R: Functions to detect linear dependence

detect_lin_dep {plm} | R Documentation

## Functions to detect linear dependence

### Description

Little helper functions to aid users to detect linear dependent columns in a two-dimensional data structure, especially in a (transformed) model matrix - typically useful in interactive mode during model building phase.

### Usage

    detect_lin_dep(object, ...)
    ## S3 method for class 'matrix'
    detect_lin_dep(object, suppressPrint = FALSE, ...)
    ## S3 method for class 'data.frame'
    detect_lin_dep(object, suppressPrint = FALSE, ...)
    ## S3 method for class 'plm'
    detect_lin_dep(object, suppressPrint = FALSE, ...)

    ## S3 method for class 'plm'
    alias(object, ...)
    ## S3 method for class 'pFormula'
    alias(object, data, model = c("pooling", "within", "Between", "between",
                                   "mean", "random", "fd"),
                        effect = c("individual", "time", "twoways"), ...)

### Arguments

`object` | for `detect_lin_dep`: an object which should be checked for linear dependence (of class `"matrix"`, `"data.frame"`, or `"plm"`); for `alias`: either an estimated model of class `"plm"` or a `"pFormula"`. Usually, one wants to input a model matrix here or check an already estimated plm model,
`suppressPrint` | for `detect_lin_dep` only: logical indicating whether a message shall be printed; defaults to printing the message, i. e. to `suppressPrint = FALSE`,
`data` | for `alias.pFormula` only: model frame (created by plm's `model.frame` method),
`model, effect` | for `alias.pFormula` only: model and effect to specify the data transformation, see `plm`,
`...` | further arguments.

### Details

Linear dependence of columns/variables is (usually) readily avoided when building one's model. However, linear dependence is sometimes not obvious and harder to detect for less experienced applied statisticians. The so called "dummy variable trap" is a common and probably the best–known fallacy of this kind (see e. g. Wooldridge (2016), sec. 7-2.). When building linear models with `lm` or `plm`'s `pooling` model, linear dependence in one's model is easily detected, at times post hoc.

However, linear dependence might also occur after some transformations of the data, albeit it is not present in the untransformed data. The within transformation (also called fixed effect transformation) used in the `"within"` model can result in such linear dependence and this is harder to come to mind when building a model. See Examples for two examples of linear dependent columns after the within transformation: ex. 1) the transformed variables have the opposite sign of one another; ex. 2) the transformed variables are identical.

During `plm`'s model estimation, linear dependent columns and their corresponding coefficients in the resulting object are silently dropped, while the corresponding model frame and model matrix still contain the affected columns. The plm object contains an element `aliased` which indicates any such aliased coefficients by a named logical.

Both functions, `detect_lin_dep` and `alias`, help to detect linear dependence and accomplish almost the same: `detect_lin_dep` is a stand alone implementation while `alias` is a wrapper around `alias.lm`, extending the `alias` generic to classes `"plm"` and `"pFormula"`. `alias` hinges on the availability of the package MASS on the system. Not all arguments of `alias.lm` are supported. Output of `alias` is more informative as it gives the linear combination of dependent columns (after data transformations, i. e. after (quasi)-demeaning) while `detect_lin_dep` only gives columns involved in the linear dependence in a simple format (thus being more suited for automatic post–processing of the information).

### Value

For `detect_lin_dep`: A named numeric vector containing column numbers of the linear dependent columns in the object after data transformation, if any are present. `NULL` if no linear dependent columns are detected.

For `alias`: return value of `alias.lm` run on the (quasi-)demeaned model, i. e. the information outputted applies to the transformed model matrix, not the original data.

### Author(s)

Kevin Tappe

### References

Wooldridge, J.M. (2016) Introductory Econometrics: A Modern Approach, 6th ed., Cengage Learning, Boston, sec. 7-2, pp. 206–211.

### See Also

`alias`. `model.matrix` and especially `plm`'s `model.matrix` for (transformed) model matrices. `model.frame`.

### Examples

    ### Example 1 ###
    # prepare the data
    data(Cigar)
    Cigar[ , "fact1"] <- c(0,1)
    Cigar[ , "fact2"] <- c(1,0)
    Cigar.p <- pdata.frame(Cigar)

    # setup a pFormula and a model frame
    pform <- pFormula(price ~ 0 + cpi + fact1 + fact2)
    mf <- model.frame(pform, data = Cigar.p)

    # no linear dependence in the pooling model's model matrix
    # (with intercept in the formula, there would be linear depedence)
    detect_lin_dep(model.matrix(pform, data = mf, model = "pooling"))

    # linear dependence present in the FE transformed model matrix
    modmat_FE <- model.matrix(pform, data = mf, model = "within")
    detect_lin_dep(modmat_FE)
    mod_FE <- plm(pform, data = Cigar.p, model = "within")
    detect_lin_dep(mod_FE)
    alias(mod_FE) # => fact1 == -1*fact2
    plm(pform, data = mf, model = "within")$aliased # "fact2" indicated as aliased

    # look at the data: after FE transformation fact1 == -1*fact2
    head(modmat_FE)
    all.equal(modmat_FE[ , "fact1"], -1*modmat_FE[ , "fact2"])

    ### Example 2 ###
    # Setup the data:
    # Assume CEOs stay with the firms of the Grunfeld data
    # for the firm's entire lifetime and assume some fictional
    # data about CEO tenure and age in year 1935 (first observation
    # in the data set) to be at 1 to 10 years and 38 to 55 years, respectively.
    # => CEO tenure and CEO age increase by same value (+1 year per year).
    data(Grunfeld, package = "plm")
    set.seed(42)
    # add fictional data
    Grunfeld$CEOtenure <- c(replicate(10, seq(from=s<-sample(1:10,  1), to=s+19, by=1)))
    Grunfeld$CEOage    <- c(replicate(10, seq(from=s<-sample(38:65, 1), to=s+19, by=1)))

    # look at the data
    head(Grunfeld, 50)

    pform <- pFormula(inv ~ value + capital + CEOtenure + CEOage)
    mf <- model.frame(pform, data=pdata.frame(Grunfeld))

    # no linear dependent columns in original data/pooling model
    modmat_pool <- model.matrix(pform, data = mf, model="pooling")
    detect_lin_dep(modmat_pool)
    mod_pool <- plm(pform, data = Grunfeld, model = "pooling")
    alias(mod_pool)

    # CEOtenure and CEOage are linear dependent after FE transformation
    # (demeaning per individual)
    modmat_FE <- model.matrix(pform, data = mf, model="within")
    detect_lin_dep(modmat_FE)
    mod_FE <- plm(pform, data = Grunfeld, model = "within")
    detect_lin_dep(mod_FE)
    alias(mod_FE)

    # look at the transformed data: after FE transformation CEOtenure == 1*CEOage
    head(modmat_FE, 50)
    all.equal(modmat_FE[ , "CEOtenure"], modmat_FE[ , "CEOage"])

[Package plm version 1.6-5 Index]