This paper presents a method for estimating sampling variances of predicted maximum-likelihood probabilities in a logic response function without the need to invert any matrix or take derivatives of the link function. The method is based on the assumption that the exponent of a linear function of the logits is lognormal. Smoothing techniques play an important role in modern nonparametric statistics. We use kernel density estimation and local polynomial regression smoothing to explain important principles of smoothing. Some selected applications show nonparametric density and regression estimation in action.
Mixed models have important advantages as compared to fixed effects models.
Complex data structures can be described in a natural way in mixed models. The analysis of unbalanced data is a straightforward extension of the analysis of balanced data in mixed model framework. Furthermore, the appropriate inference space can be chosen in the mixed model. We further try to answer the question whether the advantages of the mixed model outweigh the cost of using this methodology in the context of developing countries. Two methods for determining the optimum level of Potash required for maximum yield in any one season are compared and the rationale for either function are discussed.