Simulação de dados de área em GEE e análise da adoção de variedades melhoradas de milho em Moçambique

Abstract

Generalized Estimating Equations (GEE) are extension of Generalized Linear Models (GLM), widely applied in longitudinal data analysis. GEE are also applied in spatial data analysis through modelling the working correlation matrix based on semivariogram structure widely applied in random fields (geostatistics). In this paper we propose application of GEE for spatial lattice data modelling the working correlation matrix using the Moran’s index which is the most common index used to depict spatial autocorrelation between observations in this type of data. We present results for simulated and real data as well. For the former case, 1000 samples of a random variable defined in (0,1) interval were generated using different values of the Moran’s index. In addition, a binary and a continuous variable were also randomly generated as covariates. In each sample two models were fitted, one ignoring the spatial dependency (GLM) and other using the proposed GEE approach. Two measures of model performance were used, the relative efficiency of GEE estimator to its counterpart GLM and the working correlation selection criterions. Results showed that our proposed GEE approach have improved the efficiency of estimators due the well specification of the working correlation matrix. For real data case, the proportion of small farmers who did use improved maize varieties was considered as the response variable and a set 13 variables were used as covariates. These predictors were classified as economic, demographic, institutional and technologic factors. The spatial dependency of the response variable was assessed by global and local Moran indexes. Two models were fitted, the logistic regression model and the GEE here proposed. Results for real data showed consistence with those obtained for simulation study, i.e, the application of GEE proposed has generated better results compared to its competitor. Using the GEE approach for spatial lattice data it was possible to claim that the household size, hired labour, household head age, animal traction, information access, ownership of improved grain storage system, credit and extension services access are the main factors affecting adoption of improved maize varieties in Mozambique. Furthermore, the spatial dependence between observations of the response variable has also showed a significant positive influence in adoption of improved maize seeds.