Muhammad Imdad Ullah, Author at R Language Frequently Asked Questions

R Objects, Workspace, and .RData file

July 23, 2024March 12, 2017 by Muhammad Imdad Ullah

The post is about an introduction to workspace, R objects, and .Rdata file in R language.

R Language as Functional Language

The R program’s structure is similar to the programs written in other computer languages such as C or its successors C++ and Java. However, important differences between these languages and R are (i) R has no header files, (ii) most of the declarations are implicit, (iii) there are no pointers in R, and (iv) text and strings as vectors can be defined and manipulated directly.

R is a functional language. Most of the computation in R is handled using functions. The R language environment is designed to facilitate the development of new scientific computation tools.

R Objects

Everything (such as functions and data structure) in R is an object. To see the names of all R objects in the workspace, on the R command prompt just type,

ls()

objects() is an alternative to ls() function. Similarly, typing the name of any object on the R prompt displays (prints) the content of that object. As an example type q, mean, and lm, etc. on the R prompt.

R Workspace

It is possible to save individual objects or collections of objects into a named image file. The named image file has an extension of .RData. Some possibilities to save an object from R workspace are:

To save the content of R workspace into a file .RData, type

save.image()

To save objects in the file archive.RData, type

save.image(file = "archive.RData")

To save some required objects in data.RData, type

save(x, y, file = "data.RData")

These image files can be attached to make objects available in the next R session. For example.

attached ("arvhive.RData")

Note that when quitting, R offers the option of saving the workspace image. By default, the workspace is saved in an image file (.RData) in the working directory. The image file can be used in the next R session. Saving the workspace image will save everything from the current workspace. Therefore, use the rm() function to remove objects that are not further required in the next R session.

For further details about saving and loading R workspace visit: Save and Load R Workspace

Learn Statistics and Data Analysis

mctest R Package for Detection of Collinearity

September 21, 2024January 20, 2017 by Muhammad Imdad Ullah

In this post, I will discuss the existence and detection of collinearity among regressors using the mctest R Package.

The problem of multicollinearity plagues the numerical stability of regression estimates. It also causes some serious problems in the validation and interpretation of the regression model. Consider the usual multiple linear regression model,

$$y = X \beta+u$$

where $y$ is an $n\times 1$ vector of observation on dependent variable, $X$ is known design matrix of order $\times p$, having full-column rank $p$, $\beta$ is $p \times 1$ vector of unknown parameters and $u$ is an $n\times 1$ vector of random errors with mean zero and variance $\sigma^2 I_n$, where $I_n$ is an identity matrix of order $n$.

Collinearity Among Regressors

The existence of linear dependence (relationship) between regressors can affect the regression model’s ability to estimate the model’s parameters. Therefore, multicollinearity is a lack of independence or the presence of interdependence signified by usually high inter-correlations within a set of regressors (predictors).

In case of severe multicollinearity (mathematically when the matrix is ill-conditioned) the $X’X$ matrix cannot be inverted, implausible signs of coefficients, low t-ratios, high R-squared values, inflated standard errors, wider confidence intervals, very large condition number (CN) and non-significant and/or magnitude of regression coefficient estimates are some of the possible issues.

There are many diagnostic methods are available to check the existence of collinearity among regressors, such as variance inflation Factor (VIF), values of pair-wise correlation among regressors, eigenvalues, CN, Farrar and Glauber tests, Theil’s measure, and Klein’s rule, etc.

Our recently developed R package mctest computes several collinearity diagnostics measures to test the existence of collinearity among regressors. We classified these measures as individual collinearity diagnostics and overall collinearity diagnostics. Overall collinearity diagnostic includes determinant of $X’X$ matrix, red indicator, Farrar Chi-Square test, Theil indicator, CN, and the sum of lambda inverse values. Individual collinearity diagnostics include VIF/ TOL, Farrar and Glauber Wi test, the relationship between $R^2$ and F-test, corrected VIF (CVIF), and Klein’s rule.

How to use the mctest R Package

You must have installed and loaded the mctest R Package to start with the testing/ detection of collinearity among regressors. As an example, we used Hald data which is already bundled in the mctest R Package.

mctest R package have 4 functions namely, mctest(), omcdiag(), imcdiag() and mc.plot() functions. The mctest() function can be used to have overall and/or individual collinearity diagnostic. The mc.plot() is used to draw the graph of VIF and eigenvalues to judge collinearity among regressors.

mctest illustrative Example

Arguments of mctest with syntax are

mctest(x, y, type = c("o", "I", "b"), na.rm = TRUE, Inter = TRUE, method = NULL, corr = FALSE, detr = 0.01, red = 0.5, theil = 0.5, cn = 30, vif = 10, tol = 0.1, conf = 0.95, cvif = 10, leamer = 0.1, all = all)

See the detail of each argument and see the mctest package documentation. Following are a few commands that can be used to get different collinearity diagnostics.

x <- Hald[ ,-1]     # X variables from Hald data
> y <- Hald[ ,1]      # y variable from Hald data

mctest(x, y)        # default collinearity diagnostics
mctest(x, y, type = "i")  # individual collinearity diagnostics
mctest(x, y, type = "o") # overall collinearity diagnostics

Overall Collinearity Diagnostics in R

For overall collinearity diagnostics, eigenvalues, and condition numbers are also produced whether the intercept term is included or not. The syntax of omcdiag() function is

omcdiag(x, y, na.rm = TRUE, Inter = True, detr = 0.01, red = 0.5, conf = 0.95, theil = 0.5, cn = 30, …)

Determinant of the correlation matrix, Farrar test of Chi-square, Red indicator, the sum of lambda inverse values, Theils’ indicator, and CN.

omcdiag(x, y, Inter=FALSE)
omcdiag(x, y)[1]

omcidag(x,y, detr = 0.001, conf = 0.99)

For the last command (with the threshold for determinant and confidence interval for the Farrar and Glauber test). The output is,

mctest r package overall collinearity diagnostics

Individual Collinearity Diagnostics in R

The general syntax of individual collinearity Diagnostics in R Language through mctest packages is:

imcdiag(x, y, method = NULL, na.rm = TRUE, corr = FALSE, vif = 10, tol = 0.1, conf = 0.95, cvif = 10, leamer = 0.1, all = all)

Function imcdiag() detects the existence of multicollinearity due to certain X-variable. This includes VIF, TOL, Klein’s rule, CVIF, F&G test of Chi-square and F-test.

imcdiag(x = x, y)
imcdiag(x = x, y, corr = TRUE) # correlation matrix
imcdiag(x = x, y, vif = 5, leamer = 0.05)  # with threshold of VIF and leamer method

mctest r package individual collinearity diagnostics

imcdiag(x = x, y, all = True)
imcdiag(x = x, y, all = TRUE, vif = 5, leamer = 0.2, cvif = 5)

mctest: individual collinearity diagnostics

Graphical Representation of VIF and Eigenvalues

mc.plot(x, y, Inter = FALSE, vif = 10, ev = 0.01)
mc.plot(x, y)
mc.plot(x, y, vif = 5, ev = 0.2)

mctest: collinearity diagnostic measures

For further details about collinearity diagnostic see

Statistical Models in R Language: Secrets

September 5, 2024November 10, 2016 by Muhammad Imdad Ullah

R language provides an interlocking suite of facilities that make fitting statistical models very simple. The output from statistical models in R language is minimal and one needs to ask for the details by calling extractor functions.

Defining Statistical Models in R Language

The template for a statistical model is a linear regression model with independent, heteroscedastic errors, that is
$$\sum_{j=0}^p \beta_j x_{ij}+ e_i, \quad e_i \sim NID(0, \sigma^2), \quad i=1,2,\dots, n, j=1,2,\cdots, p$$

In matrix form, the statistical model can be written as

$$y=X\beta+e$$

where the $y$ is the dependent (response) variable, $X$ is the model matrix or design matrix (matrix of regressors), and has columns $x_0, x_1, \cdots, x_p$, the determining variables with intercept term. Usually, $x_0$ is a column of ones defining an intercept term in the statistical model.

Statistical Model Examples

Suppose $y, x, x_0, x_1, x_2, \cdots$ are numeric variables, $X$ is a matrix. Following are some examples that specify statistical models in R.

y ~ x or y ~ 1 + x
Both examples imply the same simple linear regression model of $y$ on $x$. The first formulae have an implicit intercept term and the second formulae have an explicit intercept term.
y ~ 0 + x or y ~ -1 + x or y ~ x – 1
All these imply the same simple linear regression model of $y$ on $x$ through the origin, without an intercept term.
log(y) ~ x1 + x2
Imply multiple regression of the transformed variable, $(log(y)$ on $x_1$ and $x_2$ with an implicit intercept term.
y ~ poly(x , 2) or y ~ 1 + x + I(x, 2)
Imply a polynomial regression model of $y$ on $x$ of degree 2 (second-degree polynomials) and the second formulae use explicit powers as a basis.
y~ X + poly(x, 2)
Multiple regression $y$ with a model matrix consisting of the design matrix $X$ as well as polynomial terms in $x$ to degree 2.

Note that the operator ~ defines a model formula in R language. The form of an ordinary linear regression model is, $response\,\, ~ \,\, op_1\,\, term_1\,\, op_2\,\, term_2\,\, op_3\,\, term_3\,\, \cdots $,

where

The response is a vector or matrix defining the response (dependent) variable(s).
$op_i$ is an operator, either + or -, implying the inclusion or exclusion of a term in the model. The + operator is optional.
$term_i$ is either a matrix or vector or 1. It may be a factor or a formula expression consisting of factors, vectors, or matrices connected by formula operators.

FAQS about Statistical Models in R

How statistical models are specified in R Language?
How linear regression is performed in R language using the formula?
How linear regression can be performed without intercept in r?
How polynomial regression can be performed in R?
Write about the ~ operator in R.

Statistical Models in R Language R FAQs https://rfaqs.com

https://gmstat.com
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