# Exploring Methods to Fit Discrete Values to Data with Implot in Python

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π‘ Problem Formulation: When working with data visualization in Python, you may encounter the challenge of fitting a model to data that includes one or more discrete variables. Implot function, typically available through libraries like seaborn, can handle discrete data variables, but requires specific approaches. This article provides examples of how to seamlessly incorporate discrete values into visualization and analysis to obtain valuable insights from your dataset.

## Method 1: Using FacetGrid for Multiple Discrete Values

The `FacetGrid` function in the seaborn library is a potent tool for creating a grid of axes to plot subsets of data based on the discrete variable’s values. One can then apply a fitting function to each subplot to visualize how the fit interacts with data across different categories.

Here’s an example:

```import seaborn as sns
import matplotlib.pyplot as plt

# Create a facet grid object
g = sns.FacetGrid(tips, col='time', height=4)
# Map a scatter plot to each subset of the data
g.map(sns.regplot, 'total_bill', 'tip')
plt.show()```

The output is a set of two fitted scatter plots, one for each category of the ‘time’ (lunch and dinner) discrete variable with a regression line through the points.

This code snippet first loads an example dataset provided by seaborn. It then creates a `FacetGrid` object that sets up a grid of plots based on the ‘time’ variable. The `map` method is used to apply the `sns.regplot` to each subplot, showing the relationship between ‘total_bill’ and ‘tip’, with a regression line that fits the data.

## Method 2: Stripplot Combined with Regplot

Seaborn’s `stripplot` can be combined with `regplot` to fit a regression model to a continuous and a discrete variable concurrently. By overlaying a strip plot on a regression plot, your audience can see both the raw data and the fitted values.

Here’s an example:

```import seaborn as sns
import matplotlib.pyplot as plt

# Create regression plot
sns.regplot(x='size', y='total_bill', data=tips, x_jitter=.1)
# Overlay with strip plot
sns.stripplot(x='size', y='total_bill', data=tips, color='black', alpha=0.5)
plt.show()```

The output is a scatter plot where the discrete variable ‘size’ instances are spread along the x-axis and each point represents ‘total_bill’. A line through the points shows the fitted regression model.

This code loads the ‘tips’ dataset and first plots a `regplot` which fits a regression line to the ‘size’ (discrete) and ‘total_bill’. To differentiate individual discrete values, jitter is added. Afterward, a `stripplot` is overlaid to display all individual data points, applying transparency (alpha) for better readability.

## Method 3: Using lmplot For Direct Modeling

The `lmplot` function in seaborn is a higher-level interface for fitting and plotting a regression line to a dataset, with support for modeling different data subsets using row, col, and hue parameters to represent discrete variables.

Here’s an example:

```import seaborn as sns
# Create a lmplot
sns.lmplot(x='total_bill', y='tip', col='sex', data=tips)
plt.show()```

The output is two scatter plots with regression lines, one for each level of the discrete variable ‘sex’.

By invoking `sns.lmplot` we automatically create a figure with regression lines fitted to ‘total_bill’ and ‘tip’ measurements, separated into columns by the discrete ‘sex’ variable. The `lmplot` conveniently handles discrete data and allows for easy comparison across different subgroups.

## Method 4: Swarmplot to Show Distribution with lmplot

Combining `lmplot` and `swarmplot` allows you to concurrently display the distribution of data points and the fitted regression model. This is particularly useful for understanding the data distribution relative to the fit for each category of the discrete variable.

Here’s an example:

```import seaborn as sns
import matplotlib.pyplot as plt

# Create a lmplot
sns.lmplot(x='total_bill', y='tip', data=tips, robust=True)
# Create a swarmplot
sns.swarmplot(x='total_bill', y='tip', data=tips, color='black', size=3)
plt.show()```

The output shows points distributed around the regression line, accounting for both outliers and concentrated data regions, adding more context to the regression fit.

In this snippet, `sns.lmplot` provides a regression analysis while `sns.swarmplot` gives a non-overlapping distribution of every individual point. The `robust` parameter in `lmplot` makes the fit more resistant to outliers, which is important when both fitting and visualizing discrete data points.

## Bonus One-Liner Method 5: lmplot with Order Parameter

Seaborn’s `lmplot` comes with an `order` parameter that allows you to fit polynomial regression models. This can be ideal for discrete variables that have a natural ordered relationship.

Here’s an example:

```import seaborn as sns
# Fit a second-order polynomial regression
sns.lmplot(x='size', y='total_bill', data=tips, order=2)
plt.show()```

The output is a scatter plot with a quadratic regression curve, showing a non-linear fit to the dataset considering the ‘size’ as an ordered discrete variable.

This one-liner enables fitting to discrete, ordered data by specifying the `order` parameter in the `lmplot` function. The higher the order, the more complex the model, allowing for non-linear relationships between the discrete variable and other continuous metrics.

## Summary/Discussion

• Method 1: FacetGrid. Great for comparing subsets of data based on discrete values. Requires separate plots, less suitable for a large number of categories due to space constraints.
• Method 2: Stripplot with Regplot. Allows for fitting and displaying both data points and model fit. Can overlap points if the discrete variable has many levels.
• Method 3: lmplot. Convenient for direct modeling with discrete variables. Sometimes may need customization for proper hue separation.
• Method 4: Swarmplot with lmplot. Enables comprehensive data distribution visualization along with fitting. Can become cluttered with large datasets.
• Bonus One-Liner Method 5: lmplot with Order. Fits polynomial regression, suited for ordered discrete variables. Attention needed for overfitting risks with high order polynomials.