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.
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detect.lindep(object, ...) ## S3 method for class 'matrix' detect.lindep(object, suppressPrint = FALSE, ...) ## S3 method for class 'data.frame' detect.lindep(object, suppressPrint = FALSE, ...) ## S3 method for class 'plm' detect.lindep(object, suppressPrint = FALSE, ...) ## S3 method for class 'plm' alias(object, ...) ## S3 method for class 'pdata.frame' alias(object, model = c("pooling", "within", "Between", "between", "mean", "random", "fd"), effect = c("individual", "time", "twoways"), ...)
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
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
"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.
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
which indicates any such aliased coefficients by a named logical.
alias, help to detect
linear dependence and accomplish almost the same:
is a stand alone implementation while
alias is a wrapper around
alias.lm, extending the
alias generic to
alias hinges on the
availability of the package MASS on the system. Not all
alias.lm are supported. Output of
more informative as it gives the linear combination of dependent columns
(after data transformations, i. e. after (quasi)-demeaning) while
detect.lindep only gives columns involved in the linear
dependence in a simple format (thus being more suited for automatic
post–processing of the information).
detect.lindep: 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.
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.
detect.lindep was called
detect_lin_dep initially but renamed
for naming consistency later with a back-compatible solution.
Wooldridge, J.M. (2016) Introductory Econometrics: A Modern Approach, 6th ed., Cengage Learning, Boston, sec. 7-2, pp. 206–211.
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### Example 1 ### # prepare the data data("Cigar" , package = "plm") Cigar[ , "fact1"] <- c(0,1) Cigar[ , "fact2"] <- c(1,0) Cigar.p <- pdata.frame(Cigar) # setup a formula and a model frame form <- price ~ 0 + cpi + fact1 + fact2 mf <- model.frame(Cigar.p, form) # no linear dependence in the pooling model's model matrix # (with intercept in the formula, there would be linear depedence) detect.lindep(model.matrix(mf, model = "pooling")) # linear dependence present in the FE transformed model matrix modmat_FE <- model.matrix(mf, model = "within") detect.lindep(modmat_FE) mod_FE <- plm(form, data = Cigar.p, model = "within") detect.lindep(mod_FE) alias(mod_FE) # => fact1 == -1*fact2 plm(form, 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) form <- inv ~ value + capital + CEOtenure + CEOage mf <- model.frame(pdata.frame(Grunfeld), form) # no linear dependent columns in original data/pooling model modmat_pool <- model.matrix(mf, model="pooling") detect.lindep(modmat_pool) mod_pool <- plm(form, data = Grunfeld, model = "pooling") alias(mod_pool) # CEOtenure and CEOage are linear dependent after FE transformation # (demeaning per individual) modmat_FE <- model.matrix(mf, model="within") detect.lindep(modmat_FE) mod_FE <- plm(form, data = Grunfeld, model = "within") detect.lindep(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"])
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