# Need intercept for plm (Fixed effects) in R

I have a question of fixed effects in R. So I am trying to use plm function to find fixed effects like following:

> plm(PM25 ~ policy + 1, data=subset(part2, Delhi == 1), model="within",
>     index=c("station_id", "date")) %>% summary()


The results I get:

> Oneway (individual) effect Within Model
>
> Call: plm(formula = PM25 ~ policy + 1, data = subset(part2, Delhi ==
>           1), model = "within", index = c("station_id", "date"))
>
> Unbalanced Panel: n = 7, T = 73-159, N = 992
>
> Residuals:
>      Min.   1st Qu.    Median   3rd Qu.      Max.
> -193.7049  -54.6776   -9.6843   54.7431  318.4094
>
> Coefficients:
>        Estimate Std. Error t-value  Pr(>|t|)
> policy  76.8167     9.9787  7.6981 3.354e-14 ***
> ---
> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> Total Sum of Squares:    6846900
> Residual Sum of Squares: 6458000
> R-Squared:      0.056803
> F-statistic: 59.2603 on 1 and 984 DF, p-value: 3.3535e-14


I am wondering how can I find the intercept?

The within model you specify amounts to fitting a separate intercept for each unit in your panel data set, as in $$y_{it}=a_i+\beta x_{it}+u_{it}$$ See, e.g., these posts for some context:

Difference between fixed effects dummies and fixed effects estimator?

How exactly does a "random effects model" in econometrics relate to mixed models outside of econometrics?

Hence, you cannot additionally fit an overall intercept $$a$$, as you would then have perfect collinearity between the $$a_i$$ and $$a$$, as the sum of the $$a_i$$ is identically one.

You can retrieve these estimates as follows:

data("Grunfeld", package = "plm")

wi <- plm(inv ~ value + capital,
data = Grunfeld, model = "within", effect = "twoways")

fixef(wi)


One might of course leave out one of the intercepts. Something related to what you seek seems to be achieved by this command: https://rdrr.io/rforge/plm/man/within_intercept.html