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 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.
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
indicates any such aliased coefficients by a named logical.
alias, help to
detect linear dependence and accomplish almost the same:
detect.lindep is a stand alone implementation while
alias is a wrapper around
stats::alias.lm(), extending the
generic to classes
alias hinges on the availability of the package
MASS on the system. Not all arguments of
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.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
stats::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
initially but renamed for naming consistency later with a
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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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