嵌套模型(Nested Models)和非嵌套模型(Non-Nested Models) 的统计检验(R语言)

超、凢脫俗 2023-02-28 04:30 74阅读 0赞

在R语言中，对于嵌套(nest)模型可以使用likelihood ratio tests(似然比检验)，对于非嵌套模型(Non-Nested Models) 可以使用Davidson and MacKinnon’s J-test。这两种检验在论文中经常使用如：  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3F5MjAxMTU1NDk_size_16_color_FFFFFF_t_70]

如下为其代码示例：

require(lmtest)
    ## Fit two competing, non-nested models for aggregate 
    ## consumption, as in Greene (1993), Examples 7.11 and 7.12
    
    ## load data and compute lags
    data(USDistLag)
    usdl <- na.contiguous(cbind(USDistLag, lag(USDistLag, k = -1)))
    colnames(usdl) <- c("con", "gnp", "con1", "gnp1")
    
    ## C(t) = a0 + a1*Y(t) + a2*C(t-1) + u
    fm1 <- lm(con ~ gnp + con1, data = usdl)
    
    ## C(t) = b0 + b1*Y(t) + b2*Y(t-1) + v
    fm2 <- lm(con ~ gnp + gnp1, data = usdl)
    
    fm3 <- lm(con ~ gnp, data = usdl)
    ## Cox test in both directions:
    coxtest(fm1, fm2)
    
    ## ...and do the same for jtest() and encomptest().
    ## Notice that in this particular case they are coincident.
    jtest(fm1, fm2)
    encomptest(fm1, fm2)
    # likelihood ratio tests
    lrtest(fm3, fm1)

检验结果如下图所示：  
![在这里插入图片描述][20200720105334727.png]

![在这里插入图片描述][20200720105345175.png]  
![在这里插入图片描述][2020072010540051.png]  
![在这里插入图片描述][20200720105410296.png]

# 参考 #

http://math.furman.edu/~dcs/courses/math47/R/library/lmtest/html/jtest.html  
https://www.bauer.uh.edu/rsusmel/phd/ec1-6.pdf  
http://www.empowerstats.com/cn/manuals/RCH/html/z\_lrt.pdf

[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3F5MjAxMTU1NDk_size_16_color_FFFFFF_t_70]: /images/20230209/cb22227ace2d45f5a7f47c77f665e650.png
[20200720105334727.png]: /images/20230209/d8c256cfb91b4cb4a75e339dce39ff19.png
[20200720105345175.png]: /images/20230209/8e3dab04bbc84077b3a806df4b5728b6.png
[2020072010540051.png]: /images/20230209/39c2f7a5f71b481599f26fe859f267b2.png
[20200720105410296.png]: https://img-blog.csdnimg.cn/20200720105410296.png