Is the fixed effect model decentralized
1、 The least square method (also known as the least square method) is a mathematical optimization technology. It finds the best function matching of data by minimizing the sum of squares of errors
The least square method can be used to obtain the unknown data and minimize the sum of squares of the errors between the obtained data and the actual data. The least square method can also be used for curve fitting. Other optimization problems can also be expressed by minimizing energy or maximizing entropy 
fixed effects model, namely fixed effects regression model, referred to as FEM, is a panel data analysis method
it refers to the experimental design in which the experimental results only want to compare the differences between the specific categories or categories of each self variable and the interaction effect between the specific categories or categories of other self variables, and do not want to infer other categories or categories not included in the same self variable. Fixed effect regression is a kind of variable method in spatial panel data that changes with indivials but not with time
The fixed effect model is applied to panel data analysis, while the least square method is applied to algebraextended data:
I. application of least square method in transportation
the purpose of traffic occurrence prediction is to establish the quantitative relationship between the traffic volume generated by zoning and the variables such as land use and socio-economic characteristics of zoning, and calculate the traffic volume generated by each zoning in the planning year. Since a trip has two endpoints, we need to analyze the traffic generated and the traffic attracted by a zone respectively. There are usually two methods for traffic prediction: regression analysis and cluster analysis
regression analysis is based on the statistical analysis of dependent variables and one or more independent variables to establish the relationship between dependent variables and independent variables. The simplest case is univariate regression analysis, and the general formula is y= α+β Where y is the dependent variable and X is the independent variable, α and β It's a regression coefficient
if the above formula is used to predict the traffic generation of the residential area, all variables are marked with the following I; If it is used to study the traffic attraction of a zone, all variables are marked with the following J. The regression coefficient in the above formula can be obtained according to the least square method:
where x is the independent variable value of the planning year and Y is the forecast value of the traffic generation (or attraction) of the planning year
1、 It means different:
fixed effect model, which means that the selected groups are intended to be compared
random effect model means that it is not only the groups in the design that are to be compared, but also the population that can be represented through the comparison of these groups
Second, the meaning is different:& 119886; Each treatment can be selected by the experimenter. At this time, the conclusion is only applicable to the ﹥ 119886 considered in the analysis; However, it can not be extended to the similar factor level that has not been considered clearly. In this case, the parameters of the model are & 120583&# 120591; 2, 𝜎 2 This is called the fixed effect model
𝑎 A process can be considered as a random sample from a larger population. In this case, the conclusion
can be extended to all treatments in the whole. Here, &; 2 is a random variable, obeying a certain distribution. It needs to be tested on the basis of; 2
and try to estimate this variability. This is called the random effects model
extended data:
in the panel data linear regression model, if for different sections or different time series, only the intercept term of the model is different, and the slope coefficient of the model is the same, then this model is called fixed effect model. In addition to fixed effect model, typical panel data analysis methods include random effect model and mixed effect model
the fixed effects model (FEM) assumes that all the included studies share the same real effects, while the real effects in the random effects model (REM) change with different studies. Based on the calculation of different models, the mean values of the combined effects are also different
the fixed effect model indicates that you intend to compare the selected groups. For example, I want to compare the efficacy of three drugs. My purpose is to compare the differences between the three drugs, and I don't want to promote them. These three drugs are not sampled from many kinds of drugs and do not want to be promoted to other drugs. The conclusion is limited to these three drugs“ This is the meaning of "fixed". These three drugs are fixed, not randomly selected
random effect model, which means that you want to compare not only the groups in your design, but also the population they can represent. For example, if you want to know whether the employment rate of famous universities is higher than that of ordinary universities, you choose Peking University, Tsinghua University, Beijing Business University and Beijing University of science and technology for comparison. Your purpose is not to compare the employment rate differences among these four universities, but to explain the differences between famous universities and ordinary universities they represent. Your conclusion will not be limited to these four universities, but will be extended to a wider range of famous brands and ordinary universities“ This is the meaning of "random". These four schools are randomly selected from famous and ordinary universities.
the fixed effect model indicates that you intend to compare the selected groups. For example, I want to compare the efficacy of three drugs. My purpose is to compare the differences between the three drugs, and I don't want to promote them. These three drugs are not sampled from many kinds of drugs and do not want to be promoted to other drugs. The conclusion is limited to these three drugs“ This is the meaning of "fixed". These three drugs are fixed, not randomly selected
the random effect model means that you want to compare not only the groups in your design, but also the population they can represent. For example, if you want to know whether the employment rate of famous universities is higher than that of ordinary universities, you choose Peking University, Tsinghua University, Beijing Business University and Beijing University of science and technology for comparison. Your purpose is not to compare the employment rate differences among these four universities, but to explain the differences between famous universities and ordinary universities they represent. Your conclusion will not be limited to these four universities, but will be extended to a wider range of famous brands and ordinary universities“ This is the meaning of "random". These four schools are randomly selected from famous and ordinary universities.
when doing multiple linear regression, do you pay attention to selecting the probability value of variable control? The default value is 0.05, and the default value is 0.1. If the probability value is set differently, the number of independent variables selected is certainly different
correlation analysis only considers the relationship between two variables, but does not consider the interaction between all variables. When it is found in the correlation analysis that there is a strong correlation between a variable and the dependent variable, but in the regression analysis, it is not necessarily left in the regression model, because in the multiple regression model, there is often a strong correlation between several independent variables, which affects the effect of regression, so several strongly correlated variables may only leave one or fewer variables in the model& lt;/ ol>