The modeling of generalized estimating equations used in the analysis of longitudinal data whether in continuous or discrete variables, necessarily requires the prior specification of a correlation matrix in its iterative process in order to obtain the estimates of the regression parameters. Such a matrix is called working correlation matrix and its incorrect specification produces less efficient estimates for the model parameters. Due to this fact, this study aims to propose a selection criterion of working correlation matrix based on the covariance matrix estimates of correlated responses resulting from the limiting values of the association parameter estimates. For validation of the criterion, we used simulation studies considering normal and binary correlated responses. Compared to some criteria in the literature, it was concluded that the proposed criterion resulted in a better performance when the correlation structure for exchangeable working correlation matrix was considered as true structure in the simulated samples and for large samples, the proposed criterion showed similar behavior to the other criteria, resulting in higher success rates.
This paper presents the proposal of a statistical method to analyse dependent agreement data with categorical ordinal responses for a longitudinal study in sensorial analysis of special coffee. The assessment of sensory attributes of special coffees were carried out by certified raters using a continuous scale of grades. The approach aimed to applying data categorization methods commonly used in machine learning which generated not only a concise summary of continuous attributes to describe the data but also allowed to maximize the agreement grades in a longitudinal study. A previous analysis was carried out to identify the similarity of grades in all sample unities. The categorization allowed the construction of marginal models for all distinct pairs time observed in the longitudinal study for modeling the concordance correlationskappa. It also enabled to conclude that samples of harvests related to yellow grain fruits have similar sensorial characteristics. Higher altitudes are significantly favorable to obtain samples with similar sensorial characteristics identifying the set of covariates which contributed either in positive or negative way while estimating kappa.
Maize is one of the main economic crops and staple food in Mozambique. However, despite the importance of the crop in the country, maize productivity is still low due to several factors including low adoption of improved agricultural technologies. This paper aimed to identify the main factors driving adoption of improved maize varieties applying generalized estimating equations (GEE). The motivation for this class of models is due to the fact that adoption of improved maize varieties is a spatial auto correlated variable and the traditional probit and logit models widely applied in studies of adoption of agricultural technologies do not take into account the structure of correlation existing in the response variable. The study uses data from Integrated Agrarian Survey of 2012 (IAI 2012). The proportion of small farmers who adopted improved maize varieties per district was used as response variable and a set of nine variables were used as covariates classified in social, economic, institutional and technologic factors. The spatial auto correlation of the dependent variable was assessed by global and local Moran indexes. Two classes of models were fitted: The traditional logistic regression (logit model) and the generalized estimating equations approach. The inclusion of spatial auto correlation in GEE was carried out inserting the Moran’s index in the working correlation matrix. The results have shown that the GEE approach for spatial lattice data was the best and all factors analysed in the study including the spatial dependency are the main factors driving adoption of improved maize varieties in Mozambique.
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