A- And R-optimal Designs Of Population Parameter For Two-group Hierarchical Linear Models

Hierarchical linear models have been widely used in various fields of science at present.However,optimal design issues that can effectively improve the accuracy of parameter estimation for these models have only come to the fore in the last decade or so.Given that multigroup experiments are usually conducted and the aim is often to compare the importance of various factors and their effects in different states in a phenomenon,we investigate A-and Roptimal design issues of population parameter for two-group hierarchical linear models in this paper.The content mainly includes theoretical research and numerical examples.In the theoretical part,we choose three models to be studied according to the influence of random effects.We establish equivalence theorems to confirm optimality of any design.We deduce lower bounds of efficiency to weigh the merits of any design.The numerical example part mainly includes two aspects.On the one hand,A-and R-optimal designs for three models under three different situations of fixed effects are discussed.It’s found that when the intercepts and slopes of two groups in fixed effect part are different,the A-optimal design,sensitive function and upper bound are unchanged regardless of the random effects.On the other hand,the efficiency,lower bound of efficiency and their difference of equidistant design for the general form of two-group first-order hierarchical linear models under three different situations of fixed effects are studied.It turns out that equidistant design also has high efficiency in some cases,and it can be used in practice.The research method involved in this paper is also applicable to optimal design issues of population parameter for multi-group hierarchical linear models.It can be used for theoretical and applied research similarly.