Diagnostic techniques applied in geostatistics for agricultural data analysis

Abstract

SUMMARYThe structural modeling of spatial dependence, using a geostatistical approach, is an indispensable tool to determine parameters that define this structure, applied on interpolation of values at unsampled points by kriging techniques. However, the estimation of parameters can be greatly affected by the presence of atypical observations in sampled data. The purpose of this study was to use diagnostic techniques in Gaussian spatial linear models in geostatistics to evaluate the sensitivity of maximum likelihood and restrict maximum likelihood estimators to small perturbations in these data. For this purpose, studies with simulated and experimental data were conducted. Results with simulated data showed that the diagnostic techniques were efficient to identify the perturbation in data. The results with real data indicated that atypical values among the sampled data may have a strong influence on thematic maps, thus changing the spatial dependence structure. The application of diagnostic techniques should be part of any geostatistical analysis, to ensure a better quality of the information from thematic maps.Index terms: local influence, maximum likelihood, restricted maximum likelihood.(

Comparison of maps of spatial variability of soil resistance to penetration constructed with and without covariables using a spatial linear model

“…The method of MRL estimation of θ which consists in maximizing the logarithm of the restricted likelihood function (BORSSOI et al, 2009),…”

Comparison measures of maps generated by geostatistical methods

“…In this study for the adjustment of a spatial model to the experimental semivarigram it was used the exponential, spherical and Gaussian models, for the parameters estimation it was used the ordinary least squares(OLS), the weighted least squares (WLS1),the maximum likelihood (ML) and the restricted maximum likelihood (RML) estimation methods (MARDIA& MASHALL, 1984).To choose the space model that best suits the semivariances it was used the cross-validation technique (VAUCLIN et al, 1983;FARACO et al, 2008) and to investigate the existence of influential points it was carried out a diagnostic analysis of local influence (BORSSOI et al, 2009). …”

“…The graphic elements | L max | versus i (order) may reveal what kind of perturbation hat has the greatest influence in LD (ω) in the vicinity of ω 0 (COOK, 1986;BORSSOI et al, 2009). Table 1 shows the generic form of an error matrix (GRINAND et al, 2008).In this matrix, the pixels of the reference map are quantified in columns while the pixels of the model map are quantified in the lines.…”

Influência local em um modelo espacial linear da produtividade da soja utilizando distribuição t-Student

“…Por exemplo, GALEA et al (2003) e GALEA et al (2005 consideram estudos de influência local em modelos de regressão linear e nãolinear para amostras independentes, considerando vários esquemas de perturbação. BORSSOI et al (2009) usaram técnicas de diagnósticos de influência local em modelos espaciais gaussianos empregados em geoestatística, buscando avaliar a sensibilidade dos estimadores de máxima verossimilhança. ASSUMPÇÃO et al (2011) estudaram técnicas de influência local para dados com distribuição t-Student, considerando a perturbação aditiva na variável resposta e os graus de liberdade fixos.…”