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# 统计代写|多尺度模型代写Multilevel Models代考|Stat151 Nonlinear models

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## 统计代写|多尺度模型代写Multilevel Models代考|Nonlinear models

Some kinds of data are better represented in terms of nonlinear rather than linear models. For example, the modelling of discrete response data is considered formally as a case of modelling nonlinear data. Many kinds of growth data are conveniently modelled in this way, especially during periods of rapid and complex growth such as early infancy and at the approach to adulthood when growth approaches an upper asymptote (Goldstein, 1979). Other examples arise when the response variable has inherent constraints. For example, biochemical activity patterns in patients may exhibit asymptotic behaviour, or cyclical patterns, both of which may be difficult to model using purely linear models. Chapter 9 introduces such models and shows how to extend the linear multilevel model to this case. It also considers cases where variances and covariances can be modelled as nonlinear functions of explanatory variables (see also Chapter 17).

## 统计代写|多尺度模型代写Multilevel Models代考|Measurement errors

Many variables of interest in the human sciences contain ‘noise’ or random measurement error. This may be due to observer error as when measuring the weight of an animal, or an inherent result of being able to measure only a small sample of behaviour as in educational testing. It is well known that when variables in statistical models contain relatively large components of such error the resulting statistical inferences can be very misleading unless careful adjustments are made (Fuller, 2006). In the case of simple regression, when the explanatory or independent variable is measured with error, the usual estimate of the regression line slope is an underestimate compared to that which would result if the measurement were available without error. This is particularly important in studies of school effectiveness where the fitting of intake achievement scores is important but where such scores often have large components of measurement error.

An important case is where we have a level 2 variable that is a ‘compositional’ variable. That is, it is a measurement aggregated from the characteristics of the level 1 units within the level 2 units. Thus, for example, the mean intake achievement and the standard deviation of the intake achievements of all the pupils in a school are compositional variables that may, and indeed sometimes do, affect the final achievements of each individual student. Likewise, in a household survey, we may consider that a measure of the average social status or the percentages of households in each social group, using all the households in the immediate community, are important explanatory variables to fit in a model. The problem arises when it is possible to collect data only upon some of the level 1 units, this often being the case with household sample surveys. What we then have is an estimate of a compositional variable that is measured with error, in the case of household surveys typically with a very large error. In many educational studies, this also occurs where only a small proportion of students within a class or school are sampled. Chapter 14 discusses the problems of dealing with measurement errors in multilevel models.

## Matlab代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。