Fixed effect

方差分析主要有三种模型：即固定效应模型（fixed effects model），随机效应模型（random effects model），混合效应模型（mixed effects model）。

所谓的固定、随机、混合，主要是针对分组变量而言的。

固定效应模型，表示你打算比较的就是你现在选中的这几组。

例如，我想比较3种药物的疗效，我的目的就是为了比较这三种药的差别，不想往外推广。

这三种药不是从很多种药中抽样出来的，不想推广到其他的药物，结论仅限于这三种药。

“固定”的含义正在于此，这三种药是固定的，不是随机选择的。

随机效应模型，表示你打算比较的不仅是你的设计中的这几组，而是想通过对这几组的比较，推广到他们所能代表的总体中去。

例如，你想知道是否名牌大学的就业率高于普通大学，你选择了北大、清华、北京工商大学、北京科技大学4所学校进行比较，你的目的不是为了比较这4所学校之间的就业率差异，而是为了说明他们所代表的名牌和普通大学之间的差异。

你的结论不会仅限于这4所大学，而是要推广到名牌和普通这样的一个更广泛的范围。

“随机”的含义就在于此，这4所学校是从名牌和普通大学中随机挑选出来的。

混合效应模型就比较好理解了，就是既有固定的因素，也有随机的因素。

一般来说，只有固定效应模型，才有必要进行两两比较，随机效应模型没有必要进行两两比较，因为研究的目的不是为了比较随机选中的这些组别。

固定效应和随机效应的选择是大家做面板数据常常要遇到的问题，一个常见的方法是做huasman检验，即先估计一个随机效应，然后做检验，如果拒绝零假设，则可以使用固定效应，反之如果接受零假设，则使用随机效应。

但这种方法往往得到事与愿违的结果。

另一个想法是在建立模型前根据数据性质确定使用那种模型，比如数据是从总体中抽样得到的，则可以使用随机效应，比如从N个家庭中抽出了M个样本，则由于存在随机抽样，则建议使用随机效应，反之如果数据是总体数据，比如31个省市的Gdp，则不存在随机抽样问题，可以使用固定效应。

• It is suitable for panels of states or countries, where the same individuals would be selected in each sample.
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Panel Data DGP’s (cont.)
• With longitudinal data on individual workers or consumers, we draw a different set of individuals from the population each time we collect a sample.
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A Panel Data DGP
Yit 0i 1 X 1it 2 X 2i 3 X 3t .. K X Kit it i 1...n; t 1...T E ( it ) 0 Var ( it ) 2 E ( it i 't ' ) 0 if i i ' OR t t ' E ( X jit it ) 0 for all j , i, t
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Panel Data DGP’s (cont.)
• In the Distinct Intercepts DGP, the unobserved heterogeneity is absorbed into the individual-specific intercept 0i
• In the second DGP, the unobserved heterogeneity is absorbed into the individual fixed component of the error term, vi • This DGP is an “Error Components Model误差成分模型.”

固定年份效应和行业效应的双向固定效应模型1.在双向固定效应模型中，固定年份效应代表了时间的固定影响。

In the two-way fixed effects model, the fixed year effect represents the fixed impact of time.2.行业效应则代表了不同行业对观测变量的影响。

The industry effect represents the impact of different industries on the observed variables.3.这种模型可以帮助分析时间和行业对于变量的影响。

This model can help analyze the impact of time andindustry on variables.4.当我们考虑固定年份效应和行业效应时，我们可以减少时间和行业带来的混淆。

When we consider fixed year effects and industry effects, we can reduce the confusion caused by time and industry.5.这种模型在经济学和社会科学研究中得到了广泛的应用。

This model has been widely used in economic and social science research.6.固定年份效应和行业效应可以帮助我们更准确地理解变量之间的关系。

Fixed year effects and industry effects can help usbetter understand the relationships between variables.7.通过控制固定年份效应和行业效应，我们可以更好地理解时间和行业的影响。

By controlling fixed year effects and industry effects, we can better understand the impact of time and industry.8.固定年份效应和行业效应可以帮助我们找出真正的因果关系。

固定效应混合效应英文回答：Fixed Effects.Fixed effects are used to control for unobserved time-invariant heterogeneity. This means that they absorb any time-invariant factors that may be affecting the dependent variable. This can be useful in situations where there are unobserved differences between individuals or groups that are likely to affect the outcome. For example, if we are interested in studying the effect of a policy change on economic growth, we may want to control for unobservedtime-invariant differences between countries. This could be done by using fixed effects for country.Fixed effects are estimated by subtracting the group mean from each observation. This removes any time-invariant heterogeneity from the data. The remaining variation in the dependent variable is then due to time-varying factors.Mixed Effects.Mixed effects models combine fixed effects with random effects. This allows us to control for both time-invariant and time-varying unobserved heterogeneity. Random effects are used to control for unobserved time-invariant heterogeneity that varies across groups. This can be useful in situations where there are unobserved differences between groups that are likely to affect the outcome, but these differences may vary over time. For example, if we are interested in studying the effect of a policy change on student achievement, we may want to control for unobserved time-invariant differences between schools. This could be done by using random effects for school.Mixed effects models are estimated using a maximum likelihood procedure. This procedure estimates the fixed effects and random effects simultaneously.When to Use Fixed Effects vs. Mixed Effects.The choice between fixed effects and mixed effects depends on the nature of the unobserved heterogeneity. If the unobserved heterogeneity is time-invariant, then fixed effects are sufficient. If the unobserved heterogeneity is time-varying, then mixed effects are necessary.In some cases, it may be possible to use both fixed effects and mixed effects. This is known as a fixed effects mixed effects model. This type of model can be used to control for both time-invariant and time-varying unobserved heterogeneity.Advantages and Disadvantages of Fixed Effects and Mixed Effects.Fixed effects and mixed effects have both advantages and disadvantages.Advantages of fixed effects:Fixed effects can be used to control for unobserved time-invariant heterogeneity.Fixed effects are relatively easy to estimate.Fixed effects can be used with a variety of statistical software packages.Disadvantages of fixed effects:Fixed effects can only be used to control for time-invariant heterogeneity.Fixed effects can lead to a loss of degrees of freedom.Fixed effects can be biased if the unobserved heterogeneity is not truly time-invariant.Advantages of mixed effects:Mixed effects can be used to control for both time-invariant and time-varying unobserved heterogeneity.Mixed effects are more efficient than fixed effects when the unobserved heterogeneity is time-varying.Mixed effects can be used with a variety of statistical software packages.Disadvantages of mixed effects:Mixed effects can be more difficult to estimate than fixed effects.Mixed effects can be biased if the unobserved heterogeneity is not correctly specified.中文回答：固定效应。