Comparing Tidymodels in R to Scikit Learn in Python

I did a previous blog providing a side-by-side comparisons of R’s {tidyverse} to Python for various data manipulation techniques. I’ve also talked extensively about using {tidymodels} for model fitting (see HERE and HERE). Today, we will work through a tutorial on how to fit the same random forest model in {tidyverse} and Scikit Learn.

This will be a side-by-side view of both coding languages.The tutorial will cover:

  • Loading the data
  • Basic exploratory data analysis
  • Creating a train/test split
  • Hyperparameter tuning by creating cross-validated folds on the training data
  • Identifying the optimal hyperparameters and fitting the final model
  • Applying the final model to the test data and evaluating model performance
  • Saving the model for downstream use
  • Loading the saved model and applying it to new data

To get the full code for each language and follow along with the tutorial visit my GITHUB page.

The Data

The data comes the tidytuesday project from 4/4/2023. The data set is Premier League match data (2021 – 2022) that provides a series of features with the goal of predicting the final result (Full Time Result, FTR) as to whether the home team won, the away team won, or the match resulted in a draw.

Load Data & Packages

First, we load the data directly from the tidytuesday website in both languages.

Exploratory Data Analysis

Next, we perform some exploratory data analysis to understand the potential features for our model.

  • Check each column for NAs
  • Plot a count of the outcome variable across the three levels (H = home team wins, A = away team wins, D = draw)
  • Select a few features for our model and then create box plots for each feature relative to the 3 levels of our outcome variable

Train/Test Split

We being the model building process by creating a train/test split of the data.

Create a Random Forest Classifier Instance

This is basically telling R and python that we want to build a random forest classifier. In {tidymodels} this is referred to as “specifying the model engine”.

Hyperparameter Tuning on Cross Validated Folds

The two random forest hyperparameters we will tune are:

  1. The number of variables randomly selected for candidate model at each split (R calls this mtry while Python calls it max_features)
  2. The number of trees to grow (R calls this trees and Python calls it n_estimators)

In {tidymodels} we will specify 5 cross validated folds on the training set, set up a recipe, which explains the model we want (predicting FTR from all of the other variables in the data), put all of this into a single workflow and then set up our tuning parameter grid.

In Scikit Learn, we set up a dictionary of parameters (NOTE: they must be stored in list format) and we will pass them into a cross validation structure that performs 5-fold cross-validation in parallel (to speed up the process). We then pass this into the GridSearchCV() function where we specify the model we are fitting (random forest), the parameter grid that we’ve specified, and how we want to compare the random forest models (scoring). Additionally, we’ll set n_jobs = -1 to allow Python to use all of the cores on our machine.

While the code looks different, we’ve essentially set up the same process in both languages.

Tune the model on the training data

We can now tune the hyperparameters by applying the cross-validated folds procedure to the training data.

Above, we indicated to Python that we wanted some parallel processing, to speed up the process. In {tidyverse} we specify parallel processing by setting up the number of cores we’d like to use on our machine. Additionally, we will want to save the results of each cross-validated iteration, so we use the control_sample() function to do this. All of these steps were specified in Python, above, so we are ready to now apply cross-validation to our training dataset and tune the hyperparameters.

Get the best parameters

Both R and Python provide numerous objects to explore the output for each of the cross-validated folds. I’ve placed some examples in the respective codes in the GITHUB page. For our purposes, we are most interested in the optimal number of variables and trees. Both coding languages found 4 and 400 to be the optimal number of variables and trees, respectively.

Fitting the Final Model

Now that we have the optimal hyperparameter values, we can refit the model. In both {tidymodels} and Scikit learn, we’ll just refit a random forest with those optimal values specified.

Variable Importance Plot

It’s helpful to see which variables were the most important contributors to the model’s predictions.

Side Note: This takes more code in python than in R. This is one of the drawbacks I’ve found with python compared to R. I can do things more efficiently and with less code in R than in python. I often find I have to work a lot harder in Scikit Learn to get model outputs and information about the model fit. It’s all in there but it is not clearly accessible (to me at least) and plotting in matplotlib is not as clean as plotting in ggplot2.

Get Model Predictions on the Test Set

Both languages offer some out of the box options for describing the model fit info. If you want more than this (which you should, because this isn’t much to go off of), then you’ll have to extract the predicted probabilities and the actual outcomes and code some additional analysis (potentially a future blog article).

Save The Model

If we want to use this model for any downstream analysis we will need to save it.

Load the Model and Make Predictions

Once we have the model saved we can load it and apply it to any new data that comes in. Here, our new data will just be a selection of rows from the original data set (we will pretend it is new).

NOTE: Python is 0 indexed while R is indexed starting at 1. So keep that in mind if selecting rows from the original data to make the same comparison in both languages.

Wrapping Up

Both {tidymodels} and Scikit Learn provide users with powerful machine learning frameworks for conducting analysis. While the code syntax differs, the general concepts are the same, so bouncing between the two languages shouldn’t be to cumbersome. Hopefully this tutorial provided a nice overview of how to conduct the same analysis in both languages, offering a bridge for those trying to learn Python from R and vice versa.

All code is available on my GITHUB page.

TidyX Episode 156: Using Roxygen to set up custom functions in your R packages

Join Ellis Hughes and I as we continue our work from last week and build towards creating a full package with bespoke functions. Last week we discussed the functions that we’d be using in the package as well as why it might be useful to actually create a package with your commonly used functions. This week we show how to use Roxygen to creat those functions in your R-package so that they are accessible to the end use.

 

To watch our screen cast, CLICK HERE.

To access our code, CLICK HERE.

Simulations in R Part 5: Homoskedasticity Assumption in Regression

We’ve worked through a number of tutorials on building simulations and in Part 4 we worked up to building simulations for linear regression. Here are the previous 4 parts:

  • Part 1 discussed the basic functions for simulating and sampling data in R.
  • Part 2 walked us through how to perform bootstrap resampling and then simulate bivariate and multivariate distributions.
  • Part 3 we worked making group comparisons by simulating thousands of t-tests
  • Part 4 building simulations for linear regression

There are a number of assumptions that underpin linear regression models. Simulation can be a useful way of exploring these assumptions and understanding how violating these assumptions can lead to bias, large variance in the regression coefficients, and/or poor predictions.

Some typical assumptions include:

  1. Homoskedasticity
  2. Multicollinearity of independent variables
  3. Measurement Error
  4. Serial correlation

Today, we will explore the assumption of homoskedasticity.

As always, all code is freely available in the Github repository.

Creating the baseline simulation

Before exploring how violations of the homoskedasticity assumption influence a regression model, we need a baseline model to compare it against. So, we will begin by simulating a simple linear regression with 1 predictor. Our model will look like this:

y = 2 + 5*x + e

Where e will be random error from a normal distribution with a mean of 0 and standard deviation of 1.

The code below should look familiar as we’ve been building up simulations like this in the previous 4 tutorials. We specify the intercept to be 2 and the slope to be 5. The independent variable, x, is drawn from a uniform distribution between -1 and 1. With each of the 500 iterations of the for() loop we store the simulated intercept, slope, and their corresponding standard errors, which we calculate using the variance-covariance matrix (which we discussed in the previous tutorial). Finally, we also store the residual standard error (RSE) of each of the simulated models.

library(tidymodels)
library(patchwork)

## set seed for reproducibility
set.seed(58968)

## create a data frame to store intercept values, slope values, their standard errors, and the model residual standard error, for each simulation
sim_params <- data.frame(intercept = NA,
                      slope = NA,
                      intercept_se = NA,
                      slope_se = NA,
                      model_rse = NA)

# true intercept value
intercept <- 2

# true slope value
slope <- 5

## Number of simulations to run
n <- 500

# random draw from a uniform distribution to simulate the independent variable
X <- runif(n = n, min = -1, max = 1)

## loop for regression model
for(i in 1:n){
  
  # create dependent variable, Y
  Y <- intercept + slope*X + rnorm(n = n, mean = 0, sd = 1)
  
  # build model
  model <- lm(Y ~ X)
  
  ## store predictions
  fitted_vals <- model$fitted.values

  ## store residuals
  # output_df[i, 2] &lt;- model$residuals
  
  # variance-covariance matrix for the model
  vcv <- vcov(model)
  
  # estimates for the intercept
  sim_params[i, 1] <- model$coef[1]
  
  # estimates for the slope
  sim_params[i, 2] <- model$coef[2]
  
  # SE for the intercept
  sim_params[i, 3] <- sqrt(diag(vcv)[1])
  
  # SE for the slope
  sim_params[i, 4] <- sqrt(diag(vcv)[2])
  
  # model RSE
  sim_params[i, 5] <- summary(model)$sigma
  
}

head(sim_params)

Now we summarize the data to see if we have values close to the specified model parameters.

sim_params %>%
  summarize(across(.cols = everything(),
                   ~mean(.x)))

The average intercept and slope of the 500 simulated models are pretty much identical to the specified intercept and slope of 2 and 5, respectively.

The final model of the 500 iterations is also stored from our for loop and we can look directly at it and create plots of the model fit.

# model summary
summary(model)

# model fit plots
par(mfrow = c(2,2))
plot(model)

We can also create a function that lets us evaluate how often the 95% confidence interval of our simulated beta coefficients cover the true beta coefficients that we specified for the simulation. From there, we can get a coverage probability and a 95% probability coverage interval.

 

### Create a coverage probability function
coverage_interval95 <- function(beta_coef, se_beta_coef, true_beta_val, model_df){
  
  level95 <- 1 - (1 - 0.95) / 2
  
  # lower 95
  lower95 <- beta_coef - qt(level95, df = model_df)*se_beta_coef
  
  # upper 95
  upper95 <- beta_coef + qt(level95, df = model_df)*se_beta_coef
  
  # what rate did we cover the true value (hits and misses)
  hits <- ifelse(true_beta_val >= lower95 &amp; true_beta_val <= upper95, 1, 0)
  prob_cover <- mean(hits)
  
  # create the probability coverage intervals
  low_coverage_interval <- prob_cover - 1.96 * sqrt((prob_cover * (1 - prob_cover)) / length(beta_coef))
  
  upper_coverage_interval <- prob_cover + 1.96 * sqrt((prob_cover * (1 - prob_cover)) / length(beta_coef))
  
  # results in a list
  return(list('Probability of Covering the True Value' = prob_cover,
              '95% Prob ability Coverage Intervals' = c(low_coverage_interval, upper_coverage_interval)))
  
}

Let’s apply the function to the intercept.

coverage_interval95(beta_coef = sim_params$intercept,
                    se_beta_coef = sim_params$intercept_se,
                    true_beta = intercept,
                    model_df = model$df.residual)

Now apply the function to the slope.

coverage_interval95(beta_coef = sim_params$slope,
                    se_beta_coef = sim_params$slope_se,
                    true_beta = slope,
                    model_df = model$df.residual)

In both cases we are covering the true betas around 95% of the time, with relatively small intervals.

Homoskedasticity

Linear models make an assumption that the variance of the residuals remain constant across the predicted values (homoskedastic). We can see what this looks like by plotting the fitted values relative to the residuals, which was the first plot in the model check plots we created for the 500th simulation above. We can see that the residuals exhibit relatively the same amount of variance across the fitted values.

plot(model, which = 1)

Let’s simulate a model with heteroskedastic residuals and see what it looks like. We will keep the same intercept and slope parameters as above. The only thing will we do is add an exponential parameter to the error termĀ  of the model to create a heteroskedastic outcome in the residuals.

## parameter for heteroskedasticity 
heteroskedasticity_param <- 2

## set seed for reproducibility
set.seed(22)

## data frame for results
heteroskedastic_sim_params <- data.frame(intercept = NA,
                      slope = NA,
                      intercept_se = NA,
                      slope_se = NA,
                      model_rse = NA)

## for loop
for(i in 1:n ){
  
  # the error variance of Y is a function of X plus some random noise
  Y <- intercept + slope*X + rnorm(n = n, mean = 0, sd = exp(X*heteroskedasticity_param))
  
  # model
  heteroskedastic_model <- lm(Y ~ X)
  
  
  # variance-covariance matrix
  vcv <- vcov(heteroskedastic_model)
  
  # estimates for the intercept
  heteroskedastic_sim_params[i, 1] <- heteroskedastic_model$coef[1]
  
  # estimates for the slope
  heteroskedastic_sim_params[i, 2] <- heteroskedastic_model$coef[2]
  
  # SE for the intercept
  heteroskedastic_sim_params[i, 3] <- sqrt(diag(vcv)[1])
  
  # SE for the slope
  heteroskedastic_sim_params[i, 4] <- sqrt(diag(vcv)[2])
  
  # model RSE
  heteroskedastic_sim_params[i, 5] <- summary(heteroskedastic_model)$sigma
  
}

head(heteroskedastic_sim_params)


plot(X, Y, pch = 19)

The relationship between X and Y certainly looks weird given how it starts very tightly on the left side and then fans out on the right side.

Let’s take the average across all 500 simulations for each coefficient and their corresponding standard errors.

heteroskedastic_sim_params %>%
  summarize(across(.cols = everything(),
                   ~mean(.x)))

The coefficients of 2.0 for the intercept and 5 for the slope are exactly what we set them as for the simulation. However, notice how much larger the standard errors are for the intercept and slope compared to the original model above. Additionally, notice that the model residual standard error has increased substantially compared to the previous model.

Let’s get the 500th model again and check out the fitted vs residual plot.

# fitted vs residuals
plot(heteroskedastic_model, which = 1)

That looks like a large amount of heteroskedasticity as the residual variance is no longer homogenous across the range of fitted values. Notice the large fanning out towards the right side of the plot. As the predictions get larger so two does the variability in residuals, which we noticed when we plotted Y and X above.

What we’ve learned is that the estimate of intercept and slope is unbiased for both the heteroskedastic and homoskedastic models, as they both are centered on the parameters that we specified for the simulation (intercept = 2, slope = 5). However, the heteroskedastic model creates greater variance in our coefficients. We can visualize how much uncertainty there is under the heteroskedastic model relative to the homoskedastic model by visualizing the density of the coefficient estimates from our two model simulations.

plt_intercept <- sim_params %>%
  mutate(model = 'homoskedastic model') %>%
  bind_rows(
    heteroskedastic_sim_params %>%
      mutate(model = 'heteroskedastic model')
  ) %>%
  ggplot(aes(x = intercept, fill = model)) +
  geom_density(alpha = 0.6) +
  theme_classic() +
  theme(legend.position = "top")

plt_slope <- sim_params %>%
  mutate(model = 'homoskedastic model') %>%
  bind_rows(
    heteroskedastic_sim_params %>%
      mutate(model = 'heteroskedastic model')
  ) %>%
  ggplot(aes(x = slope, fill = model)) +
  geom_density(alpha = 0.6) +
  theme_classic() +
  theme(legend.position = "none")

plt_intercept | plt_slope

Finally, let’s see how often the 95% coverage interval is covering the true intercept and slope in the heteroskedastic model.

coverage_interval95(beta_coef = heteroskedastic_sim_params$intercept,
                    se_beta_coef = heteroskedastic_sim_params$intercept_se,
                    true_beta = intercept,
                    model_df = model$df.residual)


coverage_interval95(beta_coef = heteroskedastic_sim_params$slope,
                    se_beta_coef = heteroskedastic_sim_params$slope_se,
                    true_beta = slope,
                    model_df = model$df.residual)

Notice that we are no longer covering the true model values at the 95% level.

Wrapping Up

Simulations can be useful for evaluating model assumptions and seeing how a model may be have under different circumstances. In this tutorial we saw that a model suffering from severe heteroskedasticity is still able to return the true values for the intercept and slope. However, the variance around those values is large, meaning that we have a lot of uncertainty about what those true parameters actually are. In upcoming tutorials we will explore other linear regression assumptions. If this is a topic you enjoy, a book that I recommend (which heavily influenced today’s tutorial) is Monte Carlo Simulation and Resampling Methods for Social Sciences by Carsey & Harden.

As always, all code is freely available in the Github repository.

TidyX Episode 155: Functions for Custom Packages

This week, Ellis Hughes and I start a new series were we build a custom R package with bespoke functions that we wrote. This can be a great way to be efficient in your work (e.g., if there are tasks that you always find yourself doing) and ensure that your analytics team are all using the same functions, for quality control purposes. Write a package that contains the relevant functions and then all people have to do is call the package library and they are ready to role. This week we start with the functions that the package will contain.

To watch the screen cast, CLICK HERE.

To access our code, CLICK HERE.