r - 使用 `plm()` 估计具有嵌套结构的重复测量随机效应模型

Question

是否可以使用 plm 中的 plm() 来估计一个具有嵌套结构的重复测量随机效应模型包？

我知道可以使用 lme4 中的 lmer()包裹。但是，lmer() 依赖似然框架，我很想用 plm() 来实现。

这是我的最小工作示例，灵感来自 this question .首先是一些需要的包和数据，

# install.packages(c("plm", "lme4", "texreg", "mlmRev"), dependencies = TRUE)
data(egsingle, package = "mlmRev")

数据集 egsingle 是一个不平衡的面板，由 1721 名学童组成，分为 60 所学校，跨越五个时间点。有关详细信息，请参阅 ?mlmRev::egsingle

一些轻数据管理

dta <- egsingle
dta$Female <- with(dta, ifelse(female == 'Female', 1, 0))

此外，相关数据的片段

dta[118:127,c('schoolid','childid','math','year','size','Female')]
#>     schoolid   childid   math year size Female
#> 118     2040 289970511 -1.830 -1.5  502      1
#> 119     2040 289970511 -1.185 -0.5  502      1
#> 120     2040 289970511  0.852  0.5  502      1
#> 121     2040 289970511  0.573  1.5  502      1
#> 122     2040 289970511  1.736  2.5  502      1
#> 123     2040 292772811 -3.144 -1.5  502      0
#> 124     2040 292772811 -2.097 -0.5  502      0
#> 125     2040 292772811 -0.316  0.5  502      0
#> 126     2040 293550291 -2.097 -1.5  502      0
#> 127     2040 293550291 -1.314 -0.5  502      0

现在，严重依赖Robert Long's answer ，这就是我如何使用 lme4 中的 lmer() 估计具有嵌套结构的重复测量随机效应模型包，

dta$year <- as.factor(dta$year)
require(lme4)
Model.1 <- lmer(math ~ Female + size + year + (1 | schoolid /childid), dta)
# summary(Model.1)

我在 man 页面中查找 plm()，它有一个索引命令 index，但它只需要一个索引和时间，即 index = c("childid", "year")，忽略 schoolid 模型将如下所示，

dta$year <- as.numeric(dta$year) 
library(plm)
Model.2 <- plm(math~Female+size+year, dta, index = c("childid", "year"), model="random")
# summary(Model.2)

总结问题

How can I, or is it even possible, to specify a repeated measures random effects model with a nested structure, like Model.1, using plm() from the plm package?

下面是两个模型的实际估计结果，

# require(texreg)
names(Model.2$coefficients) <- names(coefficients(Model.1)$schoolid) #ugly!
texreg::screenreg(list(Model.1, Model.2), digits = 3)  # pretty! 
#> ==============================================================
#>                                    Model 1        Model 2     
#> --------------------------------------------------------------
#> (Intercept)                           -2.693 ***    -2.671 ***
#>                                       (0.152)       (0.085)   
#> Female                                 0.008        -0.025    
#>                                       (0.042)       (0.046)   
#> size                                  -0.000        -0.000 ***
#>                                       (0.000)       (0.000)   
#> year-1.5                               0.866 ***     0.878 ***
#>                                       (0.059)       (0.059)   
#> year-0.5                               1.870 ***     1.882 ***
#>                                       (0.058)       (0.059)   
#> year0.5                                2.562 ***     2.575 ***
#>                                       (0.059)       (0.059)   
#> year1.5                                3.133 ***     3.149 ***
#>                                       (0.059)       (0.060)   
#> year2.5                                3.939 ***     3.956 ***
#>                                       (0.060)       (0.060)   
#> --------------------------------------------------------------
#> AIC                                16590.715                  
#> BIC                                16666.461                  
#> Log Likelihood                     -8284.357                  
#> Num. obs.                           7230          7230        
#> Num. groups: childid:schoolid       1721                      
#> Num. groups: schoolid                 60                      
#> Var: childid:schoolid (Intercept)      0.672                  
#> Var: schoolid (Intercept)              0.180                  
#> Var: Residual                          0.334                  
#> R^2                                                  0.004    
#> Adj. R^2                                             0.003    
#> ==============================================================
#> *** p < 0.001, ** p < 0.01, * p < 0.05    

Answer 1

基于 Helix123's comment我在 plm 的 plm() 中为 具有嵌套结构的重复测量随机效应模型 编写了以下模型规范使用 Wallace 和 Hussain 的 ( 1969 ) 方法的包，即 random.method = "walhus"，用于估计方差分量，

p_dta <- pdata.frame(dta, index = c("childid", "year", "schoolid"))        
Model.3 <- plm(math ~ Female + size + year, data = p_dta, model = "random",
               effect = "nested", random.method = "walhus")

如我所料，在下面的 Model.3 中看到的结果与 Model.1 中的估计值几乎相同。只有拦截略有不同(见下面的输出)。

I wrote the above based on the example from Baltagi, Song and Jung (2001) provided in ?plm. In the Baltagi, Song and Jung (2001)-example the variance components are estimated first using Swamy and Arora (1972), i.e. random.method = "swar", and second with using Wallace and Hussain's (1969). Only the Nerlove (1971) transformation does not converge using the Song and Jung (2001)-data. Whereas it was only Wallace and Hussain's (1969)-method that could converge using the egsingle data-set.

Any authoritative references on this would be appreciated. I'll keep working at it.

names(Model.3$coefficients) <- names(coefficients(Model.1)$schoolid) 
texreg::screenreg(list(Model.1, Model.3), digits = 3,
                  custom.model.names = c('Model 1', 'Model 3')) 
#> ==============================================================
#>                                    Model 1        Model 3     
#> --------------------------------------------------------------
#> (Intercept)                           -2.693 ***    -2.697 ***
#>                                       (0.152)       (0.152)   
#> Female                                 0.008         0.008    
#>                                       (0.042)       (0.042)   
#> size                                  -0.000        -0.000    
#>                                       (0.000)       (0.000)   
#> year-1.5                               0.866 ***     0.866 ***
#>                                       (0.059)       (0.059)   
#> year-0.5                               1.870 ***     1.870 ***
#>                                       (0.058)       (0.058)   
#> year0.5                                2.562 ***     2.562 ***
#>                                       (0.059)       (0.059)   
#> year1.5                                3.133 ***     3.133 ***
#>                                       (0.059)       (0.059)   
#> year2.5                                3.939 ***     3.939 ***
#>                                       (0.060)       (0.060)   
#> --------------------------------------------------------------
#> AIC                                16590.715                  
#> BIC                                16666.461                  
#> Log Likelihood                     -8284.357                  
#> Num. obs.                           7230          7230        
#> Num. groups: childid:schoolid       1721                      
#> Num. groups: schoolid                 60                      
#> Var: childid:schoolid (Intercept)      0.672                  
#> Var: schoolid (Intercept)              0.180                  
#> Var: Residual                          0.334                  
#> R^2                                                  0.000    
#> Adj. R^2                                            -0.001    
#> ==============================================================
#> *** p < 0.001, ** p < 0.01, * p < 0.05#>