文档介绍：Chapter 3
Statistical Methods
Paul C. Taylor
University of Hertfordshire
28th March 2001
Introduction
  Generalized Linear Models
  Special Topics in Regression Modelling
  Classical Multivariate Analysis
  Summary
1
Generalized Linear Models
  Regression
  Analysis of Variance
  Log-linear Models
  Logistic Regression
  Analysis of Survival Data
2
The fitting of generalized linear models is currently the most frequently applied
statistical technique. Generalized linear models are used to described the rela-
tionship between the mean, sometimes called the trend, of one variable and the
values taken by several other variables.
3
Regression
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How is a variable, , related to one, or more, other variables, ¢ , ¢ , . . . , ?
¡
Names for ¡ :
response; dependent variable; output.
¦
Names for the ¢ ’s:
regressors; explanatory variables; independent variables; inputs.
Here, we will use the terms output and inputs.
4
Common reasons for doing a regression analysis include:
  the output is expensive to measure, but the inputs are not, and so cheap
predictions of the output are sought;
  the values of the inputs are known earlier than the output is, and a working
prediction of the output is required;
  we can control the values of the inputs, we believe there is a causal link
between the inputs and the output, and so we want to know what values
of the inputs should be chosen to obtain a particular target value for the
output;
  it is believed that there is a causal link between some of the inputs and the
output, and we wish to identify which inputs are related to the output.
5
The (general) linear model is
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¤ ¤ £ £ ¡ ()
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¢
¢ ¢
¨
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where the ’s are independently and identically distributed as and
is the number of data points. ¤
The model is linear in the © ’s.
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