所以我非常喜欢用于显示回归模型统计数据的观星包。我一直在使用R和Stata来完成教科书中的一些问题。我发现的一个问题是由观星包打印的置信区间与stata的置信区间不对应。我确定手工操作后，stata中的CI是正确的。
因为问题可能在于我如何处理数据，所以我在此提供它作为可选选项。我主要关心的是确定CI没有回应的原因。从上一篇文章中，这是查找我正在使用的数据的一种可能方式;
install.packages("devtools") # if not already installed
library(devtools)
install_git("https://github.com/ccolonescu/PoEdata")
library(PoEdata) # loads the package in memory
library(multcomp) # for hypo testing
data(fair4) # loads the data set of interest
在Stata中，我使用的数据集的名称称为fair4.dta。对于数据本身，您可以手动使用它，
structure(list(year = structure(c(1880, 1884, 1888, 1892, 1896,
1900, 1904, 1908, 1912, 1916, 1920, 1924, 1928, 1932, 1936, 1940,
1944, 1948, 1952, 1956, 1960, 1964, 1968, 1972, 1976, 1980, 1984,
1988, 1992, 1996, 2000, 2004, 2008), label = "year", format.stata = "%9.0g"),
vote = structure(c(50.2200012207031, 49.8460006713867, 50.4140014648438,
48.2680015563965, 47.7599983215332, 53.1710014343262, 60.0060005187988,
54.4830017089844, 54.7080001831055, 51.681999206543, 36.1189994812012,
58.2439994812012, 58.8199996948242, 40.8409996032715, 62.4580001831055,
54.9990005493164, 53.773998260498, 52.3699989318848, 44.5950012207031,
57.7639999389648, 49.9129981994629, 61.3440017700195, 49.5960006713867,
61.7890014648438, 48.9480018615723, 44.6969985961914, 59.1699981689453,
53.9020004272461, 46.5449981689453, 54.7360000610352, 50.2649993896484,
51.2330017089844, 46.5999984741211), label = "Incumbent share of the two-party presidential vote", format.stata = "%9.0g"),
party = structure(c(-1, -1, 1, -1, 1, -1, -1, -1, -1, 1,
1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1,
-1, -1, 1, 1, -1, -1), label = "= 1 if Democratic incumbent at election time; -1 if a Republican incumbent", format.stata = "%9.0g"),
person = structure(c(0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1,
0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0,
1, 0), label = "= 1 if incumbent is running for election and 0 otherwise", format.stata = "%9.0g"),
duration = structure(c(1.75, 2, 0, 0, 0, 0, 1, 1.25, 1.5,
0, 1, 0, 1, 1.25, 0, 1, 1.25, 1.5, 1.75, 0, 1, 0, 1, 0, 1,
0, 0, 1, 1.25, 0, 1, 0, 1), label = "number of terms incumbent administration in power", format.stata = "%9.0g"),
war = structure(c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0), label = "= 1 for elections of 1920, 1944, and 1948 and 0 otherwise.", format.stata = "%9.0g"),
growth = structure(c(3.87899994850159, 1.58899998664856,
-5.55299997329712, 2.76300001144409, -10.0240001678467, -1.42499995231628,
-2.4210000038147, -6.2810001373291, 4.16400003433228, 2.22900009155273,
-11.4630002975464, -3.87199997901917, 4.6230001449585, -14.4989995956421,
11.7650003433228, 3.90199995040894, 4.27899980545044, 3.5789999961853,
0.690999984741211, -1.45099997520447, 0.377000004053116,
5.10900020599365, 5.04300022125244, 5.91400003433228, 3.75099992752075,
-3.59699988365173, 5.44000005722046, 2.17799997329712, 2.66199994087219,
3.12100005149841, 1.21899998188019, 2.69000005722046, 0.219999998807907
), label = "growth rate GDP in first three quarters of the election year", format.stata = "%9.0g"),
inflation = structure(c(1.97399997711182, 1.05499994754791,
0.603999972343445, 2.2739999294281, 3.41000008583069, 2.54800009727478,
1.44200003147125, 1.87899994850159, 2.17199993133545, 4.2519998550415,
0, 5.16099977493286, 0.18299999833107, 7.19999980926514,
2.49699997901917, 0.0810000002384186, 0, 0, 2.36199998855591,
1.93499994277954, 1.96700000762939, 1.25999999046326, 3.13899993896484,
4.81500005722046, 7.63000011444092, 7.83099985122681, 5.25899982452393,
2.90599989891052, 3.27999997138977, 2.06200003623962, 1.60500001907349,
2.32500004768372, 2.88000011444092), label = "growth rate of GDP deflator during first 15 quarters of admin", format.stata = "%9.0g"),
goodnews = structure(c(9, 2, 3, 7, 6, 7, 5, 8, 8, 3, 0, 10,
7, 4, 9, 8, 0, 0, 7, 5, 5, 10, 7, 4, 5, 5, 8, 4, 2, 4, 8,
1, 3), label = "number of quarters in first 15 with real GDP per capita growth > 3.2", format.stata = "%9.0g")), notes = c("more complete variable definitions in fair.def",
"1"), .Names = c("year", "vote", "party", "person", "duration",
"war", "growth", "inflation", "goodnews"), class = c("tbl_df",
"tbl", "data.frame"), row.names = c(NA, -33L))
所以这里是给我带来麻烦的观星代码：
presidential <- read_dta("~/Directory/fair4.dta")
pres.lm = lm(vote ~ growth, data = subset(presidential,
presidential$year >= 1916)
stargazer(pres.lm,
type = "text",
intercept.bottom = T,
digits = 5,
report = "vc*stp",
ci = T
)
confint(pres.lm, level = 0.95)
考虑置信区间的差异。
(0.52948, 1.24241) # in R, Stargazer
0.5087671 1.263126 # in R, confint(pres.lm)
.5087671 1.263126 # in Stata
我还手动计算了置信区间和confit()以及Stata数字。此数据集的t临界值应为t_(N-2 , prob) = t(22,.0025) = -2.073873。
此外，我确保创建一个全新的数据框架。也就是说，不是在lm()参数内进行子集化，而是先将其子集化。将此方法与前一个方法进行比较时，我仍然得到相同的确切（不正确）置信区间。
# subset into a new dataframe
presidential.1 = subset(presidential, presidential$year >= 1916)
# create the model
pres.lm.2 = lm(vote ~ growth, data = presidential.1)
# compare the two
stargazer(pres.lm,pres.lm.2,
type = "text",
intercept.bottom = F,
digits = 5,
report = "vc*stp",
ci = T,
t.auto = T)
(1) (2)
-----------------------------------------------------------------------
Constant 50.84840*** 50.84840***
(48.86384, 52.83295) (48.86384, 52.83295)
t = 50.21835 t = 50.21835
p = 0.00000 p = 0.00000
growth 0.88595*** 0.88595***
(0.52948, 1.24241) (0.52948, 1.24241)
t = 4.87126 t = 4.87126
p = 0.00008 p = 0.00008
# correct intervals from Stata and R's confint()
growth 0.5087671 1.263126
我是否错误地运行了代码？运行stargazer命令并仅打印系数和t-stats对我来说真的不是什么大不了的事情，但令人失望的是，我必须将confint()作为单独的命令运行，因为Stargazer的输出很华丽。这很奇怪，因为系数估计和t统计是完美的。置信区间有不同程度的关闭，我想知道这可能是什么原因。任何建议将不胜感激。
答案 0 :(得分：1)
简单的答案是stata和confint使用t分布计算置信区间，而stargazer的内部方法使用正态分布。结果是前两者在他们的估计中更加保守，因此与stargazer相比具有更宽的CI。 （好吧，我假设这里有stata，但因为它给出与confint相同的结果，我觉得这是一个安全的假设。）
深入研究stargazer的源代码（第688ff行），我们可以找到如何计算CI：
z.value <- qnorm((1 + .format.ci.level.use)/2)
coef <- .global.coefficients[.global.coefficient.variables[which.variable],i]
se <- .global.std.errors[.global.coefficient.variables[which.variable],i]
ci.lower.bound <- coef - z.value * se
ci.upper.bound <- coef + z.value * se
它使用qnorm来设置临界值。
与confint比较：
a <- (1 - level)/2
a <- c(a, 1 - a)
fac <- qt(a, object$df.residual) ##Relevant line, uses T-distribution
pct <- format.perc(a, 3)
ci <- array(NA, dim = c(length(parm), 2L), dimnames = list(parm,
pct))
ses <- sqrt(diag(vcov(object)))[parm]
ci[] <- cf[parm] + ses %o% fac
比较
#Using normal/z distribution
> pres.lm$coefficients[2] + sqrt(diag(vcov(pres.lm)))[2] %o% c(-qnorm((1 + 0.95)/2), qnorm((1 + 0.95)/2))
[,1] [,2]
growth 0.5294839 1.242409
#Using t-distribution with df degrees of freedom
> df <- pres.lm$df.residual
> pres.lm$coefficients[2] + sqrt(diag(vcov(pres.lm)))[2] %o% c(-qt((1 + 0.95)/2, df), qt((1 + 0.95)/2, df))
[,1] [,2]
growth 0.5087671 1.263126
如果您致力于stargazer，处理此问题的最简单方法可能是使用ci.custom参数：
> stargazer(pres.lm, type = "text", ci.custom = list(confint(pres.lm)))
===============================================
Dependent variable:
---------------------------
vote
-----------------------------------------------
growth 0.886***
(0.509, 1.263)
Constant 50.848***
(48.749, 52.948)
-----------------------------------------------
Observations 24
R2 0.519
Adjusted R2 0.497
Residual Std. Error 4.798 (df = 22)
F Statistic 23.729*** (df = 1; 22)
===============================================
Note: *p<0.1; **p<0.05; ***p<0.01
一旦样本量足够大，t分布就会收敛于z分布，CI之间的差异会变得更小。
set.seed(432)
x1 <- rnorm(10000, 100, 50)
u <- 2 * rnorm(10000)
y <- 50 + x1 * 0.752 * u
fit <- lm(y ~ x1)
> confint(fit)
2.5 % 97.5 %
(Intercept) 39.29108955 54.1821315
x1 -0.02782141 0.1061173
> stargazer(fit, type= "text", ci = T)
===============================================
Dependent variable:
---------------------------
y
-----------------------------------------------
x1 0.039
(-0.028, 0.106)
Constant 46.737***
(39.292, 54.181)
-----------------------------------------------
Observations 10,000
R2 0.0001
Adjusted R2 0.00003
Residual Std. Error 168.194 (df = 9998)
F Statistic 1.313 (df = 1; 9998)
===============================================
Note: *p<0.1; **p<0.05; ***p<0.01
样本量为24时，22自由度的t分布比z更胖！