In lamke07/stat545lamke07: Collection of functions to create quick data sets

Setup and Overview

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

library(stat545lamke07)

The purpose of the stat545lamke07 package is to be able to quickly test a method of interest on a toy data set. To that end, the functions starting with generate_ aim to create data sets based on the normal distribution.

Generating only X

The key component of the stat545lamke07 package is the generate_X() function, which generates a data set $S = (X)$ where the columns of $X$ are normally distributed. The usage of such a data set is extremely flexible, as we can transform the data set quickly. To run the generate_X(), all we require is the number of data samples, as well as the right parametrization of $\mu$ and $\sigma$ (mu and sigma).

df_X <- generate_X(n = 10, mu = rep(0,5), sigma = rep(2, 5))
print(head(df_X))

It is then possible to perform experiments of interest, such as the eigendecomposition of the correlation matrix.

eigen(cor(df_X))

Generating only X and Y

Suppose we would like to understand the effect of including more variables in our linear model. In addition to just generating $X$ using generate_X(), we can now specify the exact linear coefficients using the beta_coefficients parameter to obtain $$Y = X^T \beta$$ which leads to the data set $S = (X,Y)$. Note that we need to ensure that the number of columns of $X$ are the same as the number of coefficients in beta_coefficients. With the use of generate_XY(), we first generate the data set.

df <- generate_XY(n = 1000, mu = rep(0,10), sigma = rep(2,10), beta_coefficients = 1:10)
print(head(df))

Having generated the data set, we can now fit some linear models as well.

# Test a linear model with 3 variables
m1 <- lm(Y~ X1 + X2 + X3, data = df)
summary(m1)

# Test a linear model with 6 variables
m2 <- lm(Y~ X1 + X2 + X3 + X4 + X5 + X6, data = df)
summary(m2)

We can quickly modify our assumptions about the data set by changing the relevant parameters in the generate_XY() function, namely mu, sigma, and beta_coefficients.

df <- generate_XY(n = 1000, mu = 51:55, sigma = seq(10,15, length.out = 5), beta_coefficients = 21:25)
print(head(df))

Generating X with categorical variables

So far we have assumed that $X$ contains only continuous variables. However, it is also possible to include categorical variables in the data set. To this end, we have written the generate_X_cat() function that additionally computes categorical factors, which can be achieved through the no_of_cat parameter. For example, no_of_cat = c(4,5) is a vector where each entry corresponds to the number of categories in each column. In this case, we would have one column with 4 categories and 5 categories each.

df_cat <- generate_X_cat(n = 40, mu = 1:5, sigma = rep(1, 5), no_of_cat = c(4,5))
print(head(df_cat))

lamke07/stat545lamke07 documentation built on Dec. 21, 2021, 8:49 a.m.