felm固定效应回归报错：chol.default维度大于0问题求助

问题描述 #

尝试运行以下固定效应线性回归模型：

regression1 <- felm(average_score ~ giveaway + giveaway:factor(copytype) +
                                       giveaway:winning_odds | movie_id + year_month ,
                    data = movielist)

持续触发错误：

Error in chol.default(mat[ok, ok]) : 'a' must have dims > 0
In addition: Warning message:
In chol.default(mat, pivot = TRUE, tol = tol) :
  the matrix is either rank-deficient or indefinite

已排查确定报错与movie_id变量相关，该变量为电影唯一标识符，用于控制电影间差异。尝试过移除NA值、将movie_id转为因子等方法，均未解决问题。

数据集示例 #

> movie_id  title       average score  giveaway copytype winning_odds year month
> 259764   Romeo & juliet     4.68       0       1        NA          1689-04
> 58697    James Bond         3.98       1       3        0.0036      2008-07

可复现代码 #

movielist <- structure(list(c(49207064L, 40610763L, 18342451L, 24611562L,
18112455L, 37954232L, 41559097L, 32982694L, 30078050L, 26205520L,
45212165L, 25257581L, 39838159L, 28146924L, 48977227L, 28152663L,
19358557L, 20295281L, 40011514L, 12407923L, 13631830L, 22889883L,
1538505L, 37823518L, 13614942L, 48919775L, 14553840L, 6098580L,
17868537L, 11787536L), c("True Blue Cowboy", "SEVENTEEN: 17",
"Translations from Bark Beetle: Poems", "Hard Beat (Driven, #7)",
"House of Steel (Unraveled, #1)", "Rx", "Ethic 2", "Black History In
Its Own Words",  "My Hope Next Door", "The Dragon's Egg", "The Memory
Thief",  "The Big Old House And The Scary Storm", "Hong Kong Noir",
"The Messengers: Discovered",  "Trouble", "Altered", "What Goes on
Tour", "About Matters of the Hurt: Love Stories - Round the Clock",
"The 21: A Journey Into the Land of Coptic Martyrs", "These Arms of
Mine",  "The Breast of Everything", "The Ghost Network",
"Unconventional Flying Objects: A Scientific Analysis: A Scientific
Analysis",  "The Way of Life: Experiencing the Culture of Heaven on
Earth",  "Land", "Alan Cumming: Legal Immigrant", "I Could Pee On
This: And Other Poems By Cats",  "Heaven is Small", "The Wayang at
Eight Milestone: Stories & Essays",  "Turning Point"), c(2020L, 2018L,
2014L, 2015L, 2013L, 2018L,  2018L, 2017L, 2016L, 2015L, 2019L, 2014L,
2018L, 2016L, 2019L,  2016L, 2014L, 2013L, 2019L, 2012L, 2012L, 2015L,
1995L, 2018L,  2012L, 2019L, 2012L, 2009L, 2013L, 2011L), c(2L, 9L,
4L, 11L,  6L, 9L, 10L, 2L, 9L, 8L, 4L, 10L, 12L, 5L, 11L, 2L, 2L, 12L,
2L, 1L, 4L, 5L, 12L, 9L, 4L, 11L, 8L, 4L, 10L, 10L), c(4.27,
3.71, 4.09, 4.19, 3.48, 3.81, 4.74, 4.16, 4.36, 3.98, 4.08, 5,
3.8, 4.34, 3.72, 3.75, 3.62, 3.91, 4.09, 4.06, 4.67, 3.1, 4.04,
4.63, 3.89, 4.24, 3.96, 3.31, 3.97, 3.95), c(385L, 17L, 22L,  3887L, 132L, 817L, 1792L, 454L, 1139L, 1113L, 1154L, 4L, 127L,  108L, 446L,
49L, 1680L, 11L, 113L, 88L, 12L, 1359L, 34L, 224L,  2490L, 226L,
8182L, 140L, 30L, 51L), c(52L, 0L, 4L, 397L, 27L,  120L, 246L, 103L,
190L, 82L, 213L, 1L, 27L, 35L, 57L, 39L, 174L,  6L, 50L, 23L, 6L,
273L, 7L, 23L, 246L, 26L, 1243L, 31L, 3L, 17L ), c(2L, 2L, 1L, 1L, 1L,
1L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 1L,  2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 2L, 3L, 1L, 1L, 1L, 1L ), c("2020-2", "2018-9", "2014-04",
"2015-11", "2013-06", "2018-09",  "2018-10", "2017-02", "2016-9",
"2015-8", "2019-4", "2014-10",  "2018-12", "2016-05", "2019-11",
"2016-02", "2014-2", "2013-12",  "2019-02", "2012-01", "2012-04",
"2015-05", "1995-12", "2018-9",  "2012-4", "2019-11", "2012-08",
"2009-4", "2013-10", "2011-10" ), c(0L, 0L, 1L, 1L, 1L, 1L, 0L, 1L,
0L, 0L, 0L, 1L, 0L, 1L,  0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 0L,
0L, 1L, 0L, 1L, 1L ), c(0, 0, 0.0173913043478261, 0.0114285714285714,
0.00134952766531714,
0.00715307582260372, 0, 0.00154798761609907, 0, 0, 0, 0.333333333333333,  0, 0.00201207243460765, 0, 0.00590841949778434, 0, 0.00284900284900285,
0.0109170305676856, 0.00323624595469256, 0.00627615062761506,
0.000873362445414847, 0.00354609929078014, 0, 0, 0, 0.00109289617486339,  0, 0.00148809523809524, 0.08110300081103)), row.names = c(NA,
-30L), class = c("data.table", "data.frame"), .internal.selfref = <pointer: 0x00000191ca3c32b0>, names = c("movie_id",  "title",
"publication_year", "publication_month", "average_rating",
"ratings_count", "text_reviews_count", "copytype", "year_month",
"giveaway", "winning_odds"))

解决方案 #

1. 修正变量名匹配错误 #

模型中使用的average_score在数据集中实际名为average_rating，变量名不匹配会导致模型无法识别响应变量，直接引发矩阵维度异常。修正后的模型代码：

regression1 <- felm(average_rating ~ giveaway + giveaway:factor(copytype) +
                                       giveaway:winning_odds | movie_id + year_month ,
                    data = movielist)

2. 解决固定效应共线性问题 #

你的数据集中每个movie_id仅对应1条观测记录，同时加入movie_id和year_month固定效应会导致完全共线性——电影固定效应已吸收了时间固定效应的全部信息，反之亦然。可选择以下两种方案：

• 仅保留一组固定效应（推荐保留movie_id以控制电影异质性）：

  regression1 <- felm(average_rating ~ giveaway + giveaway:factor(copytype) +
                                           giveaway:winning_odds | movie_id ,
                        data = movielist)
  

• 若后续能获取多时间点的电影数据，再同时加入两组固定效应。

3. 处理交互项与主效应的共线性 #

giveaway是0/1二分类变量，与factor(copytype)的交互项可能和主效应存在共线性。可通过中心化连续变量缓解：

# 中心化winning_odds，减少共线性影响
movielist$winning_odds_centered <- movielist$winning_odds - mean(movielist$winning_odds, na.rm = TRUE)

regression1 <- felm(average_rating ~ giveaway + giveaway:factor(copytype) +
                                           giveaway:winning_odds_centered | movie_id ,
                        data = movielist)

4. 彻底清理NA值 #

重新确认并移除含NA的观测：

movielist_clean <- na.omit(movielist)

5. 调整felm的共线性检测阈值 #

若仍存在秩亏警告，可通过tol参数放宽共线性检测的阈值：

regression1 <- felm(average_rating ~ giveaway + giveaway:factor(copytype) +
                                       giveaway:winning_odds | movie_id ,
                    data = movielist_clean, tol = 1e-6)

内容的提问来源于stack exchange，提问作者Pinot1999