboratory to investigate soil properties influence on soil potassium forms (water soluble K, exchangeable K, non-exchangeable K). Furthermore, path analysis based on proposed path model was carried out to evaluate the relationship between potassium forms and soil properties. Research findings were achieved as followings. Firstly, key direct factors were soil S, ratio of sodium-potassium (Na/K), the chemical index of alteration (CIA), Soil Organic Matter in soil solution (SOM), Na and total nitrogen in soil solution (TN), and key indirect factors were Carbonate (CO₃), Mg, pH, Na, S, and SOM. Secondly, path model can effectively determine direction and quantities of potassium status changes between Exchangeable potassium (eK), Non-exchangeable potassium (neK) and water-soluble potassium (wsK) under influences of specific environmental parameters. In reversible equilibrium state of , K balance state was inclined to be moved into β and χ directions in treatments of potassium shortage. However in reversible equilibrium of , K balance state was inclined to be moved into θ and λ directions in treatments of water shortage. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0076712#s3" target="_blank">Results</a> showed that the proposed path model was able to quantitatively disclose moving direction of K status and quantify its equilibrium threshold. It provided a theoretical and practical basis for scientific and effective fertilization in agricultural plants growth.</p></div

Correlation analysis of environmental parameters of soil potassium.

<p>Correlation analysis of environmental parameters of soil potassium.</p

Soil organic matter, humic acid, Total Carbon (TC), Total nitrogen (TN) of Laboratory measurement for different parameters of 256 soil samples (R, rhizosphere soil; NR, non-rhizosphere).

<p>Soil organic matter, humic acid, Total Carbon (TC), Total nitrogen (TN) of Laboratory measurement for different parameters of 256 soil samples (R, rhizosphere soil; NR, non-rhizosphere).</p

Total contents of soil elements of Laboratory measurement for different parameters of 256 soil samples (R, rhizosphere soil; NR, non-rhizosphere).

<p>Total contents of soil elements of Laboratory measurement for different parameters of 256 soil samples (R, rhizosphere soil; NR, non-rhizosphere).</p

Dynamic equilibrium of non-exchangeable potassium in rhizosphere/non-rhizosphere soils.

<p>Dynamic equilibrium of non-exchangeable potassium in rhizosphere/non-rhizosphere soils.</p

Direct and indirect correlation coefficients of non-exchangeable potassium (<i>neK</i>).

<p>Direct and indirect correlation coefficients of non-exchangeable potassium (<i>neK</i>).</p

Direct and indirect correlation coefficients in exchangable potassium (<i>eK</i>).

<p>Direct and indirect correlation coefficients in exchangable potassium (<i>eK</i>).</p

Direct and indirect correlation coefficients of water-soluble potassium (<i>wsK</i>).

<p>Direct and indirect correlation coefficients of water-soluble potassium (<i>wsK</i>).</p

Fertilizing rates of different treatments (unit: g).

<p>Fertilizing rates of different treatments (unit: g).</p