This function gives an overall intercept for within models and its accompanying standard error or an within model with the overall intercept
within_intercept(object, ...) ## S3 method for class 'plm' within_intercept(object, vcov = NULL, return.model = FALSE, ...)
object of class
further arguments (currently none).
a logical to indicate whether only the overall intercept
The (somewhat artificial) intercept for within models (fixed effects models) was made popular by Stata of StataCorp \insertCite@see @GOUL:13plm, EViews of IHS, and gretl \insertCite@see @GRETL:2021, p. 200-201, listing 23.1plm, see for treatment in the literature, e.g., \insertCiteGREE:12;textualplm, Ch. 11.4.4, p. 364. It can be considered an overall intercept in the within model framework and is the weighted mean of fixed effects (see Examples for the relationship).
within_intercept estimates a new model which is
computationally more demanding than just taking the weighted
mean. However, with
within_intercept one also gets the
associated standard error and it is possible to get an overall
intercept for twoway fixed effect models.
Users can set argument
vcov to a function to calculate a
specific (robust) variance–covariance matrix and get the
respective (robust) standard error for the overall intercept,
e.g., the function
vcovHC(), see examples for
usage. Note: The argument
vcov must be a function, not a
matrix, because the model to calculate the overall intercept for
the within model is different from the within model itself.
return.model = TRUE is set, the full model object is returned,
while in the default case only the intercept is returned.
Depending on argument
FALSE (default), a named
numeric of length one: The overall intercept for the estimated within model
along attribute "se" which contains the standard error for the intercept.
return.model = TRUE, the full model object, a within model with the
overall intercept (NB: the model identifies itself as a pooling model, e.g.,
fixef() to extract the fixed effects of a within model.
data("Hedonic", package = "plm") mod_fe <- plm(mv ~ age + crim, data = Hedonic, index = "townid") overallint <- within_intercept(mod_fe) attr(overallint, "se") # standard error # overall intercept is the weighted mean of fixed effects in the # one-way case weighted.mean(fixef(mod_fe), pdim(mod_fe)$Tint$Ti) ### relationship of type="dmean", "level" and within_intercept ## one-way balanced case data("Grunfeld", package = "plm") gi <- plm(inv ~ value + capital, data = Grunfeld, model = "within") fx_level <- fixef(gi, type = "level") fx_dmean <- fixef(gi, type = "dmean") overallint <- within_intercept(gi) all.equal(overallint + fx_dmean, fx_level, check.attributes = FALSE) # TRUE ## two-ways unbalanced case gtw_u <- plm(inv ~ value + capital, data = Grunfeld[-200, ], effect = "twoways") int_tw_u <- within_intercept(gtw_u) fx_dmean_tw_i_u <- fixef(gtw_u, type = "dmean", effect = "individual")[index(gtw_u)[[1L]]] fx_dmean_tw_t_u <- fixef(gtw_u, type = "dmean", effect = "time")[index(gtw_u)[[2L]]] fx_level_tw_u <- as.numeric(fixef(gtw_u, "twoways", "level")) fx_level_tw_u2 <- int_tw_u + fx_dmean_tw_i_u + fx_dmean_tw_t_u all.equal(fx_level_tw_u, fx_level_tw_u2, check.attributes = FALSE) # TRUE ## overall intercept with robust standard error within_intercept(gi, vcov = function(x) vcovHC(x, method="arellano", type="HC0")) ## have a model returned mod_fe_int <- within_intercept(gi, return.model = TRUE) summary(mod_fe_int) # replicates Stata's robust standard errors summary(mod_fe_int, vcvov = function(x) vcovHC(x, type = "sss"))
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