First, Stata uses a finite sample correction that R does not use when clustering. Second, areg is designed for datasets with many groups, but not a number that grows with the sample size. One example is states in the US. Your plm is much more like xtreg, fe. Although the point estimates produced by areg and xtreg, fe are the same, the estimated VCEs differ with clustering because the commands make different assumptions about whether the number of groups/sensors increases with the sample size. When you cluster with xtreg, fe, the asymptotics relies on the number of groups going to infinity. So this is not an apples to apples comparison.
In your setting, xtreg, fe seems more suitable since many sensors could be added. If you have to replicate areg's output, you can use felm.
Here is an econometrically stupid example demonstrating these claims. Here I am using Roger Newson's rsource to run R from within Stata, but it is not strictly necessary:
. rsource, terminator(END_OF_R)
Assumed R program path: "/usr/local/bin/R"
Beginning of R output
> suppressPackageStartupMessages({
+ require(plm)
+ require(lmtest)
+ library(foreign)
+ library(lfe)
+ data(Cigar)
+ })
> xtregfe <- plm(sales ~ price, model = 'within', data = Cigar)
> G <- length(unique(Cigar$state))
> c <- G/(G - 1)
> coeftest(xtregfe,c * vcovHC(xtregfe, type = "HC1", cluster = "group"))
t test of coefficients:
Estimate Std. Error t value Pr(>|t|)
price -0.20984 0.03575 -5.8697 5.503e-09 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> areg<-felm(sales ~ price | state | 0 | state, Cigar)
> coeftest(areg)
t test of coefficients:
Estimate Std. Error t value Pr(>|t|)
price -0.209840 0.036348 -5.7731 9.672e-09 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> write.dta(Cigar,"~/Desktop/Cigar.dta")
>
End of R output
.
. use "~/Desktop/Cigar.dta", clear
(Written by R. )
. xtset state year
panel variable: state (strongly balanced)
time variable: year, 63 to 92
delta: 1 unit
. xtreg sales price, fe cluster(state)
Fixed-effects (within) regression Number of obs = 1,380
Group variable: state Number of groups = 46
R-sq: Obs per group:
within = 0.2559 min = 30
between = 0.1007 avg = 30.0
overall = 0.0969 max = 30
F(1,45) = 34.45
corr(u_i, Xb) = 0.0329 Prob > F = 0.0000
(Std. Err. adjusted for 46 clusters in state)
------------------------------------------------------------------------------
| Robust
sales | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
price | -.2098402 .0357498 -5.87 0.000 -.281844 -.1378364
_cons | 138.3669 2.456008 56.34 0.000 133.4202 143.3135
-------------+----------------------------------------------------------------
sigma_u | 25.678164
sigma_e | 15.174773
rho | .74116131 (fraction of variance due to u_i)
------------------------------------------------------------------------------
. areg sales price, absorb(state) cluster(state)
Linear regression, absorbing indicators Number of obs = 1,380
Absorbed variable: state No. of categories = 46
F( 1, 45) = 33.33
Prob > F = 0.0000
R-squared = 0.7682
Adj R-squared = 0.7602
Root MSE = 15.1748
(Std. Err. adjusted for 46 clusters in state)
------------------------------------------------------------------------------
| Robust
sales | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
price | -.2098402 .0363482 -5.77 0.000 -.2830493 -.1366312
_cons | 138.3669 2.497119 55.41 0.000 133.3374 143.3963
------------------------------------------------------------------------------
As you can see, areg/felm give you a price coefficient of -0.20984 with a clustered standard error of 0.03635. The panel fixed effect approaches both give you -0.20984, but with a smaller CSE of 0.03575.
