In dclarkboucher/MLR: Multiple Linear Regression

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

library(MLR)

Example 1: Simple Linear Regression

Fit linear model on dataset

To fit a linear model, simply input a formula and dataset to the regression_fit() fit function. This produces a list containing the following objects:

• formula: the model formula
• dimensions: the number of observations and covariates
• residuals: the model residuals, as a vector
• fitted_values: the fitted values of the model, as a vector
• coefficients: the estimated coefficients, as a table, which also contains the results of a two-sided t-test
• confidence_intervals: (1-alpha)% confidence intervals for each coefficient, as a matrix
• variances: the variance-covariance matrix
• anova: the results of an ANOVA test, as a list
• r_squared: the R-squared and adjusted R-square, as a vector of length 2

data(iris)
form <- Sepal.Length ~ Sepal.Width

model1 <- regression_fit(formula = form, data = iris)
print(model1$coefficients)

Compare results to base functions

Below, we test to ensure that our results align with the standard output from base R alternatives. One advantage of regression_fit(), you might observe, is that we can access important model components without needing to use additional functions like summary() or vcov().

model2 <- lm(formula = form, data = iris)
model2_sum <- summary(model2)

#Check coefficients
all.equal(model1$coefficients, model2_sum$coefficients)

#Check confidence intervals
all.equal(model1$confidence_intervals,confint(model2))

#Check residuals
all.equal(model1$residuals, model2$residuals, check.attributes = F)

#Check fitted values
all.equal(model1$fitted_values, model2$fitted.values, check.attributes = F)

#Check variance-covariance
all.equal(model1$variances, vcov(model2), check.attributes = F)

#Check F test
all.equal(model1$anova$f_value, model2_sum$fstatistic["value"], check.attributes = F)

#Check R-squared
model2_rsq <- c(model2_sum$r.squared, model2_sum$adj.r.squared)
all.equal(model1$r_squared, model2_rsq, check.attributes = F)

Compare speed to base functions

Next, we compare the efficiency of regression_fit() to lm() using the bench package. We can see in the output table below that the lm() function is marginally faster on average.

library(bench)

bench::mark(
  regression_fit(form, iris)$coefficients,
  summary(lm(form, iris))$coefficients
)

Example 2: Multiple Linear Regression

Fit linear model on dataset

We can fit a multiple regression model in the same way as an SLR. Here, we have also specified a particular alpha to use in our confidence intervals, instead of using the default of 0.05.

form2 <- Sepal.Length ~ Sepal.Width + Petal.Length + Species

model1 <- regression_fit(formula = form2, data = iris, alpha = 0.1)
print(model1$coefficients)

Compare results to base functions

Once again, we test the results below. All match the output provided by base R functions.

model2 <- lm(formula = form2, 
             data = iris)

model2_sum <- summary(model2)

#Check coefficients
all.equal(model1$coefficients, model2_sum$coefficients)

#Check confidence intervals
all.equal(model1$confidence_intervals,confint(model2, level = 0.9))

#Check residuals
all.equal(model1$residuals, model2$residuals, check.attributes = F)

#Check fitted values
all.equal(model1$fitted_values, model2$fitted.values, check.attributes = F)

#Check variance-covariance
all.equal(model1$variances, vcov(model2), check.attributes = F)

#Check F test
all.equal(model1$anova$f_value, model2_sum$fstatistic["value"], check.attributes = F)

#Check R-squared
model2_rsq <- c(model2_sum$r.squared, model2_sum$adj.r.squared)
all.equal(model1$r_squared, model2_rsq, check.attributes = F)

Compare speed to base functions

Lastly, we compare the speed of regression_fit() and lm() for multiple linear regression. Like before, we find that the base R function might be marginally faster, but the results do vary slightly from one trial to the next.

bench::mark(
  regression_fit(form2, iris)$coefficients,
  summary(lm(form2, iris))$coefficients
)

dclarkboucher/MLR documentation built on Dec. 31, 2020, 11:14 p.m.