vastorbit.machine_learning.model_selection.statistical_tests.ols.variance_inflation_factor

vastorbit.machine_learning.model_selection.statistical_tests.ols.variance_inflation_factor(input_relation: Annotated[str | VastFrame, ''], X: Annotated[str | list[str], 'STRING representing one column or a list of columns'], X_idx: int | None = None) → float | TableSample

Computes the variance inflation factor (VIF). It can be used to detect multicollinearity in an OLS Regression Analysis.

Parameters:

• input_relation (SQLRelation) – Input relation.

• X (list) – Input Variables.

• X_idx (int) – Index of the exogenous variable in X. If empty, a TableSample is returned with all the variables VIF.

Returns:

VIF.

Return type:

float / TableSample

Examples

Initialization

Let’s try this test on a dummy dataset that has the following elements:

• data with multiple columns

Before we begin we can import the necessary libraries:

import vastorbit as vo
import numpy as np

Next, we can create some exogenous columns with varying collinearity:

N = 50
x_val_1 = list(range(N))
x_val_2 = [2 * x + np.random.normal(scale = 4) for x in x_val_1]
x_val_3 = np.random.normal(0, 4, N)

We can use those values to create the VastFrame:

vdf = vo.VastFrame(
    {
        "x1": x_val_1,
        "x2": x_val_2,
        "x3": x_val_3,
    }
)

Data Visualization

We can plot the data to see any underlying collinearity:

Let us first draw x1 with x2:

vdf.scatter(["x1", "x2"])

We can see that x1 and x2 are very correlated.

Next let us observe x1 and x3:

vdf.scatter(["x1", "x3"])

We can see that the two are not correlated.

Now we can confirm our observations by carrying out the VIC test. First, we can import the test:

from vastorbit.machine_learning.model_selection.statistical_tests import variance_inflation_factor

And then apply it on the exogenous columns:

variance_inflation_factor(vdf, X = ["x1", "x2", "x3"])

	X_idx	VIF
1	"x1"	55.00370692278499
2	"x2"	55.07402738733522
3	"x3"	1.017220571654422

Rows: 1-3 | Columns: 2

Note

We can clearly see that x1 and x2 are correlated because of the high value of VIC. But there is no correlation with x3 as the VIC value is close to 1.