Package 'miscTools' reference manual

Title:	Miscellaneous Tools and Utilities
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.
Authors:	Arne Henningsen, Ott Toomet
Maintainer:	Arne Henningsen <[email protected]>
License:	GPL (>= 2)
Version:	0.6-29
Built:	2024-10-24 03:28:47 UTC
Source:	https://github.com/arne-henningsen/misctools

Coefficient Table

Description

Generate Table for Coefficients, Std. Errors, t-values and P-values.

Usage

   coefTable( coef, stdErr, df = NULL )
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 )
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 )
colMedians( x, na.rm = FALSE )

Arguments

`x`	a data.frame or array.
`na.rm`	a logical value indicating whether `NA` values should be stripped before the computation proceeds.

Value

A vector or array of the medians of each column (non-row) of x with dimension dim( x )[-1].

Author(s)

Arne Henningsen

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" ]
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, ... )
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 `plot`.

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" )
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 )
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

Examples

ddnorm( c( -1, 0, 1 ) )
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", ... )
histDens( x, breaks = "Sturges", ... )

Arguments

`x`	values of the variable.
`breaks`	passed to `hist`.
`...`	further arguments are passed to `hist`.

Author(s)

Arne Henningsen

Examples

   set.seed( 123 )
   x <- rnorm( 100 )
   histDens( x )
   histDens( x, 20 )
   histDens( x, 20, main = "My Title" )
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 = "" )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

Examples

   m <- matrix( 1:4, 2 )
   insertCol( m, 2, 5:6 )
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 = "" )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

Examples

   m <- matrix( 1:4, 2 )
   insertRow( m, 2, 5:6 )
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, ... )
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 `TRUE`, default) or for negative semidefiniteness (if `FALSE`).
`tol`	tolerance level (values between `-tol` and `tol` are considered to be zero).
`method`	method to test for semidefiniteness, either checking the signs of the principal minors (if `"det"`, default for matrices with up to 12 rows/columns) or checking the signs of the eigenvalues (if `"eigen"`, default for matrices with 13 or more rows/columns).
`...`	further arguments of `isSemidefinite.list` are passed to `isSemidefinite.matrix`;. further arguments of `semidefiniteness` are passed to `isSemidefinite`; further arguments of other functions are currently ignored.

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 )
# 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, ... )
margEff( object, ... )

Arguments

`object`	an object of which marginal effects should be calculated.
`...`	further arguments for methods

Author(s)

Arne Henningsen

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, ...)
nObs(x, ...)
## Default S3 method:
nObs(x, ...)
## S3 method for class 'lm'
nObs(x, ...)

Arguments

`x`	a statistical model, such as created by `lm`
`...`	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, [email protected]

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)
# 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, ...)
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, [email protected]

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
# 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 )
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 `-tol` and `tol` are considered to be zero).

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 )
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 )
rowMedians( x, na.rm = FALSE )

Arguments

`x`	a data.frame or matrix.
`na.rm`	a logical value indicating whether `NA` values should be stripped before the computation proceeds.

Value

A vector of the medians of each row of x.

Author(s)

Arne Henningsen

Examples

   m <- matrix( 1:12, nrow = 4 )
   rowMedians( m )
m <- matrix( 1:12, nrow = 4 )
   rowMedians( m )

Calculate R squared value

Description

Calculate R squared value.

Usage

rSquared( y, resid )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 )$r.squared  # returns the same value
data( "Electricity", package = "Ecdat" )
   reg <- lm( cost ~ q + pl + pk + pf, Electricity )
   rSquared( Electricity$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, ...)
stdEr(x, ...)
## Default S3 method:
stdEr(x, ...)
## S3 method for class 'lm'
stdEr(x, ...)

Arguments

`x`	a statistical model, such as created by `lm`
`...`	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 [email protected]

Examples

data(cars)
lmRes <- lm(dist ~ speed, data=cars)
stdEr( lmRes )
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 )
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`x` be assigned to the returned sum? (only relevant if codex has only one element).
`na.rm`	logical. Passed to `sum`. Should missing values be removed?

Value

the sum (see sum).

Author(s)

Arne Henningsen

Examples

a <- 1:10
attr( a, "min" ) <- 1
attr( a, "max" ) <- 10
sum(a)
sumKeepAttr(a)
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, ... )
summarizeDF( dat, printValues = TRUE, maxLevel = 20, file = NULL, ... )

Arguments

`dat`	a data.frame.
`printValues`	logical. If `FALSE` only MD5 checksums are returned, which could be desirable if the data frame contains confidential data that should not be included in the output.
`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 `printValues` is `TRUE`), a frequency table is included in the output.
`file`	a character string or a writable connection naming the file to write to.
`...`	further arguments forwarded to `sink()` if argument `file` is not `NULL`.

Author(s)

Arne Henningsen

Symmetric Matrix

Description

Create a Symmetric Matrix.

Usage

   symMatrix( data = NA, nrow = NULL, byrow = FALSE,
   upper = FALSE )
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

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 )
# 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 )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

Examples

   v <- c( 1:5 )
   triang( v, 3 )
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 )vecli( m )

Arguments

`m`	symmetric matrix

Author(s)

Arne Henningsen

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
# 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 )vecli2m( v )

Arguments

v

a vector.

Author(s)

Arne Henningsen

Examples

   v <- c( 11, 12, 13, 22, 23, 33 )
   vecli2m( v )
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 )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

Examples

   veclipos( 1, 2, 3 )  # returns: 2
veclipos( 1, 2, 3 )  # returns: 2

Package 'miscTools'

Help Index

Coefficient Table

Description

Usage

Arguments

Value

Author(s)

Examples

Medians of Columns

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Scatterplot to Compare two Variables

Description

Usage

Arguments

Author(s)

Examples

Derivative of the Normal Distribution's Density Function

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Histogram with a Density Line

Description

Usage

Arguments

Author(s)

Examples

Insert Column into a Matrix

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Insert Row into a Matrix

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Positive or Negative Semidefiniteness

Description

Usage

Arguments

Details

Value

Author(s)

References

Examples

Method for Returning Marginal Effects

Description

Usage

Arguments

Author(s)

Return number of observations for statistical models

Description

Usage

Arguments

Details

Value

Author(s)

Examples

Number of model parameters

Description

Usage

Arguments

Details