Ranked Predictive Power of Cross-Features (x2y)

The relative reduction in error when we go from a baseline model (average for continuous and most frequent for categorical features) to a predictive model, can measure the strength of the relationship between two features. In other words, x2y measures the ability of x to predict y. We use CART (Classification And Regression Trees) models to be able to 1) compare numerical and non-numerical features, 2) detect non-linear relationships, and 3) because they are easy/quick to train.

Usage

x2y(
  df,
  target = NULL,
  symmetric = FALSE,
  target_x = FALSE,
  target_y = FALSE,
  plot = FALSE,
  top = 20,
  quiet = "auto",
  ohse = FALSE,
  corr = FALSE,
  ...
)

x2y_metric(x, y, confidence = FALSE, bootstraps = 20, max_cat = 20)

# S3 method for class 'x2y_preds'
plot(x, corr = FALSE, ...)

# S3 method for class 'x2y'
plot(x, type = 1, ...)

x2y_preds(x, y, max_cat = 10)

Arguments

df: data.frame. Note that variables with no variance will be ignored.
target: Character vector. If you are only interested in the x2y values between particular variable(s) in df, set name(s) of the variable(s) you are interested in. Keep NULL to calculate for every variable (column). Check target_x and target_y parameters as well.
symmetric: Boolean. x2y metric is not symmetric with respect to x and y. The extent to which x can predict y can be different from the extent to which y can predict x. Set symmetric=TRUE if you wish to average both numbers.
target_x, target_y: Boolean. Force target features to be part of x OR y?
plot: Boolean. Return a plot? If not, only a data.frame with calculated results will be returned.
top: Integer. Show/plot only top N predictive cross-features. Set to NULL to return all.
quiet: Boolean. Keep quiet? If not, show progress bar.
ohse: Boolean. Use lares::ohse() to pre-process the data?
corr: Boolean. Add correlation and pvalue data to compare with? For more custom studies, use lares::corr_cross() directly.
...: Additional parameters passed to x2y_metric()
x, y: Vectors. Categorical or numerical vectors of same length.
confidence: Boolean. Calculate 95% confidence intervals estimated with N bootstraps.
bootstraps: Integer. If confidence=TRUE, how many bootstraps? The more iterations we run the more precise the confidence internal will be.
max_cat: Integer. Maximum number of unique x or y values when categorical. Will select then most frequent values and the rest will be passed as "".
type: Integer. Plot type: 1 for tile plot, 2 for ranked bar plot.

Value

Depending on plot input, a plot or a data.frame with x2y results.

Details

This x2y metric is based on Rama Ramakrishnan's post: An Alternative to the Correlation Coefficient That Works For Numeric and Categorical Variables. This analysis complements our lares::corr_cross() output.

Examples

# \donttest{
data(dft) # Titanic dataset
x2y_results <- x2y(dft, quiet = TRUE, max_cat = 10, top = NULL)
head(x2y_results, 10)
#> # A tibble: 10 × 4
#>    x        y        obs_p   x2y
#>    <chr>    <chr>    <dbl> <dbl>
#>  1 Fare     Pclass     100  65.2
#>  2 Fare     Embarked   100  45.3
#>  3 Sex      Survived   100  44.4
#>  4 Fare     Parch      100  40.0
#>  5 Survived Sex        100  39.5
#>  6 Fare     SibSp      100  35.4
#>  7 Pclass   Fare       100  32.1
#>  8 Ticket   SibSp      100  25.3
#>  9 SibSp    Parch      100  21.6
#> 10 Fare     Survived   100  20.5
plot(x2y_results, type = 2)


# Confidence intervals with 10 bootstrap iterations
x2y(dft,
  target = c("Survived", "Age"),
  confidence = TRUE, bootstraps = 10, top = 8
)
#> # A tibble: 8 × 6
#>   x        y        obs_p   x2y lower_ci upper_ci
#>   <chr>    <chr>    <dbl> <dbl>    <dbl>    <dbl>
#> 1 Sex      Survived 100   44.4     35.2      48.1
#> 2 Survived Sex      100   39.5     33.6      45.8
#> 3 Fare     Survived 100   20.5     -6.4      17.0
#> 4 Age      Parch     80.1 18.9     12.8      21.4
#> 5 Pclass   Survived 100   16.4     11.9      24.5
#> 6 Age      Pclass    80.1 14.8      7.57     15.3
#> 7 Age      SibSp     80.1 10.6      3.5      12.4
#> 8 Cabin    Survived 100    8.19     5.95     10.5

# Compare with mean absolute correlations
x2y(dft, "Fare", corr = TRUE, top = 6, target_x = TRUE)
#> # A tibble: 6 × 6
#>   x     y        obs_p   x2y mean_abs_corr mean_pvalue
#>   <chr> <chr>    <dbl> <dbl>         <dbl>       <dbl>
#> 1 Fare  Pclass     100  65.2         0.375    1.30e- 4
#> 2 Fare  Embarked   100  45.3         0.150    4.35e- 2
#> 3 Fare  Parch      100  40.0         0.216    6.92e-11
#> 4 Fare  SibSp      100  35.4         0.160    1.67e- 6
#> 5 Fare  Survived   100  20.5         0.257    6.12e-15
#> 6 Fare  Sex        100  13.7         0.182    4.23e- 8

# Plot (symmetric) results
symm <- x2y(dft, target = "Survived", symmetric = TRUE)
plot(symm, type = 1)


# Symmetry: x2y vs y2x
on.exit(set.seed(42))
x <- seq(-1, 1, 0.01)
y <- sqrt(1 - x^2) + rnorm(length(x), mean = 0, sd = 0.05)

# Knowing x reduces the uncertainty about the value of y a lot more than
# knowing y reduces the uncertainty about the value of x. Note correlation.
plot(x2y_preds(x, y), corr = TRUE)

plot(x2y_preds(y, x), corr = TRUE)

# }