Extract the Fixed Effects
Function to extract the fixed effects from a plm object and
associated summary method.
## S3 method for class 'plm'
fixef(
object,
effect = NULL,
type = c("level", "dfirst", "dmean"),
vcov = NULL,
...
)
## S3 method for class 'fixef'
print(
x,
digits = max(3, getOption("digits") - 2),
width = getOption("width"),
...
)
## S3 method for class 'fixef'
summary(object, ...)
## S3 method for class 'summary.fixef'
print(
x,
digits = max(3, getOption("digits") - 2),
width = getOption("width"),
...
)
## S3 method for class 'pggls'
fixef(
object,
effect = NULL,
type = c("level", "dfirst", "dmean"),
vcov = NULL,
...
)effect |
one of |
type |
one of |
vcov |
a variance–covariance matrix furnished by the user or a function to calculate one (see Examples), |
... |
further arguments. |
x, object |
an object of class |
digits |
digits, |
width |
the maximum length of the lines in the print output, |
Function fixef calculates the fixed effects and returns an object
of class c("fixef", "numeric"). By setting the type argument,
the fixed effects may be returned in levels ("level"), as
deviations from the first value of the index ("dfirst"), or as
deviations from the overall mean ("dmean"). If the argument
vcov was specified, the standard errors (stored as attribute "se"
in the return value) are the respective robust standard errors.
For two-way fixed-effect models, argument effect controls which
of the fixed effects are to be extracted: "individual", "time", or
the sum of individual and time effects ("twoways").
NB: See Examples for how the sum of effects can be split in an individual
and a time component.
For one-way models, the effects of the model are extracted and the
argument effect is disrespected.
The associated summary method returns an extended object of class
c("summary.fixef", "matrix") with more information (see sections
Value and Examples).
References with formulae (except for the two-ways unbalanced case) are, e.g., Greene (2012), Ch. 11.4.4, p. 364, formulae (11-25); Wooldridge (2010), Ch. 10.5.3, pp. 308-309, formula (10.58).
For function fixef, an object of class c("fixef", "numeric")
is returned: It is a numeric vector containing
the fixed effects with attribute se which contains the
standard errors. There are two further attributes: attribute
type contains the chosen type (the value of argument type
as a character); attribute df.residual holds the residual
degrees of freedom (integer) from the fixed effects model (plm
object) on which fixef was run. For the two-way unbalanced case, only
attribute type is added.
For function summary.fixef, an object of class
c("summary.fixef", "matrix") is returned: It is a matrix with four
columns in this order: the estimated fixed effects, their standard
errors and associated t–values and p–values.
For the two-ways unbalanced case, the matrix contains only the estimates.
The type of the fixed effects and the standard errors in the
summary.fixef object correspond to was requested in the fixef
function by arguments type and vcov, respectively.
Yves Croissant
Greene WH (2012).
Econometric Analysis, 7th edition.
Prentice Hall.
Wooldridge JM (2010).
Econometric Analysis of Cross–Section and Panel Data.
MIT press.
within_intercept() for the overall intercept of fixed
effect models along its standard error, plm() for plm objects
and within models (= fixed effects models) in general. See
ranef() to extract the random effects from a random effects
model.
data("Grunfeld", package = "plm")
gi <- plm(inv ~ value + capital, data = Grunfeld, model = "within")
fixef(gi)
summary(fixef(gi))
summary(fixef(gi))[ , c("Estimate", "Pr(>|t|)")] # only estimates and p-values
# relationship of type = "dmean" and "level" and overall intercept
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
# extract time effects in a twoways effects model
gi_tw <- plm(inv ~ value + capital, data = Grunfeld,
model = "within", effect = "twoways")
fixef(gi_tw, effect = "time")
# with supplied variance-covariance matrix as matrix, function,
# and function with additional arguments
fx_level_robust1 <- fixef(gi, vcov = vcovHC(gi))
fx_level_robust2 <- fixef(gi, vcov = vcovHC)
fx_level_robust3 <- fixef(gi, vcov = function(x) vcovHC(x, method = "white2"))
summary(fx_level_robust1) # gives fixed effects, robust SEs, t- and p-values
# calc. fitted values of oneway within model:
fixefs <- fixef(gi)[index(gi, which = "id")]
fitted_by_hand <- fixefs + gi$coefficients["value"] * gi$model$value +
gi$coefficients["capital"] * gi$model$capital
# calc. fittes values of twoway unbalanced within model via effects:
gtw_u <- plm(inv ~ value + capital, data = Grunfeld[-200, ], effect = "twoways")
yhat <- as.numeric(gtw_u$model[ , 1] - gtw_u$residuals) # reference
pred_beta <- as.numeric(tcrossprod(coef(gtw_u), as.matrix(gtw_u$model[ , -1])))
pred_effs <- as.numeric(fixef(gtw_u, "twoways")) # sum of ind and time effects
all.equal(pred_effs + pred_beta, yhat) # TRUE
# Splits of summed up individual and time effects:
# use one "level" and one "dfirst"
ii <- index(gtw_u)[[1L]]; it <- index(gtw_u)[[2L]]
eff_id_dfirst <- c(0, as.numeric(fixef(gtw_u, "individual", "dfirst")))[ii]
eff_ti_dfirst <- c(0, as.numeric(fixef(gtw_u, "time", "dfirst")))[it]
eff_id_level <- as.numeric(fixef(gtw_u, "individual"))[ii]
eff_ti_level <- as.numeric(fixef(gtw_u, "time"))[it]
all.equal(pred_effs, eff_id_level + eff_ti_dfirst) # TRUE
all.equal(pred_effs, eff_id_dfirst + eff_ti_level) # TRUEPlease choose more modern alternatives, such as Google Chrome or Mozilla Firefox.