| Version: | 0.6-28 |
| Date: | 2023-05-03 |
| Title: | Miscellaneous Tools and Utilities |
| Author: | Arne Henningsen, Ott Toomet |
| Maintainer: | Arne Henningsen <arne.henningsen@gmail.com> |
| Depends: | R (≥ 2.14.0) |
| Imports: | digest |
| Suggests: | Ecdat (≥ 0.1-5) |
| Description: | Miscellaneous small tools and utilities. Many of them facilitate the work with matrices, e.g. inserting rows or columns, creating symmetric matrices, or checking for semidefiniteness. Other tools facilitate the work with regression models, e.g. extracting the standard errors, obtaining the number of (estimated) parameters, or calculating R-squared values. |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| URL: | https://github.com/arne-henningsen/miscTools |
| BugReports: | https://github.com/arne-henningsen/miscTools/issues |
| NeedsCompilation: | no |
| Packaged: | 2023-05-03 14:01:50 UTC; gsl324 |
| Repository: | CRAN |
| Date/Publication: | 2023-05-03 14:40:02 UTC |
Coefficient Table
Description
Generate Table for Coefficients, Std. Errors, t-values and P-values.
Usage
coefTable( coef, stdErr, df = NULL )
Arguments
coef |
vector that contains the coefficients. |
stdErr |
vector that contains the standard errors of the coefficients. |
df |
degrees of freedom of the t-test used to calculate P-values. |
Value
a matrix with 4 columns: coefficients, standard errors, t-values
and P-values.
If argument df is not provided, the last column (P-values)
is filled with NAs.
Author(s)
Arne Henningsen
Examples
coefTable( rnorm( 10 ), 0.5 * abs( rnorm( 10 ) ), 20 )
Medians of Columns
Description
Compute the sample medians of the columns (non-rows) of a data.frame or array.
Usage
colMedians( x, na.rm = FALSE )
Arguments
x |
a data.frame or array. |
na.rm |
a logical value indicating whether |
Value
A vector or array of the medians of each column (non-row) of x
with dimension dim( x )[-1].
Author(s)
Arne Henningsen
See Also
Examples
data( "Electricity", package = "Ecdat" )
colMedians( Electricity )
a4 <- array( 1:120, dim = c(5,4,3,2),
dimnames = list( c("a","b","c","d","e"), c("A","B","C","D"),
c("x","y","z"), c("Y","Z") ) )
colMedians( a4 )
median( a4[ , "B", "x", "Z" ] ) # equal to
colMedians( a4 )[ "B", "x", "Z" ]
Scatterplot to Compare two Variables
Description
Plot a scatterplot to compare two variables.
Usage
compPlot( x, y, lim = NULL, ... )
Arguments
x |
values of the first variable (on the X axis). |
y |
values of the second variable (on the Y axis). |
lim |
optional vector of two elements specifying the limits of both axes). |
... |
further arguments are passed to |
Author(s)
Arne Henningsen
Examples
set.seed( 123 )
x <- runif( 25 )
y <- 2 + 3 * x + rnorm( 25 )
ols <- lm( y ~ x )
compPlot( y, fitted( ols ) )
compPlot( y, fitted( ols ), lim = c( 0, 10 ) )
compPlot( y, fitted( ols ), pch = 20 )
compPlot( y, fitted( ols ), xlab = "observed", ylab = "fitted" )
compPlot( y, fitted( ols ), log = "xy" )
Derivative of the Normal Distribution's Density Function
Description
This function returns the derivative(s) of the density function
of the normal (Gaussian) distribution with respect to the quantile,
evaluated at the quantile(s), mean(s), and standard deviation(s)
specified by arguments x, mean, and sd, respectively.
Usage
ddnorm( x, mean = 0, sd = 1 )
Arguments
x |
quantile or vector of quantiles. |
mean |
mean or vector of means. |
sd |
standard deviation or vector of standard deviations. |
Value
numeric value(s): derivative(s) of the density function of the normal distribution with respect to the quantile
Author(s)
Arne Henningsen
See Also
Examples
ddnorm( c( -1, 0, 1 ) )
Histogram with a Density Line
Description
Plot a histrogram and add a kernel density line.
Usage
histDens( x, breaks = "Sturges", ... )
Arguments
x |
values of the variable. |
breaks |
passed to |
... |
further arguments are passed to |
Author(s)
Arne Henningsen
Examples
set.seed( 123 )
x <- rnorm( 100 )
histDens( x )
histDens( x, 20 )
histDens( x, 20, main = "My Title" )
Insert Column into a Matrix
Description
Insert a new column into a matrix.
Usage
insertCol( m, c, v = NA, cName = "" )Arguments
m |
matrix. |
c |
column number where the new column should be inserted. |
v |
optional values of the new column. |
cName |
optional character string: the name of the new column. |
Value
a matrix with one more column than the provided matrix m.
Author(s)
Arne Henningsen
See Also
Examples
m <- matrix( 1:4, 2 )
insertCol( m, 2, 5:6 )
Insert Row into a Matrix
Description
Insert a new row into a matrix.
Usage
insertRow( m, r, v = NA, rName = "" )Arguments
m |
matrix. |
r |
row number where the new row should be inserted. |
v |
optional values for the new row. |
rName |
optional character string: the name of the new row. |
Value
a matrix with one more row than the provided matrix m.
Author(s)
Arne Henningsen
See Also
Examples
m <- matrix( 1:4, 2 )
insertRow( m, 2, 5:6 )
Positive or Negative Semidefiniteness
Description
Check whether a symmetric matrix is positive or negative semidefinite.
Usage
isSemidefinite( m, ... )
## Default S3 method:
isSemidefinite( m, ... )
## S3 method for class 'matrix'
isSemidefinite( m, positive = TRUE,
tol = 100 * .Machine$double.eps,
method = ifelse( nrow( m ) < 13, "det", "eigen" ), ... )
## S3 method for class 'list'
isSemidefinite( m, ... )
semidefiniteness( m, ... )
Arguments
m |
a symmetric quadratic matrix or a list containing symmetric quadratic matrices. |
positive |
logical. Check for positive semidefiniteness
(if |
tol |
tolerance level (values between |
method |
method to test for semidefiniteness, either
checking the signs of the principal minors
(if |
... |
further arguments of |
Details
Function semidefiniteness() passes all its arguments
to isSemidefinite().
It is only kept for backward-compatibility
and may be removed in the future.
If argument positive is set to FALSE,
isSemidefinite() checks for negative semidefiniteness
by checking for positive semidefiniteness
of the negative of argument m, i.e. -m.
If method "det" is used
(default for matrices with up to 12 rows/columns),
isSemidefinite() checks whether all principal minors
(not only the leading principal minors)
of the matrix m
(or of the matrix -m if argument positive is FALSE)
are larger than -tol.
Due to rounding errors,
which are unavoidable on digital computers,
the calculated determinants of singular (sub-)matrices
(which should theoretically be zero)
can considerably deviate from zero.
In order to reduce the probability of incorrect results
due to rounding errors,
isSemidefinite() does not calculate the determinants
of (sub-)matrices with reciprocal condition numbers
smaller than argument tol
but sets the corresponding principal minors to (exactly) zero.
The number of principal minors of an N \times N matrix is
\sum_{k=1}^N ( N choose k ),
which gets very large for large matrices.
Therefore, it is not recommended to use method "det"
for matrices with, say, more than 12 rows/columns.
If method "eigen"
(default for matrices with 13 or more rows/columns) is used,
isSemidefinite() checks whether all eigenvalues
of the matrix m
(or of the matrix -m if argument positive is FALSE)
are larger than -tol.
In case of a singular or nearly singular matrix,
some eigenvalues
that theoretically should be zero
can considerably deviate from zero
due to rounding errors,
which are unavoidable on digital computers.
isSemidefinite() uses the following procedure
to reduce the probability of incorrectly returning FALSE
due to rounding errors in the calculation of eigenvalues
of singular or nearly singular matrices:
if the reciprocal condition number of an N \times N matrix
is smaller than argument tol
and not all of the eigenvalues of this matrix are larger than -tol,
isSemidefinite() checks
whether all ( N choose (N-k) )
(N-k) \times (N-k) submatrices
are positive semidefinite,
where k with 0 < k < N is the number of eigenvalues
in the interval -tol and tol.
If necessary, this procedure is done recursively.
Please note that a matrix can be neither positive semidefinite nor negative semidefinite.
Value
isSemidefinite() and semidefiniteness()
return a locigal value (if argument m is a matrix)
or a logical vector (if argument m is a list)
indicating whether the matrix (or each of the matrices)
is positive/negative (depending on argument positive)
semidefinite.
Author(s)
Arne Henningsen
References
Chiang, A.C. (1984): Fundamental Methods of Mathematical Economics, 3rd ed., McGraw-Hill.
Gantmacher, F.R. (1959): The Theory of Matrices, Chelsea Publishing.
Examples
# a positive semidefinite matrix
isSemidefinite( matrix( 1, 3, 3 ))
# a negative semidefinite matrix
isSemidefinite( matrix(-1, 3, 3 ), positive = FALSE )
# a matrix that is positive and negative semidefinite
isSemidefinite( matrix( 0, 3, 3 ))
isSemidefinite( matrix( 0, 3, 3 ), positive = FALSE )
# a matrix that is neither positive nor negative semidefinite
isSemidefinite( symMatrix( 1:6 ) )
isSemidefinite( symMatrix( 1:6 ), positive = FALSE )
# checking a list of matrices
ml <- list( matrix( 1, 3, 3 ), matrix(-1, 3, 3 ), matrix( 0, 3, 3 ) )
isSemidefinite( ml )
isSemidefinite( ml, positive = FALSE )
Method for Returning Marginal Effects
Description
Currently, this package just defines the generic function margEff
so that it can be used
to define margEff methods for objects of specific classes
in other packages.
Usage
margEff( object, ... )
Arguments
object |
an object of which marginal effects should be calculated. |
... |
further arguments for methods |
Author(s)
Arne Henningsen
Undocumented miscTools Functions
Description
Undocumented miscTools Functions
Details
These are various methods or functions waiting for proper documentation to be written :).
Return number of observations for statistical models
Description
Returns number of observations for statistical models. The default
method assumes presence of a component param$nObs in x.
Usage
nObs(x, ...)
## Default S3 method:
nObs(x, ...)
## S3 method for class 'lm'
nObs(x, ...)
Arguments
x |
a statistical model, such as created by |
... |
further arguments for methods |
Details
This is a generic function. The default method returns the component
x$param$nObs. The lm-method is based on
qr-decomposition, in the same way as the does summary.lm.
Value
numeric, number of observations
Author(s)
Ott Toomet, otoomet@econ.au.dk
Examples
# Construct a simple OLS regression:
x1 <- runif(100)
x2 <- runif(100)
y <- 3 + 4*x1 + 5*x2 + rnorm(100)
m <- lm(y~x1+x2) # estimate it
nObs(m)
Number of model parameters
Description
This function returns the number of model parameters. The default
method returns the component x$param$nParam.
Usage
nParam(x, free=FALSE, ...)
## Default S3 method:
nParam(x, ...)
## S3 method for class 'lm'
nParam(x, ...)
Arguments
x |
a statistical model |
free |
logical, whether to report only the free parameters or the total number of parameters (default) |
... |
other arguments for methods |
Details
Free parameters are the parameters with no equality restrictions. Some parameters may be restricted (e.g. sum of two probabilities may be restricted to equal unity). In this case the total number of parameters may depend on the normalisation.
Value
Number of parameters in the model
Author(s)
Ott Toomet, otoomet@econ.au.dk
See Also
nObs for number of observations
Examples
# Construct a simple OLS regression:
x1 <- runif(100)
x2 <- runif(100)
y <- 3 + 4*x1 + 5*x2 + rnorm(100)
m <- lm(y~x1+x2) # estimate it
summary(m)
nParam(m) # you get 3
Test for quasiconcavity / quasiconvexity
Description
Test wether a function is quasiconcave or quasiconvex.
The bordered Hessian of this function is checked by
quasiconcavity() or quasiconvexity().
Usage
quasiconcavity( m, tol = .Machine$double.eps )
quasiconvexity( m, tol = .Machine$double.eps )
Arguments
m |
a bordered Hessian matrix or a list containing bordered Hessian matrices |
tol |
tolerance level (values between |
Value
locigal or a logical vector (if m is a list).
Author(s)
Arne Henningsen
References
Chiang, A.C. (1984) Fundamental Methods of Mathematical Economics, 3rd ed., McGraw-Hill.
Examples
quasiconcavity( matrix( 0, 3, 3 ) )
quasiconvexity( matrix( 0, 3, 3 ) )
m <- list()
m[[1]] <- matrix( c( 0,-1,-1, -1,-2,3, -1,3,5 ), 3, 3 )
m[[2]] <- matrix( c( 0,1,-1, 1,-2,3, -1,3,5 ), 3, 3 )
quasiconcavity( m )
quasiconvexity( m )
Medians of Rows
Description
Compute the sample medians of the rows of a data.frame or matrix.
Usage
rowMedians( x, na.rm = FALSE )
Arguments
x |
a data.frame or matrix. |
na.rm |
a logical value indicating whether |
Value
A vector of the medians of each row of x.
Author(s)
Arne Henningsen
See Also
Examples
m <- matrix( 1:12, nrow = 4 )
rowMedians( m )
Calculate R squared value
Description
Calculate R squared value.
Usage
rSquared( y, resid )Arguments
y |
vector of endogenous variables |
resid |
vector of residuals |
Author(s)
Arne Henningsen
Examples
data( "Electricity", package = "Ecdat" )
reg <- lm( cost ~ q + pl + pk + pf, Electricity )
rSquared( Electricity$cost, reg$residuals )
summary( reg )$r.squared # returns the same value
Standard deviations
Description
Extract standard deviations from estimated models.
Usage
stdEr(x, ...)
## Default S3 method:
stdEr(x, ...)
## S3 method for class 'lm'
stdEr(x, ...)
Arguments
x |
a statistical model, such as created by |
... |
further arguments for methods |
Details
stdEr is a generic function with methods for objects of "lm"
class. The default method returns the square root of the diagonal of
the variance-covariance matrix.
Value
numeric, the estimated standard errors of the coefficients.
Author(s)
Ott Toomet otoomet@ut.ee
See Also
Examples
data(cars)
lmRes <- lm(dist ~ speed, data=cars)
stdEr( lmRes )
Sum of an Array While Keeping its Attributes
Description
This function returns the sum of an numeric array (e.g. vector or matrix) while keeping its attributes.
Usage
sumKeepAttr( x, keepNames = FALSE, na.rm = FALSE )
Arguments
x |
an numeric array (e.g. vector or matrix). |
keepNames |
logical. Should the name(s) of the element(s) of |
na.rm |
logical. Passed to |
Value
the sum (see sum).
Author(s)
Arne Henningsen
See Also
Examples
a <- 1:10
attr( a, "min" ) <- 1
attr( a, "max" ) <- 10
sum(a)
sumKeepAttr(a)
Summarize a data.rrame
Description
This function summarizes each variable that is in a data.frame. It can be used, e.g., in an R script to write summary information about a data.frame into a text file that is in a version control system so that one can see in the version control system whether one or more variables in the data frame have changed.
Usage
summarizeDF( dat, printValues = TRUE, maxLevel = 20, file = NULL, ... )
Arguments
dat |
a data.frame. |
printValues |
logical. If |
maxLevel |
integer. If the number of unique values in a variable
is less than or equal to the number specified in this argument
(and argument |
file |
a character string or a writable connection naming the file to write to. |
... |
further arguments forwarded to |
Author(s)
Arne Henningsen
Symmetric Matrix
Description
Create a Symmetric Matrix.
Usage
symMatrix( data = NA, nrow = NULL, byrow = FALSE,
upper = FALSE )
Arguments
data |
an optional data vector. |
nrow |
the desired number of rows and columns. |
byrow |
logical. If 'FALSE' (the default) the matrix is filled by columns, otherwise the matrix is filled by rows. |
upper |
logical. If 'FALSE' (the default) the lower triangular part of the matrix (including the diagonal) is filled, otherwise the upper triangular part of the matrix is filled. |
Value
a symmetric matrix.
Author(s)
Arne Henningsen
See Also
Examples
# fill the lower triangular part by columns
symMatrix( 1:10, 4 )
# fill the upper triangular part by columns
symMatrix( 1:10, 4, upper = TRUE )
# fill the lower triangular part by rows
symMatrix( 1:10, 4, byrow = FALSE )
Upper triangular matrix from a vector
Description
Creates an upper triangular square matrix from a vector.
Usage
triang( v, n )Arguments
v |
vector |
n |
desired dimension of the returned square matrix |
Note
If the vector has less elements than the upper triangular matrix, the last elements are set to zero.
Author(s)
Arne Henningsen
See Also
Examples
v <- c( 1:5 )
triang( v, 3 )
Vector of linear independent values
Description
Returns a vector containing the linear independent elements of a symmetric matrix (of full rank).
Usage
vecli( m )Arguments
m |
symmetric matrix |
Author(s)
Arne Henningsen
See Also
Examples
# a symmetric n x n matrix
m <- cbind(c(11,12,13),c(12,22,23),c(13,23,33))
vecli(m) # returns: 11 12 13 22 23 33
Convert vector of linear independent values into a Matrix
Description
Converts a vector into a symmetric matrix that the original vector contains the linear independent values of the returned symmetric matrix.
Usage
vecli2m( v )Arguments
v |
a vector. |
Author(s)
Arne Henningsen
See Also
Examples
v <- c( 11, 12, 13, 22, 23, 33 )
vecli2m( v )
Position in a vector of linear independent values
Description
Returns the position of the [i,j]th element of a symmetric
n \times n matrix that this element has in a vector
of the linear independent values of the matrix.
Usage
veclipos( i, j, n )Arguments
i |
row of the element in the matrix. |
j |
column of the element in the matrix. |
n |
dimension of the matrix. |
Note
A symmetric n \times n matrix has n*(n+1)/2
independent values.
The function is: n*(n-1)/2-((n-min(i,j))*(n-min(i,j)+1)/2)+max(i,j)
Author(s)
Arne Henningsen
See Also
Examples
veclipos( 1, 2, 3 ) # returns: 2