R: Fixed Effects Individual Slope Estimator

feis {feisr}

R Documentation

Fixed Effects Individual Slope Estimator

Description

Estimates fixed effects individual slope estimators by applying linear lm models to "detrended" data.

Usage

feis(
  formula,
  data,
  id,
  weights = NULL,
  robust = FALSE,
  intercept = FALSE,
  dropgroups = FALSE,
  tol = .Machine$double.eps,
  ...
)

## S3 method for class 'feis'
formula(x, lhs = NULL, rhs = NULL, ...)

## S3 method for class 'feis'
terms(x, lhs = NULL, rhs = NULL, ...)

## S3 method for class 'feis'
residuals(object, ...)

## S3 method for class 'feis'
df.residual(object, ...)

## S3 method for class 'feis'
coef(object, ...)

## S3 method for class 'feis'
sigma(object, ...)

## S3 method for class 'feis'
deviance(object, ...)

## S3 method for class 'feis'
nobs(object, ...)

## S3 method for class 'feis'
fitted(object, ...)

## S3 method for class 'feis'
hatvalues(model, ...)

Arguments

`formula`	a symbolic description for the model to be fitted (see Details).
`data`	a `data.frame` containing the specified variables.
`id`	the name of a unique group / person identifier (as string).
`weights`	an optional vector of weights to be used in the fitting process. See `lm`.
`robust`	logical. If `TRUE` estimates cluster robust standard errors (default is `FALSE`).
`intercept`	logical. If `TRUE` estimates the model with an intercept (default is `FALSE`).
`dropgroups`	logical. If `TRUE` groups without any within variance on a slope variable are dropped , if `FALSE` those variables are omitted for the respective groups only (default is `FALSE`).
`tol`	the tolerance for detecting linear dependencies in the residual maker transformation (see `solve`). The argument is forwarded to `bsfeistest`.
`...`	further arguments.
`lhs`, `rhs`	indexes of the left- and right-hand side for the methods formula and terms.
`object`, `x`, `model`	an object of class "`feis`".

Details

feis is a special function to estimate linear fixed effects models with individual-specific slopes. In contrast to conventional fixed effects models, data are not person "demeaned", but "detrended" by the predicted individual slope of each person (Bruederl and Ludwig 2015; Ruettenauer and Ludwig 2020; Wooldridge 2010).

Estimation requires at least q+1 observations per unit, where q is the number of slope parameters (including a constant). feis automatically selects only those groups from the current data set which have at least q+1 observations. The function returns a warning if units with <q+1 observations are dropped.

The function requires a two-part formula, in which the second part indicates the slope parameter(s). If, for example, the model is y ~ x1 + x2, with the slope variables x3 and x4, the model can be estimated with:

formula = y ~ x1 + x2 | x3 + x4

To estimate a conventional fixed effects model without individual slopes, please use y ~ x1 + x2 | 1 to indicate that the slopes should only contain an individual-specific intercept.

If specified, feis estimates panel-robust standard errors. Panel-robust standard errors are robust to arbitrary forms of serial correlation within groups formed by id as well as heteroscedasticity across groups (see Wooldridge 2010, pp. 379-381).

The model output can be exported using the texreg package.

Value

An object of class "feis", containing the following elements:

`coefficients`	the vector of coefficients.
`vcov`	the scaled (if specified, robust) variance-covariance matrix of the coefficients. See `vcov.feis` for unscaled vcov

`residuals`	the vector of residuals (computed from the "detrended" data).
`df.residual`	degrees of freedom of the residuals.
`formula`	an object of class "`Formula`" describing the model.
`model`	the original model frame as a `data.frame` containing the original variables used for estimation.
`modelhat`	a constructed model frame as a `data.frame` containing the predicted values from the first stage regression using the slope variable(s) as predictor(s).
`modeltrans`	a constructed model frame as a `data.frame` containing the "detrended" variables used for the final model estimation. Note that the weights are already used for detrending if specified.
`response`	the vector of the "detrended" response variable.
`fitted.values`	the vector of fitted values (computed from the "detrended" data).
`id`	a vector containing the unique person identifier.
`weights`	a vector containing weights used in fitting, or integer 1 if not speficied in call.
`call`	the matched call.
`assign`	assign attributes of the formula.
`na.omit`	(where relevant) a vector of the omitted observations. The only handling method of `NA`s is "`omit`".
`contrasts`	(only where relevant) the contrasts used.
`arg`	a list containing the used methods. Only "`feis`" and "`individual`" effects available.
`slopevars`	a character vector containing the names of the slope variables.
`r2`	R squared of the "detrended" model.
`adj.r2`	adjusted R squared of the "detrended" model.
`vcov_arg`	a character containing the method used to compute the variance-covariance matrix.
`tol`	the tolerance parameter (for use in bsfeistest).

References

Bruederl J, Ludwig V (2015). “Fixed-Effects Panel Regression.” In Best H, Wolf C (eds.), The Sage Handbook of Regression Analysis and Causal Inference, 327–357. Sage, Los Angeles. ISBN 1446252442.

Ruettenauer T, Ludwig V (2020). “Fixed Effects Individual Slopes: Accounting and Testing for Heterogeneous Effects in Panel Data or Other Multilevel Models.” Sociological Methods and Research, OnlineFirst. ISSN 0049-1241, doi: 10.1177/0049124120926211.

Wooldridge JM (2010). Econometric Analysis of Cross Section and Panel Data. MIT Press, Cambridge, Mass. ISBN 0262294354.

Examples

data("mwp", package = "feisr")
feis.mod <- feis(lnw ~ marry + enrol + as.factor(yeargr) | exp + I(exp^2),
                 data = mwp, id = "id", robust = TRUE)
summary(feis.mod)

[Package feisr version 1.3.0 Index]