The Logit Model
The Logit Model
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逻辑模型
DOI：
10.1007/978-3-642-97225-6_8
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发表时间：
1990
期刊：
影响因子：
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通讯作者：
E. B. Andersen
中科院分区：
文献类型：
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作者：
E. B. Andersen
在第4、5、6章中，分类变量以对称的方式出现在模型中。在许多情况下，例如在第6章的示例6.1和6.2中，其中一个变量是特别有趣的。对于例6.1中的生存数据，生存是我们特别感兴趣的变量，问题是研究其他三个变量是否影响了生存的机会。因此，例6.1中的变量B可以称为响应变量，变量A、C和解释变量。这一术语与回归分析中使用的术语相同，当生存率被视为响应变量时，例6.1中的数据实际上可以通过回归模型进行分析。在例6.2中，碰撞在卡车上的位置可以看作是一个响应变量。我们在这里主要对解释变量A的影响感兴趣，即1971年11月引入的安全措施，但必须考虑到其他解释变量，即卡车是否停放以及光线条件如何，可能对碰撞的位置很重要。当响应变量为二元而解释变量为分类变量时，适当的回归模型称为逻辑模型。更准确地说，logit模型的假设是：(a)响应变量是二元的。(b)响应变量和解释变量形成的列联表可以用对数线性模型来描述。
In chapters 4, 5 and 6 the categorical variables appeared in the model in a symmetrical way. In many situations, for example in examples 6.1 and 6.2 in chapter 6, one of the variable is of special interest. For the survival data in example 6.1, survival is the variable of special interest, and the problem is to study if the other three variables have influenced the chance of survival. Variable B in example 6.1 may, therefore, be called aresponse variableand variables A, C and Dexplanatory variables. This terminology is the same as the one used in regression analysis, and when survival is regarded as a response variable the data in example 6.1 can in fact be analysed by a regression model. In example 6.2 the position on the truck of the collision can be regarded as a response variable. We are here primarily interested in the effect of explanatory variable A, i.e. the introduction of the safety measure in November 1971, but have to take into account that the other explanatory variables, i.e. whether the truck was parked or not and what the light conditions were, may be of importance for the location of the collision. When the response variable is binary and the explanatory variables are categorical, the appropriate regression model is known as thelogit model. More precisely the assumptions for a logit model are:(a)The response variable is binary.(b)The contingency table formed by the reponse variable and the explanatory variables can be described by a log-linear model.