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        <full_title>International Journal of Computational and Applied Mathematics &amp; Computer Science</full_title>
        <issn media_type="electronic">2769-2477</issn>
      </journal_metadata>
      <journal_issue>
        <publication_date media_type="online">
          <month>06</month>
          <day>10</day>
          <year>2026</year>
        </publication_date>
        <publication_date media_type="print">
          <month>06</month>
          <day>10</day>
          <year>2026</year>
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          <volume>6</volume>
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      <journal_article publication_type="full_text" language="en">
        <titles>
          <title>Comparative Analysis of Spatial Statistical Methods for Modelling Rice Yield Variability in Uniformity Trials</title>
        </titles>
        <contributors>
          <person_name sequence="first" contributor_role="author">
            <given_name>Adebayo</given_name>
            <surname>O. P</surname>
            <affiliations>
              <institution>
                <institution_name>Department of Statistics Federal University of Agriculture and Technology Okeho Oyo State NIGERIA</institution_name>
              </institution>
            </affiliations>
          </person_name>
          <person_name sequence="additional" contributor_role="author">
            <given_name>Ahmed</given_name>
            <surname>I</surname>
            <affiliations>
              <institution>
                <institution_name>Department of Statistics Nasarawa State University Pmb 1022 Keffi Nasarawa State NIGERIA</institution_name>
              </institution>
            </affiliations>
          </person_name>
          <person_name sequence="additional" contributor_role="author">
            <given_name>Garba</given_name>
            <surname>I. M</surname>
            <affiliations>
              <institution>
                <institution_name>Department of Agriculture Phoenix University Agwada Pmb 1019 Keffi Nasarawa State NIGERIA</institution_name>
              </institution>
            </affiliations>
          </person_name>
          <person_name sequence="additional" contributor_role="author">
            <given_name>Mustaph</given_name>
            <surname>A. D</surname>
            <affiliations>
              <institution>
                <institution_name>National Bureau of Statistics NIGERIA</institution_name>
              </institution>
            </affiliations>
          </person_name>
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        <jats:abstract xml:lang="en"><jats:p>Spatial heterogeneity is a fundamental characteristic of agricultural landscapes, and accurately modelling its impact on crop yield is critical for precision agriculture. This study presents a comparative analysis of spatial statistical and machine learning approaches to model yield variability in a field exhibiting strong spatial dependence. Initial geostatistical analysis confirmed significant positive spatial autocorrelation (Moran's I = 0.7355, p &lt; 2.2e-16). A series of models were evaluated, progressing from linear and polynomial trend surfaces to spatial regression (Lag and Error), mixed effects, and a Random Forest ensemble. The results demonstrate that while traditional spatial models effectively captured and explained the spatial autocorrelation, a Random Forest model significantly outperformed all others in predictive accuracy, achieving a 31% lower Root Mean Square Error (36.05) than the best spatial regression model and explaining 71.02% of the variance. Among the spatial models, a quadratic trend surface with a row × column interaction provided the most parsimonious fit, revealing an accelerating yield increase along rows and a U-shaped pattern across columns. The Random Forest model's residuals showed no statistically significant remaining spatial autocorrelation (Moran's I p-value = 0.97); however, we caution that failure to reject spatial randomness does not prove its absence. Equivalence testing (TOST) and power analysis support the conclusion that spatial dependence was adequately captured. We conclude that machine learning ensembles like Random Forest offer superior predictive power for yield mapping, though spatial regression models remain valuable for providing parsimonious, interpretable insights into the underlying structural gradients driving yield variability.</jats:p></jats:abstract>
        <publication_date media_type="online">
          <month>10</month>
          <day>12</day>
          <year>2026</year>
        </publication_date>
        <publication_date media_type="print">
          <month>10</month>
          <day>12</day>
          <year>2026</year>
        </publication_date>
        <pages>
          <first_page>101</first_page>
        </pages>
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          <item_number item_number_type="article_number">9</item_number>
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          <doi>10.37394/232028.2026.6.9</doi>
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        <citation_list>
          <citation type="journal_article" key="ref1"><unstructured_citation>FAO. (2023). The future of food and agriculture: Drivers and triggers for transformation. Food and Agriculture Organization of the United Nations.</unstructured_citation></citation>
          <citation type="journal_article" key="ref2"><unstructured_citation>Piepho, H. P., Richter, C., &amp; Williams, E. (2023). Statistical methods for plant variety evaluation: Current practices and future directions. Journal of Agricultural Science, 161(1), 1– 15.</unstructured_citation></citation>
          <citation type="journal_article" key="ref3"><unstructured_citation>López, M., Fernández, J., &amp; García, P. (2024). Spatial variability in agricultural fields: Sources, consequences, and management strategies. Agronomy Journal, 116(2), 445–462.</unstructured_citation></citation>
          <citation type="journal_article" key="ref4"><unstructured_citation>Stroup, W. W. (2023). Generalized linear mixed models: Modern concepts, methods and applications (2nd ed.). CRC Press.</unstructured_citation></citation>
          <citation type="journal_article" key="ref5"><unstructured_citation>Gomez, K. A., &amp; Gomez, A. A. (1984). Statistical procedures for agricultural research. John Wiley &amp; Sons.</unstructured_citation></citation>
          <citation type="journal_article" key="ref6"><unstructured_citation>Pinheiro, J. C., &amp; Bates, D. M. (2023). Mixed-effects models in S and S-PLUS. Springer Science &amp; Business Media.</unstructured_citation></citation>
          <citation type="journal_article" key="ref7"><unstructured_citation>Webster, R., &amp; Oliver, M. A. (2023). Geostatistics for environmental scientists (3rd ed.). John Wiley &amp; Sons.</unstructured_citation></citation>
          <citation type="journal_article" key="ref8"><unstructured_citation>Anselin, L. (2023). Spatial econometrics: Methods and models. Springer International Publishing.</unstructured_citation></citation>
          <citation type="journal_article" key="ref9"><unstructured_citation>Liang, H., Wang, J., &amp; Zhang, X. (2024). Machine learning approaches for spatial prediction in agricultural systems: A comparative study. Computers and Electronics in Agriculture, 218, 106712.</unstructured_citation></citation>
          <citation type="journal_article" key="ref10"><unstructured_citation>Rodríguez, A., Martínez, C., &amp; González, L. (2023). Comparative analysis of spatial statistical methods in agricultural field trials: A review. Spatial Statistics, 54, 100745.</unstructured_citation></citation>
          <citation type="journal_article" key="ref11"><unstructured_citation>R Core Team. (2023). R: A language and environment for statistical computing. R Foundation for Statistical Computing.</unstructured_citation></citation>
          <citation type="journal_article" key="ref12"><unstructured_citation>Pebesma, E. (2023). Multivariable geostatistics in R: The gstat package. Computers &amp; Geosciences, 167, 105211.</unstructured_citation></citation>
          <citation type="journal_article" key="ref13"><unstructured_citation>Bivand, R. S., Pebesma, E., &amp; Gomez-Rubio, V. (2023). Applied spatial data analysis with R (2nd ed.). Springer.</unstructured_citation></citation>
          <citation type="journal_article" key="ref14"><unstructured_citation>Bates, D., Mächler, M., Bolker, B., &amp; Walker, S. (2023). Fitting linear mixed-effects models using lme4. Journal of Statistical Software, 67(1), 1–48.</unstructured_citation></citation>
          <citation type="journal_article" key="ref15"><unstructured_citation>Bivand, R. S. (2023). Spatial dependence: Weighting schemes, statistics and models. R package version 1.3-1.</unstructured_citation></citation>
          <citation type="journal_article" key="ref16"><unstructured_citation>Liaw, A., &amp; Wiener, M. (2023). Classification and regression by randomForest. R News, 2(3), 18–22.</unstructured_citation></citation>
          <citation type="journal_article" key="ref17"><unstructured_citation>Wickham, H. (2023). ggplot2: Elegant graphics for data analysis (3rd ed.). Springer.</unstructured_citation></citation>
          <citation type="journal_article" key="ref18"><unstructured_citation>Legendre, P., &amp; Legendre, L. (2023). Numerical ecology (3rd ed.). Elsevier.</unstructured_citation></citation>
          <citation type="journal_article" key="ref19"><unstructured_citation>Fox, J., &amp; Weisberg, S. (2023). An R companion to applied regression (3rd ed.). Sage.</unstructured_citation></citation>
          <citation type="journal_article" key="ref20"><unstructured_citation>Breiman, L. (2001). Random forests. Machine Learning, 45(1), 5–32.</unstructured_citation></citation>
          <citation type="journal_article" key="ref21"><unstructured_citation>Scornet, E., Biau, G., &amp; Vert, J.-P. (2015). Consistency of random forests. Annals of Statistics, 43(4), 1716–1741.</unstructured_citation></citation>
          <citation type="journal_article" key="ref22"><unstructured_citation>Burnham, K. P., &amp; Anderson, D. R. (2002). Model selection and multimodel inference: A practical information-theoretic approach (2nd ed.). Springer.</unstructured_citation></citation>
          <citation type="journal_article" key="ref23"><unstructured_citation>Bender, R., &amp; Lange, S. (2023). Multiple test procedures in clinical trials. Statistics in Medicine, 42(5), 675–692.</unstructured_citation></citation>
          <citation type="journal_article" key="ref24"><unstructured_citation>Cliff, A. D., &amp; Ord, J. K. (1981). Spatial processes: Models and applications. Pion.</unstructured_citation></citation>
          <citation type="journal_article" key="ref25"><unstructured_citation>Lee, L.-F. (2004). Asymptotic distributions of quasi-maximum likelihood estimators for spatial autoregressive models. Econometrica, 72(6), 1899–1925.</unstructured_citation></citation>
          <citation type="journal_article" key="ref26"><unstructured_citation>Kelejian, H. H., &amp; Prucha, I. R. (2010). Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances. Journal of Econometrics, 157(1), 53–67.</unstructured_citation></citation>
          <citation type="journal_article" key="ref27"><unstructured_citation>Newey, W. K., &amp; McFadden, D. (1994). Large sample estimation and hypothesis testing. In R. F. Engle &amp; D. L. McFadden (Eds.), Handbook of econometrics (Vol. 4, pp. 2111–2245). Elsevier.</unstructured_citation></citation>
          <citation type="journal_article" key="ref28"><unstructured_citation>Anselin, L. (1988). Spatial econometrics: Methods and models. Springer.</unstructured_citation></citation>
          <citation type="journal_article" key="ref29"><unstructured_citation>Biau, G., &amp; Scornet, E. (2016). A random forest guided tour. TEST, 25(2), 197–227.</unstructured_citation></citation>
          <citation type="journal_article" key="ref30"><unstructured_citation>Claeskens, G., &amp; Hjort, N. L. (2008). Model selection and model averaging. Cambridge University Press.</unstructured_citation></citation>
          <citation type="journal_article" key="ref31"><unstructured_citation>Cressie, N. A. C. (1993). Statistics for spatial data (Rev. ed.). Wiley.</unstructured_citation></citation>
          <citation type="journal_article" key="ref32"><unstructured_citation>Diggle, P. J., &amp; Ribeiro, P. J. (2007). Model-based geostatistics. Springer.</unstructured_citation></citation>
          <citation type="journal_article" key="ref33"><unstructured_citation>Elhorst, J. P. (2014). Spatial econometrics: From cross-sectional data to spatial panels. Springer.</unstructured_citation></citation>
          <citation type="journal_article" key="ref34"><unstructured_citation>Genuer, R., Poggi, J.-M., &amp; Tuleau-Malot, C. (2010). Variable selection using random forests. Pattern Recognition Letters, 31(14), 2225–2236.</unstructured_citation></citation>
          <citation type="journal_article" key="ref35"><unstructured_citation>Goovaerts, P. (1997). Geostatistics for natural resources evaluation. Oxford University Press.</unstructured_citation></citation>
          <citation type="journal_article" key="ref36"><unstructured_citation>Journel, A. G., &amp; Huijbregts, C. J. (1978). Mining geostatistics. Academic Press.</unstructured_citation></citation>
          <citation type="journal_article" key="ref37"><unstructured_citation>LeSage, J. P., &amp; Pace, R. K. (2009). Introduction to spatial econometrics. CRC Press.</unstructured_citation></citation>
          <citation type="journal_article" key="ref38"><unstructured_citation>Piepho, H. P., Büchse, A., &amp; Emrich, K. (2013). A Hitchhiker's guide to mixed models for randomized experiments. Journal of Agronomy and Crop Science, 189(5), 310–322.</unstructured_citation></citation>
          <citation type="journal_article" key="ref39"><unstructured_citation>Plant, R. E. (2018). Spatial data analysis in ecology and agriculture using R (2nd ed.). CRC Press.</unstructured_citation></citation>
          <citation type="journal_article" key="ref40"><unstructured_citation>Ripley, B. D. (1981). Spatial statistics. Wiley.</unstructured_citation></citation>
          <citation type="journal_article" key="ref41"><unstructured_citation>Stroup, W. W. (2013). Generalized linear mixed models: Modern concepts, methods and applications. CRC Press.</unstructured_citation></citation>
        </citation_list>
      </journal_article>
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