plm包随机效应模型（Swamy-Arora估计）奇异矩阵错误排查求助

使用R的plm包拟合随机效应模型（默认Swamy-Arora估计）时，加入年份虚拟变量后出现奇异矩阵错误，具体情况如下：

运行代码 #

library(plm)
plm(y ~ x + factor(year), index = "panel", model = "random", data = df)

错误信息 #

Error in solve.default(crossprod(ZBeta)) : 
 Lapack routine dgesv: system is exactly singular: U[15,15] = 0

问题细节 #

• 错误由factor(year)引发，但相同数据和模型在Stata中执行xtreg y x i.year, re sa（sa对应Swamy-Arora估计）可正常运行
• 已尝试移除仅含单个观测的年份，问题仍未解决

数据dput输出 #

> dput(df)
structure(list(y = c(0.32, 0.51, 0.26, 0.99, 0.59, 0.43, 0.6, 
0.86, 1, 0.97, 0.89, 0.63, 0.55, 0.58, 0.26, 0.69, 0.87, 0.17, 
0.09, 0, 0.87, 0.39, 0.36, 0.73, 0.13, 0.61, 0.36, 0.64, 0.72, 
0.95, 0.8, 0.96, 0.32, 0.91, 0.77, 0.14, 0.37, 0.57, 0.81, 0.98, 
0.5, 0.23, 0.8, 0.04, 0.84, 0.12, 0.56, 0.22, 0.49, 0.65, 0.59, 
0.98, 0.71, 0.58, 0.75, 0.77, 0.49, 0.72, 0.29, 0.2, 0.67, 0.06, 
0.36, 0.44, 0.65, 0.29, 0.85, 0.75, 0.2, 0.44, 0.7, 0.54, 0.19, 
0.47, 0.83, 0.47, 0.23, 0.43, 0.6, 0.48, 0.63, 0.95, 1, 0.46, 
0.28, 0.88, 0.82, 0.71, 0.57, 0.25, 0.78, 0.07, 0.45, 0.7, 0.08, 
0.2, 0.5, 0.13, 0.56, 0.12, 0.08, 0.29, 0.89, 0.37, 0.96, 0.83, 
0.81, 0.02, 0.96, 0.83, 0.51, 0.04, 0.04, 0.06, 0.44, 0.61, 0.99, 
0.83, 0.31, 0.82, 0.12, 0.18, 0.89, 0.23, 0.46, 0.73, 0.76, 0.49, 
0.32, 0.87, 0.11, 0.01, 0.96, 0.86, 0.91, 0.68, 0.8, 0.63, 0.94, 
1, 0.59, 0.5, 0.01, 0.48, 0.86, 0.92, 0.07, 0.15, 0.07, 0.33, 
0.6, 0.52, 0.12, 0.59, 0.56, 0.56, 0.55, 0.18, 0.11, 0.16, 0.27, 
0.06, 0.62, 0.34, 0.69, 0.87, 0.32, 0.31, 0.1, 0.44, 0.99, 0.96, 
0.72, 0.19, 0.81), x = c(0.25, 0.41, 0.55, 0.77, 0.95, 0.2, 0.36, 
0.58, 0.27, 0.56, 0.53, 0.88, 0.55, 0.43, 0.19, 0.54, 0.2, 0.37, 
0.18, 0.09, 0.26, 0.15, 0.75, 0.08, 0.55, 0.06, 0.23, 0.9, 0.12, 
0.51, 0.58, 0.54, 0.88, 0.24, 0.9, 0.85, 0.32, 0.43, 0.66, 0.12, 
0.09, 0.75, 0.5, 0.11, 0.07, 0.04, 0.6, 0.96, 0.39, 0.61, 0.23, 
0.28, 0.45, 0.55, 0.52, 0.99, 0.96, 0.64, 0.31, 0.47, 0.01, 0.56, 
0.7, 0.88, 0.13, 0.87, 0.2, 0.62, 0.42, 0.85, 0.5, 0.22, 0.52, 
0.15, 0.31, 0.23, 0.09, 0.76, 0.56, 0.29, 0.42, 0.87, 0.75, 0.78, 
0.67, 0.94, 0.69, 0.74, 0.07, 0.22, 0.47, 0.52, 0.85, 0.28, 0.47, 
0.39, 0.34, 0.94, 0.14, 0.5, 0.16, 0.2, 0.22, 0.71, 0.66, 0.68, 
0.54, 0.24, 0.04, 0.1, 0.44, 0.54, 0.23, 0.53, 0.24, 0.14, 0.99, 
0.18, 0.93, 0.99, 0.49, 0.39, 0.78, 0.41, 0.31, 0.11, 0.75, 0.59, 
0.85, 0.31, 0.8, 0.21, 0.67, 0.31, 0.21, 0.88, 0.84, 0.32, 0.36, 
0.89, 0.4, 0.82, 0.54, 0.18, 0.4, 0.71, 0.28, 0.83, 0.78, 0.07, 
0.93, 0.47, 0.44, 0.49, 0.71, 0.69, 0, 0.47, 0.72, 0.06, 0.13, 
0.65, 0.12, 0.26, 0.67, 0.8, 0.4, 0.82, 0.22, 0.16, 0.32, 0.01, 
0.53, 0.26, 0.99), panel = c("p1", "p1", "p1", "p1", "p1", "p1", 
"p2", "p2", "p2", "p2", "p2", "p2", "p2", "p2", "p2", "p3", "p3", 
"p3", "p3", "p4", "p4", "p4", "p4", "p5", "p5", "p5", "p5", "p6", 
"p6", "p6", "p6", "p6", "p6", "p6", "p6", "p6", "p7", "p7", "p7", 
"p7", "p7", "p7", "p7", "p7", "p7", "p8", "p8", "p8", "p8", "p8", 
"p8", "p8", "p8", "p9", "p9", "p9", "p9", "p10", "p10", "p10", 
"p10", "p10", "p10", "p11", "p11", "p11", "p11", "p11", "p11", 
"p11", "p11", "p11", "p12", "p12", "p12", "p12", "p12", "p12", 
"p12", "p12", "p12", "p13", "p13", "p13", "p13", "p13", "p13", 
"p13", "p13", "p13", "p14", "p14", "p14", "p15", "p15", "p15", 
"p15", "p16", "p16", "p16", "p16", "p16", "p16", "p16", "p16", 
"p16", "p17", "p17", "p17", "p17", "p17", "p17", "p17", "p17", 
"p17", "p18", "p18", "p18", "p18", "p19", "p19", "p19", "p19", 
"p19", "p19", "p19", "p19", "p19", "p20", "p20", "p20", "p20", 
"p21", "p21", "p21", "p21", "p22", "p22", "p22", "p22", "p22", 
"p22", "p22", "p22", "p22", "p23", "p23", "p23", "p23", "p24", 
"p24", "p24", "p24", "p24", "p24", "p24", "p24", "p25", "p25", 
"p25", "p25", "p26", "p26", "p26", "p26", "p27", "p27", "p27", 
"p27", "p28", "p28", "p28", "p28", "p28", "p28"), year = c(8, 
9, 10, 12, 14, 15, 1, 3, 5, 6, 9, 10, 12, 14, 15, 11, 12, 14, 
15, 10, 12, 14, 15, 10, 12, 14, 15, 1, 3, 5, 6, 9, 10, 12, 14, 
15, 1, 3, 5, 6, 9, 10, 12, 14, 15, 4, 5, 6, 9, 10, 12, 14, 15, 
10, 12, 14, 15, 8, 9, 10, 12, 14, 15, 1, 3, 5, 6, 9, 10, 12, 
14, 15, 1, 3, 5, 6, 9, 10, 12, 14, 15, 2, 3, 5, 6, 9, 10, 12, 
14, 15, 13, 14, 15, 10, 12, 14, 15, 1, 3, 5, 6, 9, 10, 12, 14, 
15, 1, 3, 5, 6, 9, 10, 12, 14, 15, 10, 12, 14, 15, 1, 3, 5, 6, 
9, 10, 12, 14, 15, 10, 12, 14, 15, 10, 12, 14, 15, 1, 3, 5, 6, 
9, 10, 12, 14, 15, 10, 12, 14, 15, 4, 5, 6, 9, 10, 12, 14, 15, 
11, 12, 14, 15, 10, 12, 14, 15, 10, 12, 14, 15, 7, 9, 10, 12, 
14, 15)), row.names = c(NA, -175L), class = "data.frame")

请求解决思路 #

求各位提供可行的解决思路，解决plm包中因年份虚拟变量导致的奇异矩阵错误。

内容的提问来源于stack exchange，提问作者Fr.