collapse (version 1.7.6)

fhdbetween-fhdwithin: Higher-Dimensional Centering and Linear Prediction

Description

fhdbetween is a generalization of fbetween to efficiently predict with multiple factors and linear models (i.e. predict with vectors/factors, matrices, or data frames/lists where the latter may contain multiple factor variables). Similarly, fhdwithin is a generalization of fwithin to center on multiple factors and partial-out linear models.

The corresponding operators HDB and HDW additionally allow to predict / partial out full lm() formulas with interactions between variables.

Usage

fhdbetween(x, …)
 fhdwithin(x, …)
       HDB(x, …)
       HDW(x, …)
# S3 method for default
fhdbetween(x, fl, w = NULL, na.rm = TRUE, fill = FALSE, lm.method = "qr", …)
# S3 method for default
fhdwithin(x, fl, w = NULL, na.rm = TRUE, fill = FALSE, lm.method = "qr", …)
# S3 method for default
HDB(x, fl, w = NULL, na.rm = TRUE, fill = FALSE, lm.method = "qr", …)
# S3 method for default
HDW(x, fl, w = NULL, na.rm = TRUE, fill = FALSE, lm.method = "qr", …)
# S3 method for matrix
fhdbetween(x, fl, w = NULL, na.rm = TRUE, fill = FALSE, lm.method = "qr", …)
# S3 method for matrix
fhdwithin(x, fl, w = NULL, na.rm = TRUE, fill = FALSE, lm.method = "qr", …)
# S3 method for matrix
HDB(x, fl, w = NULL, na.rm = TRUE, fill = FALSE, stub = "HDB.", lm.method = "qr", …)
# S3 method for matrix
HDW(x, fl, w = NULL, na.rm = TRUE, fill = FALSE, stub = "HDW.", lm.method = "qr", …)
# S3 method for data.frame
fhdbetween(x, fl, w = NULL, na.rm = TRUE, fill = FALSE,
           variable.wise = FALSE, lm.method = "qr", …)
# S3 method for data.frame
fhdwithin(x, fl, w = NULL, na.rm = TRUE, fill = FALSE,
          variable.wise = FALSE, lm.method = "qr", …)
# S3 method for data.frame
HDB(x, fl, w = NULL, cols = is.numeric, na.rm = TRUE, fill = FALSE,
    variable.wise = FALSE, stub = "HDB.", lm.method = "qr", …)
# S3 method for data.frame
HDW(x, fl, w = NULL, cols = is.numeric, na.rm = TRUE, fill = FALSE,
    variable.wise = FALSE, stub = "HDW.", lm.method = "qr", …)
# Methods for compatibility with plm:
# S3 method for pseries
fhdbetween(x, effect = "all", w = NULL, na.rm = TRUE, fill = TRUE, …)
# S3 method for pseries
fhdwithin(x, effect = "all", w = NULL, na.rm = TRUE, fill = TRUE, …)
# S3 method for pseries
HDB(x, effect = "all", w = NULL, na.rm = TRUE, fill = TRUE, …)
# S3 method for pseries
HDW(x, effect = "all", w = NULL, na.rm = TRUE, fill = TRUE, …)
# S3 method for pdata.frame
fhdbetween(x, effect = "all", w = NULL, na.rm = TRUE, fill = TRUE,
           variable.wise = TRUE, …)
# S3 method for pdata.frame
fhdwithin(x, effect = "all", w = NULL, na.rm = TRUE, fill = TRUE,
          variable.wise = TRUE, …)
# S3 method for pdata.frame
HDB(x, effect = "all", w = NULL, cols = is.numeric, na.rm = TRUE,
    fill = TRUE, variable.wise = TRUE, stub = "HDB.", …)
# S3 method for pdata.frame
HDW(x, effect = "all", w = NULL, cols = is.numeric, na.rm = TRUE,
    fill = TRUE, variable.wise = TRUE, stub = "HDW.", …)

Arguments

x

a numeric vector, matrix, data frame, panel series (plm::pseries) or panel data frame (plm::pdata.frame).

fl

a numeric vector, factor, matrix, data frame or list (which may or may not contain factors). In the data frame method fl can also be a one-or two sided lm() formula with variables contained in x. Interactions (:) and full interactions (*) are supported. See Examples and the Note.

w

a vector of (non-negative) weights.

cols

data.frame methods: Select columns to center (partial-out) or predict using column names, indices, a logical vector or a function. Unless specified otherwise all numeric columns are selected. If NULL, all variables are selected.

na.rm

remove missing values from both x and fl. by default rows with missing values in x or fl are removed. In that case an attribute "na.rm" is attached containing the rows removed.

fill

If na.rm = TRUE, fill = TRUE will not remove rows with missing values in x or fl, but fill them with NA's.

variable.wise

(p)data.frame methods: Setting variable.wise = TRUE will process each column individually i.e. use all non-missing cases in each column and in fl (fl is only checked for missing values if na.rm = TRUE). This is a lot less efficient but uses all data available in each column.

effect

plm methods: Select which panel identifiers should be used for centering. 1L takes the first variable in the plm::index, 2L the second etc.. Index variables can also be called by name using a character vector. The keyword "all" uses all identifiers.

stub

a prefix or stub to rename all transformed columns. FALSE will not rename columns.

lm.method

character. The linear fitting method. Supported are "chol" and "qr". See flm.

…

further arguments passed to fixest::demean (other than notes and im_confident) and chol / qr. Possible choices are tol to set a uniform numerical tolerance for the entire fitting process, or nthreads and iter to govern the higher-order centering process.

Value

HDB returns fitted values of regressing x on fl. HDW returns residuals. See Details and Examples.

Details

fhdbetween/HDB and fhdwithin/HDW are powerful functions for high-dimensional linear prediction problems involving large factors and datasets, but can just as well handle ordinary regression problems. They are implemented as efficient wrappers around fbetween / fwithin, flm and some C++ code from the fixest package that is imported for higher-order centering tasks (thus fixest needs to be installed for problems involving more than one factor).

Intended areas of use are to efficiently obtain residuals and predicted values from data, and to prepare data for complex linear models involving multiple levels of fixed effects. Such models can now be fitted using lm() on data prepared with fhdwithin / HDW (relying on bootstrapped SE's for inference, or implementing the appropriate corrections). See Examples.

If fl is a vector or matrix, the result are identical to lm i.e. fhdbetween / HDB returns fitted(lm(x ~ fl)) and fhdwithin / HDW residuals(lm(x ~ fl)). If fl is a list containing factors, all variables in x and non-factor variables in fl are centered on these factors using either fbetween / fwithin for a single factor or fixest C++ code for multiple factors. Afterwards the centered data is regressed on the centered predictors. If fl is just a list of factors, fhdwithin/HDW returns the centered data and fhdbetween/HDB the corresponding means. Take as a most general example a list fl = list(fct1, fct2, ..., var1, var2, ...) where fcti are factors and vari are continuous variables. The output of fhdwithin/HDW | fhdbetween/HDB will then be identical to calling resid | fitted on lm(x ~ fct1 + fct2 + ... + var1 + var2 + ...). The computations performed by fhdwithin/HDW and fhdbetween/HDB are however much faster and more memory efficient than lm because factors are not passed to model.matrix and expanded to matrices of dummies but projected beforehand.

The formula interface to the data.frame method (only supported by the operators HDW | HDB) provides ease of use and allows for additional modeling complexity. For example it is possible to project out formulas like HDW(data, ~ fct1*var1 + fct2:fct3 + var2:fct2:fct3 + var2:var3 + poly(var5,3)*fct5) containing simple (:) or full (*) interactions of factors with continuous variables or polynomials of continuous variables, and two-or three-way interactions of factors and continuous variables. If the formula is one-sided as in the example above (the space left of (~) is left empty), the formula is applied to all variables selected through cols. The specification provided in cols (default: all numeric variables not used in the formula) can be overridden by supplying one-or more dependent variables. For example HDW(data, var1 + var2 ~ fct1 + fct2) will return a data.frame with var1 and var2 centered on fct1 and fct2.

The special methods for plm::pseries and plm::pdata.frame center a panel series or variables in a panel data frame on all panel-identifiers. By default in these methods fill = TRUE and variable.wise = TRUE, so missing values are kept. This change in the default arguments was done to ensure a coherent framework of functions and operators applied to plm panel data classes.

See Also

fbetween, fwithin, fscale, TRA, flm, fFtest, Data Transformations, Collapse Overview

Examples

# NOT RUN {
HDW(mtcars$mpg, mtcars$carb)                   # Simple regression problems
HDW(mtcars$mpg, mtcars[-1])
HDW(mtcars$mpg, qM(mtcars[-1]))
head(HDW(qM(mtcars[3:4]), mtcars[1:2]))
head(HDW(iris[1:2], iris[3:4]))                # Partialling columns 3 and 4 out of colums 1 and 2
head(HDW(iris[1:2], iris[3:5]))                # Adding the Species factor -> fixed effect
# }
# NOT RUN {
 <!-- % We don't test because this code depends on suggested package. -->
head(HDW(wlddev, PCGDP + LIFEEX ~ iso3c + qF(year))) # Partialling out 2 fixed effects
head(HDW(wlddev, PCGDP + LIFEEX ~ iso3c + qF(year), variable.wise = TRUE)) # Variable-wise
head(HDW(wlddev, PCGDP + LIFEEX ~ iso3c + qF(year) + ODA)) # Adding ODA as a continuous regressor
head(HDW(wlddev, PCGDP + LIFEEX ~ iso3c:qF(decade) + qF(year) + ODA)) # Country-decade and year FE's

head(HDW(wlddev, PCGDP + LIFEEX ~ iso3c*year))          # Country specific time trends
head(HDW(wlddev, PCGDP + LIFEEX ~ iso3c*poly(year, 3))) # Country specific cubic trends

# More complex examples
lm(HDW.mpg ~ HDW.hp, data = HDW(mtcars, ~ factor(cyl)*carb + vs + wt:gear + wt:gear:carb))
lm(mpg ~ hp + factor(cyl)*carb + vs + wt:gear + wt:gear:carb, data = mtcars)

lm(HDW.mpg ~ HDW.hp, data = HDW(mtcars, ~ factor(cyl)*carb + vs + wt:gear))
lm(mpg ~ hp + factor(cyl)*carb + vs + wt:gear, data = mtcars)

lm(HDW.mpg ~ HDW.hp, data = HDW(mtcars, ~ cyl*carb + vs + wt:gear))
lm(mpg ~ hp + cyl*carb + vs + wt:gear, data = mtcars)

lm(HDW.mpg ~ HDW.hp, data = HDW(mtcars, mpg + hp ~ cyl*carb + factor(cyl)*poly(drat,2)))
lm(mpg ~ hp + cyl*carb + factor(cyl)*poly(drat,2), data = mtcars)
# }
# NOT RUN {
# }