openavmkit.utilities.stats

calc_chds

calc_chds(df_in, field_cluster, field_value)

Calculate the Coefficient of Horizontal Dispersion (CHD) for each cluster in a DataFrame.

CHD is the same statistic as COD, the Coefficient of Dispersion, but calculated for horizontal equity clusters and used to measure horizontal dispersion, on the theory that similar properties in similar locations should have similar valuations. The use of the name "CHD" is chosen to avoid confusion because assessors strongly associate "COD" with sales ratio studies.

This function computes the CHD for each unique cluster in the input DataFrame based on the values in the specified field.

Parameters:

Name	Type	Description	Default
df_in	DataFrame	Input DataFrame	required
field_cluster	str	Name of the column representing cluster identifiers.	required
field_value	str	Name of the column containing the values for COD calculation	required

Returns:

Type	Description
A Series of COD values for each row, aligned with df_in

Source code in openavmkit/utilities/stats.py

def calc_chds(df_in: pd.DataFrame, field_cluster: str, field_value: str):
    """Calculate the Coefficient of Horizontal Dispersion (CHD) for each cluster in a
    DataFrame.

    CHD is the same statistic as COD, the Coefficient of Dispersion, but
    calculated for horizontal equity clusters and used to measure horizontal dispersion, on
    the theory that similar properties in similar locations should have similar valuations.
    The use of the name "CHD" is chosen to avoid confusion because assessors strongly
    associate "COD" with sales ratio studies.

    This function computes the CHD for each unique cluster in the input DataFrame based on
    the values in the specified field.

    Parameters
    ----------
    df_in : pd.DataFrame
        Input DataFrame
    field_cluster : str
        Name of the column representing cluster identifiers.
    field_value : str
        Name of the column containing the values for COD calculation

    Returns
    -------
    A Series of COD values for each row, aligned with df_in
    """
    # Create a dataframe matching the index of df_in with only the cluster id.
    df = df_in[[field_cluster]].copy()
    df["chd"] = 0.0

    clusters = df[field_cluster].unique()

    for cluster in clusters:
        df_cluster = df[df[field_cluster].eq(cluster)]
        # exclude negative and null values:
        df_cluster = df_cluster[
            ~pd.isna(df_cluster[field_value]) & df_cluster[field_value].gt(0)
        ]

        chd = calc_cod(df_cluster[field_value].values)
        df.loc[df[field_cluster].eq(cluster), "chd"] = chd

    return df["chd"]

calc_cod

calc_cod(values)

Calculate the Coefficient of Dispersion (COD) for an array of values.

COD is defined as the average absolute deviation from the median, divided by the median, multiplied by 100. Special cases are handled if the median is zero.

Parameters:

Name	Type	Description	Default
values	ndarray	Array of numeric values.	required

Returns:

Type	Description
float	The COD percentage.

Source code in openavmkit/utilities/stats.py

def calc_cod(values: np.ndarray) -> float:
    """
    Calculate the Coefficient of Dispersion (COD) for an array of values.

    COD is defined as the average absolute deviation from the median, divided by the
    median, multiplied by 100. Special cases are handled if the median is zero.

    Parameters
    ----------
    values : numpy.ndarray
        Array of numeric values.

    Returns
    -------
    float
        The COD percentage.
    """
    if len(values) == 0:
        return float("nan")

    median_value = np.median(values)
    abs_delta_values = np.abs(values - median_value)
    avg_abs_deviation = np.sum(abs_delta_values) / len(values)
    if median_value == 0:
        # if every value is zero, the COD is zero:
        if np.all(values == 0):
            return 0.0
        else:
            # if the median is zero but not all values are zero, return infinity
            return float("inf")
    cod = avg_abs_deviation / median_value
    cod *= 100
    return cod

calc_cod_bootstrap

calc_cod_bootstrap(values, confidence_interval=0.95, iterations=10000, seed=777)

Calculate COD using bootstrapping.

This function bootstraps the input values (resampling with replacement) to generate a distribution of CODs, then returns the median COD along with the lower and upper bounds of the confidence interval.

Parameters:

Name	Type	Description	Default
values	ndarray	Array of numeric values.	required
confidence_interval	float	The desired confidence level. Defaults to 0.95.	0.95
iterations	int	Number of bootstrap iterations. Defaults to 10000.	10000
seed	int	Random seed for reproducibility. Defaults to 777.	777

Returns:

Type	Description
tuple[float, float, float]	A tuple containing the median COD, lower bound, and upper bound of the confidence interval.

Source code in openavmkit/utilities/stats.py

def calc_cod_bootstrap(
    values: np.ndarray,
    confidence_interval: float = 0.95,
    iterations: int = 10000,
    seed: int = 777
) -> tuple[float, float, float]:
    """
    Calculate COD using bootstrapping.

    This function bootstraps the input values (resampling with replacement) to
    generate a distribution of CODs, then returns the median COD along with the
    lower and upper bounds of the confidence interval.

    Parameters
    ----------
    values : numpy.ndarray
        Array of numeric values.
    confidence_interval : float, optional
        The desired confidence level. Defaults to 0.95.
    iterations : int, optional
        Number of bootstrap iterations. Defaults to 10000.
    seed : int, optional
        Random seed for reproducibility. Defaults to 777.

    Returns
    -------
    tuple[float, float, float]
        A tuple containing the median COD, lower bound, and upper bound of the confidence interval.
    """

    n = len(values)
    if n == 0:
        return float("nan"), float("nan"), float("nan")
    np.random.seed(seed)

    # Replace negative values with zero:
    values = np.where(values < 0, 0, values)

    median = np.median(values)
    samples = np.random.choice(values, size=(iterations, n), replace=True)
    abs_delta_values = np.abs(samples - median)
    bootstrap_cods = np.mean(abs_delta_values, axis=1) / median * 100
    alpha = (1.0 - confidence_interval) / 2
    lower_bound, upper_bound = np.quantile(bootstrap_cods, [alpha, 1.0 - alpha])
    median_cod = np.median(bootstrap_cods)
    return median_cod, lower_bound, upper_bound

calc_correlations

calc_correlations(X, threshold=0.1, do_plots=False)

Calculate correlations and iteratively drop variables with low combined scores.

This function computes the correlation matrix of X, then calculates a combined score for each variable based on its correlation strength with the target variable and its average correlation with other variables. Variables whose scores fall below the specified threshold are removed.

Parameters:

Name	Type	Description	Default
X	DataFrame	Input DataFrame containing the variables to evaluate.	required
threshold	float	Minimum acceptable combined score for variables. Variables with a score below this value will be dropped. Defaults to 0.1.	0.1
do_plots	bool	If True, plot the initial and final correlation heatmaps. Defaults to False.	False

Returns:

Type	Description
dict	Dictionary with two keys: "initial": pandas.Series of combined scores from the first iteration. "final": pandas.Series of combined scores after dropping low-scoring variables.

Source code in openavmkit/utilities/stats.py

def calc_correlations(
    X: pd.DataFrame,
    threshold: float = 0.1,
    do_plots: bool = False
) -> dict:
    """
    Calculate correlations and iteratively drop variables with low combined scores.

    This function computes the correlation matrix of `X`, then calculates a combined score
    for each variable based on its correlation strength with the target variable and its
    average correlation with other variables. Variables whose scores fall below the
    specified `threshold` are removed.

    Parameters
    ----------
    X : pandas.DataFrame
        Input DataFrame containing the variables to evaluate.
    threshold : float, optional
        Minimum acceptable combined score for variables. Variables with a score below this
        value will be dropped. Defaults to 0.1.
    do_plots : bool, optional
        If True, plot the initial and final correlation heatmaps. Defaults to False.

    Returns
    -------
    dict
        Dictionary with two keys:

        - "initial": pandas.Series of combined scores from the first iteration.
        - "final": pandas.Series of combined scores after dropping low-scoring variables.
    """
    X = X.copy()
    first_run = None

    # Normalize all numerical values prior to computation:
    for col in X.columns:
        if X[col].dtype != "object":
            X[col] = (X[col] - X[col].mean()) / X[col].std()

    while True:
        # Compute the correlation matrix
        naive_corr = X.corr()

        # Identify variables with the highest correlation with the target variable (the first column)
        target_corr = naive_corr.iloc[:, 0].abs().sort_values(ascending=False)

        # Sort naive_corr by the correlation of the target variable
        naive_corr = naive_corr.loc[target_corr.index, target_corr.index]

        naive_corr_sans_target = naive_corr.iloc[1:, 1:]

        # Get the (absolute) strength of the correlation with the target variable
        strength = naive_corr.iloc[:, 0].abs()

        # drop the target variable from strength:
        strength = strength.iloc[1:]

        # Calculate the clarity of the correlation: how correlated it is with all other variables *except* the target variable
        clarity = 1 - (
            (naive_corr_sans_target.abs().sum(axis=1) - 1.0)
            / (len(naive_corr_sans_target.columns) - 1)
        )

        # Combine the strength and clarity into a single score -- bigger is better, and we want high strength and high clarity
        score = strength * clarity * clarity

        # Identify the variable with the lowest score
        min_score_idx = score.idxmin()

        if pd.isna(min_score_idx):
            min_score = score[0]
        else:
            min_score = score[min_score_idx]

        data = {"corr_strength": strength, "corr_clarity": clarity, "corr_score": score}
        df_score = pd.DataFrame(data)
        df_score = df_score.reset_index().rename(columns={"index": "variable"})

        if first_run is None:
            first_run = df_score
            first_run = first_run.sort_values("corr_score", ascending=False)

        if min_score < threshold:
            X = X.drop(min_score_idx, axis=1)
        else:
            break

    # sort by score:
    df_score = df_score.sort_values("corr_score", ascending=False)

    if do_plots:
        plot_correlation(naive_corr, "Correlation of Variables (initial)")

    # recompute the correlation matrix
    final_corr = X.corr()

    if do_plots:
        plot_correlation(final_corr, "Correlation of Variables (final)")

    return {"initial": first_run, "final": df_score}

calc_cross_validation_score

calc_cross_validation_score(X, y)

Calculate cross-validation score using negative mean squared error.

This function fits a LinearRegression model using 5-fold cross validation and returns the mean cross-validated MSE (positive value).

Parameters:

Name	Type	Description	Default
X	array - like or DataFrame	Input features for modeling.	required
y	array - like or Series	Target variable.	required

Returns:

Type	Description
float	The mean cross-validated mean squared error.

Source code in openavmkit/utilities/stats.py

def calc_cross_validation_score(
    X: pd.DataFrame | np.ndarray,
    y: pd.Series | np.ndarray
) -> float:
    """
    Calculate cross-validation score using negative mean squared error.

    This function fits a LinearRegression model using 5-fold cross validation and
    returns the mean cross-validated MSE (positive value).

    Parameters
    ----------
    X : array-like or pandas.DataFrame
        Input features for modeling.
    y : array-like or pandas.Series
        Target variable.

    Returns
    -------
    float
        The mean cross-validated mean squared error.
    """
    model = LinearRegression()
    # Use negative MSE and negate it to return positive MSE
    try:
        scores = cross_val_score(model, X, y, cv=5, scoring="neg_mean_squared_error")
    except ValueError:
        return float("nan")

    return -scores.mean()  # Convert negative MSE to positive

calc_elastic_net_regularization

calc_elastic_net_regularization(X, y, threshold_fraction=0.05)

Calculate Elastic Net regularization coefficients while iteratively dropping variables with low coefficients.

This function standardizes X, fits an Elastic Net model, and iteratively removes variables whose absolute coefficients fall below a fraction of the maximum coefficient.

Parameters:

Name	Type	Description	Default
X	DataFrame	Input features DataFrame.	required
y	Series	Target variable series.	required
threshold_fraction	float	Fraction of the maximum coefficient below which variables are dropped. Defaults to 0.05.	0.05

Returns:

Type	Description
dict	Dictionary with two keys: "initial": pandas.Series of coefficients from the first Elastic Net fit. "final": pandas.Series of coefficients after dropping low-magnitude variables.

Source code in openavmkit/utilities/stats.py

def calc_elastic_net_regularization(
    X: pd.DataFrame,
    y: pd.Series,
    threshold_fraction: float = 0.05
) -> dict:
    """
    Calculate Elastic Net regularization coefficients while iteratively dropping variables with low coefficients.

    This function standardizes `X`, fits an Elastic Net model, and iteratively removes
    variables whose absolute coefficients fall below a fraction of the maximum coefficient.

    Parameters
    ----------
    X : pd.DataFrame
        Input features DataFrame.
    y : pd.Series
        Target variable series.
    threshold_fraction : float, optional
        Fraction of the maximum coefficient below which variables are dropped. Defaults to 0.05.

    Returns
    -------
    dict
        Dictionary with two keys:

        - "initial": pandas.Series of coefficients from the first Elastic Net fit.
        - "final": pandas.Series of coefficients after dropping low-magnitude variables.
    """

    X = X.copy()

    # Standardize the features
    scaler = StandardScaler()
    X_scaled = scaler.fit_transform(X)

    first_run = None

    while True:

        # Apply Elastic Net regularization
        elastic_net = ElasticNet(alpha=1.0, l1_ratio=0.5)
        elastic_net.fit(X_scaled, y)

        # Calculate the absolute values of the coefficients
        abs_coefficients = np.abs(elastic_net.coef_)

        # Determine the threshold as a fraction of the largest coefficient
        max_coef = np.max(abs_coefficients)
        threshold = max_coef * threshold_fraction

        coefficients = elastic_net.coef_
        # align coefficients into a dataframe with variable names:
        coefficients = pd.DataFrame(
            {
                "variable": X.columns,
                "enr_coef": coefficients,
                "enr_coef_sign": np.sign(coefficients),
            }
        )
        coefficients = coefficients.sort_values(
            "enr_coef", ascending=False, key=lambda x: x.abs()
        )

        # identify worst variable:
        min_coef_idx = np.argmin(abs_coefficients)
        min_coef = abs_coefficients[min_coef_idx]

        if first_run is None:
            first_run = coefficients

        if min_coef < threshold:
            # remove the worst variable from X_scaled:
            X_scaled = np.delete(X_scaled, min_coef_idx, axis=1)
            # remove corresponding column from X:
            X = X.drop(X.columns[min_coef_idx], axis=1)
        else:
            break

    return {"initial": first_run, "final": coefficients}

calc_mse

calc_mse(prediction, ground_truth)

Calculate the Mean Squared Error (MSE) between predictions and ground truth.

Parameters:

Name	Type	Description	Default
prediction	ndarray	Array of predicted values.	required
ground_truth	ndarray	Array of true values.	required

Returns:

Type	Description
float	The MSE value.

Source code in openavmkit/utilities/stats.py

def calc_mse(
    prediction: np.ndarray,
    ground_truth: np.ndarray
) -> float:
    """
    Calculate the Mean Squared Error (MSE) between predictions and ground truth.

    Parameters
    ----------
    prediction : numpy.ndarray
        Array of predicted values.
    ground_truth : numpy.ndarray
        Array of true values.

    Returns
    -------
    float
        The MSE value.
    """
    return float(np.mean((prediction - ground_truth) ** 2))

calc_mse_r2_adj_r2

calc_mse_r2_adj_r2(predictions, ground_truth, num_vars)

Calculate the Mean Squared Error (MSE), r-squared, and adjusted r-squared

Parameters:

Name	Type	Description	Default
predictions	ndarray	Array of predicted values.	required
ground_truth	ndarray	Array of true values.	required
num_vars	int	Number of independent variables used to produce the predictions	required

Returns:

Type	Description
tuple[float, float, float]	A tuple containing three values: The MSE value The r-squared value The adjusted r-squared value

Source code in openavmkit/utilities/stats.py

def calc_mse_r2_adj_r2(
    predictions: np.ndarray, ground_truth: np.ndarray, num_vars: int
):
    """
    Calculate the Mean Squared Error (MSE), r-squared, and adjusted r-squared

    Parameters
    ----------
    predictions : numpy.ndarray
        Array of predicted values.
    ground_truth : numpy.ndarray
        Array of true values.
    num_vars : int
        Number of independent variables used to produce the predictions

    Returns
    -------
    tuple[float, float, float]

        A tuple containing three values:

        - The MSE value
        - The r-squared value
        - The adjusted r-squared value
    """

    mse = np.mean((ground_truth - predictions) ** 2)
    ss_res = np.sum((ground_truth - predictions) ** 2)
    ss_tot = np.sum((ground_truth - np.mean(ground_truth)) ** 2)

    r2 = 1 - (ss_res / ss_tot) if ss_tot != 0 else float("inf")

    n = len(predictions)
    k = num_vars
    divisor = n - k - 1
    if divisor == 0:
        adj_r2 = float("inf")
    else:
        adj_r2 = 1 - ((1 - r2) * (n - 1) / divisor)
    return mse, r2, adj_r2

calc_p_values_recursive_drop

calc_p_values_recursive_drop(X, y, sig_threshold=0.05)

Recursively drop variables with p-values above a specified significance threshold.

Fits an OLS model on X and iteratively removes the variable with the highest p-value until all remaining variables have p-values below the threshold.

Parameters:

Name	Type	Description	Default
X	DataFrame	Input features DataFrame.	required
y	Series	Target variable series.	required
sig_threshold	float	Significance threshold for p-values. Variables with p-values above this threshold will be dropped. Defaults to 0.05.	0.05

Returns:

Type	Description
dict	Dictionary with two keys: "initial": pd.Series of p-values from the first OLS fit. "final": pd.Series of p-values after recursively dropping high-p-value variables.

Raises:

Type	Description
ValueError	If the OLS regression fails or no variables remain.

Source code in openavmkit/utilities/stats.py

def calc_p_values_recursive_drop(
    X: pd.DataFrame,
    y: pd.Series,
    sig_threshold: float = 0.05
) -> dict:
    """
    Recursively drop variables with p-values above a specified significance threshold.

    Fits an OLS model on `X` and iteratively removes the variable with the highest
    p-value until all remaining variables have p-values below the threshold.

    Parameters
    ----------
    X : pd.DataFrame
        Input features DataFrame.
    y : pd.Series
        Target variable series.
    sig_threshold : float, optional
        Significance threshold for p-values. Variables with p-values above this
        threshold will be dropped. Defaults to 0.05.

    Returns
    -------
    dict
        Dictionary with two keys:

        - "initial": pd.Series of p-values from the first OLS fit.
        - "final": pd.Series of p-values after recursively dropping high-p-value variables.

    Raises
    ------
    ValueError
        If the OLS regression fails or no variables remain.
    """

    X = X.copy()
    X = sm.add_constant(X)
    X = X.astype(np.float64)
    model = sm.OLS(y, X).fit()
    first_run = None
    while True:
        max_p_value = model.pvalues.max()
        p_values = model.pvalues
        if first_run is None:
            first_run = p_values
        if max_p_value > sig_threshold:
            var_to_drop = p_values.idxmax()
            if var_to_drop == "const":
                # don't pick const, pick the next variable to drop:
                try:
                    var_to_drop = p_values.iloc[1:].idxmax()
                except ValueError as e:
                    break
            if pd.isna(var_to_drop):
                break
            X = X.drop(var_to_drop, axis=1)
            try:
                new_model = sm.OLS(y, X).fit()
            except ValueError as e:
                print(f"Error fitting model after dropping {var_to_drop}: {e}")
                break
            model = new_model
        else:
            break

    # align p_values into a dataframe with variable names:
    p_values = (
        pd.DataFrame({"p_value": model.pvalues})
        .sort_values("p_value", ascending=True)
        .reset_index()
        .rename(columns={"index": "variable"})
    )

    # do the same for "first_run":
    first_run = (
        pd.DataFrame({"p_value": first_run})
        .sort_values("p_value", ascending=True)
        .reset_index()
        .rename(columns={"index": "variable"})
    )

    return {
        "initial": first_run,
        "final": p_values,
    }

calc_prb

calc_prb(predictions, ground_truth, confidence_interval=0.95)

Calculate the Price Related Bias (PRB) metric using a regression-based approach.

This function fits an OLS model on the transformed ratios of predictions to ground truth, then returns the PRB value along with its lower and upper confidence bounds.

Parameters:

Name	Type	Description	Default
predictions	ndarray	Array of predicted values.	required
ground_truth	ndarray	Array of ground truth values.	required
confidence_interval	float	Desired confidence interval. Defaults to 0.95.	0.95

Returns:

Type	Description
tuple[float, float, float]	A tuple containing: PRB value Lower bound of the confidence interval Upper bound of the confidence interval

Raises:

Type	Description
ValueError	If predictions and ground_truth have different lengths.

Source code in openavmkit/utilities/stats.py

def calc_prb(
    predictions: np.ndarray,
    ground_truth: np.ndarray,
    confidence_interval: float = 0.95
) -> tuple[float, float, float]:
    """
    Calculate the Price Related Bias (PRB) metric using a regression-based approach.

    This function fits an OLS model on the transformed ratios of predictions to ground
    truth, then returns the PRB value along with its lower and upper confidence bounds.

    Parameters
    ----------
    predictions : np.ndarray
        Array of predicted values.
    ground_truth : np.ndarray
        Array of ground truth values.
    confidence_interval : float, optional
        Desired confidence interval. Defaults to 0.95.

    Returns
    -------
    tuple[float, float, float]
        A tuple containing:

        - PRB value
        - Lower bound of the confidence interval
        - Upper bound of the confidence interval

    Raises
    ------
    ValueError
        If `predictions` and `ground_truth` have different lengths.
    """
    # 1. Basic shape checks --------------------------------------------------
    predictions = np.asarray(predictions, dtype=float)
    ground_truth = np.asarray(ground_truth, dtype=float)
    if predictions.shape != ground_truth.shape:
        raise ValueError("predictions and ground_truth must have the same length/shape")

    # 2. Clean rows that cannot be used --------------------------------------
    mask = (
        ~np.isnan(predictions)
        & ~np.isnan(ground_truth)
        & (predictions > 0)          # cannot take log2 of non‑positive numbers
        & (ground_truth > 0)
    )
    n_ok = int(mask.sum())
    if n_ok < 3:                     # OLS needs at least 3 rows
        warnings.warn(
            f"Only {n_ok} valid observation(s) after cleaning – PRB not computed."
        )
        return np.nan, np.nan, np.nan

    preds = predictions[mask]
    truth = ground_truth[mask]

    # 3. Build transformed variables -----------------------------------------
    ratios = preds / truth
    median_ratio = np.median(ratios)

    left = (ratios - median_ratio) / median_ratio
    right = np.log2(preds / median_ratio + truth)
    right = sm.add_constant(right)   # adds intercept term

    # 4. Fit model + CI -------------------------------------------------------
    with np.errstate(all="ignore"):  # silence harmless internal numpy warnings
        model = sm.OLS(left, right).fit()

    # Guard against degenerate fit (rare but better to be explicit)
    if model.df_resid <= 0 or not np.isfinite(model.params[0]):
        return np.nan, np.nan, np.nan

    prb = float(model.params[0])
    prb_lower, prb_upper = (
        model.conf_int(alpha=1.0 - confidence_interval)[0].tolist()
    )

    return prb, prb_lower, prb_upper

calc_prd

calc_prd(predictions, ground_truth)

Calculate the Price Related Differential (PRD).

PRD is computed as the ratio of the mean ratio to the weighted mean ratio of predictions to ground truth.

Parameters:

Name	Type	Description	Default
predictions	ndarray	Array of predicted values.	required
ground_truth	ndarray	Array of ground truth values.	required

Returns:

Type	Description
float	The PRD value.

Source code in openavmkit/utilities/stats.py

def calc_prd(predictions: np.ndarray, ground_truth: np.ndarray) -> float:
    """
    Calculate the Price Related Differential (PRD).

    PRD is computed as the ratio of the mean ratio to the weighted mean ratio of
    predictions to ground truth.

    Parameters
    ----------
    predictions : numpy.ndarray
        Array of predicted values.
    ground_truth : numpy.ndarray
        Array of ground truth values.

    Returns
    -------
    float
        The PRD value.
    """
    ratios = div_series_z_safe(predictions, ground_truth)
    if len(ratios) == 0:
        return float("nan")
    mean_ratio = np.mean(ratios)
    sum_ground_truth = np.sum(ground_truth)
    if sum_ground_truth == 0:
        return float("inf")
    weighted_mean_ratio = np.sum(predictions) / sum_ground_truth
    if weighted_mean_ratio == 0:
        return float("inf")
    prd = mean_ratio / weighted_mean_ratio
    return prd

calc_prd_bootstrap

calc_prd_bootstrap(predictions, ground_truth, confidence_interval=0.95, iterations=10000, seed=777)

Calculate PRD with bootstrapping.

This function bootstraps the prediction-to-ground_truth ratios to produce a distribution of PRD values and returns the lower bound, median, and upper bound of the confidence interval.

Parameters:

Name	Type	Description	Default
predictions	ndarray	Array of predicted values.	required
ground_truth	ndarray	Array of ground truth values.	required
confidence_interval	float	The desired confidence level. Defaults to 0.95.	0.95
iterations	int	Number of bootstrap iterations. Defaults to 10000.	10000
seed	int	Random seed for reproducibility. Defaults to 777.	777

Returns:

Type	Description
tuple[float, float, float]	A tuple containing the lower bound, median PRD, and upper bound of the confidence interval.

Source code in openavmkit/utilities/stats.py

def calc_prd_bootstrap(
    predictions: np.ndarray,
    ground_truth: np.ndarray,
    confidence_interval: float = 0.95,
    iterations: int = 10000,
    seed: int = 777,
) -> tuple[float, float, float]:
    """
    Calculate PRD with bootstrapping.

    This function bootstraps the prediction-to-ground_truth ratios to produce a
    distribution of PRD values and returns the lower bound, median, and upper bound of the
    confidence interval.

    Parameters
    ----------
    predictions : np.ndarray
        Array of predicted values.
    ground_truth : np.ndarray
        Array of ground truth values.
    confidence_interval : float, optional
        The desired confidence level. Defaults to 0.95.
    iterations : int, optional
        Number of bootstrap iterations. Defaults to 10000.
    seed : int, optional
        Random seed for reproducibility. Defaults to 777.

    Returns
    -------
    tuple[float, float, float]
        A tuple containing the lower bound, median PRD, and upper bound of the confidence interval.
    """

    np.random.seed(seed)
    n = len(predictions)
    ratios = predictions / ground_truth
    samples = np.random.choice(ratios, size=(iterations, n), replace=True)
    mean_ratios = np.mean(samples, axis=1)
    weighted_mean_ratios = np.sum(predictions) / np.sum(ground_truth)
    prds = mean_ratios / weighted_mean_ratios
    alpha = (1.0 - confidence_interval) / 2
    lower_bound, upper_bound = np.quantile(prds, [alpha, 1.0 - alpha])
    median_prd = np.median(prds)
    return lower_bound, median_prd, upper_bound

calc_r2

calc_r2(df, variables, y)

Calculate R² and adjusted R² values for each variable.

For each variable in the provided list, an OLS model is fit and the R², adjusted R², and the sign of the coefficient are recorded.

Parameters:

Name	Type	Description	Default
df	DataFrame	DataFrame containing the variables.	required
variables	list[str]	List of variable names to evaluate.	required
y	Series	Target variable series.	required

Returns:

Type	Description
DataFrame	DataFrame with columns for variable, R², adjusted R², and coefficient sign.

Source code in openavmkit/utilities/stats.py

def calc_r2(
    df: pd.DataFrame,
    variables: list[str],
    y: pd.Series
) -> pd.DataFrame:
    """
    Calculate R² and adjusted R² values for each variable.

    For each variable in the provided list, an OLS model is fit and the R², adjusted R²,
    and the sign of the coefficient are recorded.

    Parameters
    ----------
    df : pandas.DataFrame
        DataFrame containing the variables.
    variables : list[str]
        List of variable names to evaluate.
    y : pandas.Series
        Target variable series.

    Returns
    -------
    pandas.DataFrame
        DataFrame with columns for variable, R², adjusted R², and coefficient sign.
    """
    results = {"variable": [], "r2": [], "adj_r2": [], "coef_sign": []}
    for var in variables:
        data = pd.concat([df[var], y], axis=1).dropna()
        if len(data) < 3 or data[var].nunique() < 2:
            results["variable"].append(var)
            results["r2"].append(float("nan"))
            results["adj_r2"].append(float("nan"))
            results["coef_sign"].append(float("nan"))
            continue                          # skip ill-posed models

        X = sm.add_constant(data[var].astype(float))
        try:
            model = sm.OLS(y, X).fit()
        except MissingDataError as e:
            print(f"Error fitting model for variable {var}: {e}")
            for var in variables:
                # check for missing/null/nan values:
                if df[var].isna().any():
                    n = df[var].isna().sum()
                    print(f'Variable "{var}" has {n} missing values.')
            raise e

        results["variable"].append(var)
        results["r2"].append(model.rsquared)
        results["adj_r2"].append(model.rsquared_adj)
        results["coef_sign"].append(1 if model.params[var] >= 0 else -1)
    df_results = pd.DataFrame(data=results)
    return df_results

calc_t_values

calc_t_values(X, y)

Calculate t-values for an OLS model.

Fits an ordinary least squares regression of y on X and returns the t-values of the estimated coefficients.

Parameters:

Name	Type	Description	Default
X	DataFrame	Input features DataFrame (should include a constant term column).	required
y	Series	Target variable series.	required

Returns:

Type	Description
Series	Series of t-values corresponding to each coefficient in X.

Source code in openavmkit/utilities/stats.py

def calc_t_values(X: pd.DataFrame, y: pd.Series) -> pd.Series:
    """
    Calculate t-values for an OLS model.

    Fits an ordinary least squares regression of `y` on `X` and returns the t-values
    of the estimated coefficients.

    Parameters
    ----------
    X : pandas.DataFrame
        Input features DataFrame (should include a constant term column).
    y : pandas.Series
        Target variable series.

    Returns
    -------
    pandas.Series
        Series of t-values corresponding to each coefficient in `X`.
    """
    linear_model = sm.OLS(y, X)
    fitted_model = linear_model.fit()
    return fitted_model.tvalues

calc_t_values_recursive_drop

calc_t_values_recursive_drop(X, y, threshold=2)

Recursively drop variables with t-values below a given threshold.

Fits an OLS model on X and iteratively removes the variable with the smallest absolute t-value until all remaining variables have |t-value| above the threshold.

Parameters:

Name	Type	Description	Default
X	DataFrame	Input features DataFrame.	required
y	Series	Target variable series.	required
threshold	float	Minimum acceptable absolute t-value. Variables with |t-value| below this threshold will be dropped. Defaults to 2.	2

Returns:

Type	Description
dict	Dictionary with two keys: "initial": pandas.Series of t-values and their signs from the first OLS fit. "final": pandas.Series of t-values and their signs after recursive dropping.

Source code in openavmkit/utilities/stats.py

def calc_t_values_recursive_drop(
    X: pd.DataFrame,
    y: pd.Series,
    threshold: float = 2
) -> dict:
    """
    Recursively drop variables with t-values below a given threshold.

    Fits an OLS model on `X` and iteratively removes the variable with the smallest
    absolute t-value until all remaining variables have |t-value| above the threshold.

    Parameters
    ----------
    X : pandas.DataFrame
        Input features DataFrame.
    y : pandas.Series
        Target variable series.
    threshold : float, optional
        Minimum acceptable absolute t-value. Variables with |t-value| below this threshold
        will be dropped. Defaults to 2.

    Returns
    -------
    dict
        Dictionary with two keys:

        - "initial": pandas.Series of t-values and their signs from the first OLS fit.
        - "final": pandas.Series of t-values and their signs after recursive dropping.
    """

    X = X.copy()
    X = sm.add_constant(X)
    X = X.astype(np.float64)

    first_run = None
    i = 0
    while True:
        i += 1
        try:
            t_values = calc_t_values(X, y)
        except ValueError as e:
            t_values = pd.Series([float("nan")] * X.shape[1], index=X.columns)
        if first_run is None:
            first_run = t_values

        if t_values.isna().all():
            min_t_var = float("nan")
        else:
            min_t_var = t_values.abs().idxmin()

        if pd.isna(min_t_var):
            min_t_var = 0

        if len(t_values) > 0:
            min_t_val = float("nan")
        else:
            min_t_val = t_values[min_t_var]

        if min_t_val < threshold:
            X = X.drop(min_t_var, axis=1)
        else:
            break

    # align t_values into a dataframe with variable names:
    t_values = (
        pd.DataFrame({"t_value": t_values, "t_value_sign": np.sign(t_values)})
        .sort_values("t_value", ascending=False, key=lambda x: x.abs())
        .reset_index()
        .rename(columns={"index": "variable"})
    )

    # do the same for "first_run":
    first_run = (
        pd.DataFrame({"t_value": first_run, "t_value_sign": np.sign(first_run)})
        .sort_values("t_value", ascending=False, key=lambda x: x.abs())
        .reset_index()
        .rename(columns={"index": "variable"})
    )

    return {"initial": first_run, "final": t_values}

calc_vif

calc_vif(X)

Calculate the Variance Inflation Factor (VIF) for each variable in a DataFrame.

Parameters:

Name	Type	Description	Default
X	DataFrame	Input features DataFrame.	required

Returns:

Type	Description
DataFrame	DataFrame with columns: "variable": Name of each feature in X. "VIF": Variance Inflation Factor value for that feature.

Source code in openavmkit/utilities/stats.py

def calc_vif(X: pd.DataFrame) -> pd.DataFrame:
    """
    Calculate the Variance Inflation Factor (VIF) for each variable in a DataFrame.

    Parameters
    ----------
    X : pandas.DataFrame
        Input features DataFrame.

    Returns
    -------
    pandas.DataFrame
        DataFrame with columns:

        - "variable": Name of each feature in `X`.
        - "VIF": Variance Inflation Factor value for that feature.
    """
    vif_data = pd.DataFrame()
    vif_data["variable"] = X.columns

    if len(X.values) < 5:
        warnings.warn("Can't calculate VIF for less than 5 samples")
        vif_data["vif"] = [float("nan")] * len(X.columns)
        return vif_data

    # Calculate VIF for each column
    vif_data["vif"] = [
        variance_inflation_factor(X.values, i) for i in range(X.shape[1])
    ]

    return vif_data

calc_vif_recursive_drop

calc_vif_recursive_drop(X, threshold=10.0, settings=None)

Recursively drop variables with a Variance Inflation Factor (VIF) exceeding the threshold.

Parameters:

Name	Type	Description	Default
X	DataFrame	Input features DataFrame.	required
threshold	float	Maximum acceptable VIF. Variables with VIF above this threshold will be removed. Defaults to 10.0.	10.0
settings	dict	Settings dictionary containing field classifications, if needed for VIF computation. Defaults to None.	None

Returns:

Type	Description
dict	Dictionary with two keys: "initial": pandas.DataFrame of VIF values before dropping variables. "final": pandas.DataFrame of VIF values after recursively dropping high-VIF variables.

Raises:

Type	Description
ValueError	If no columns remain for VIF calculation.

Source code in openavmkit/utilities/stats.py

def calc_vif_recursive_drop(
    X: pd.DataFrame,
    threshold: float = 10.0,
    settings: dict = None
) -> dict:
    """
    Recursively drop variables with a Variance Inflation Factor (VIF) exceeding the threshold.

    Parameters
    ----------
    X : pandas.DataFrame
        Input features DataFrame.
    threshold : float, optional
        Maximum acceptable VIF. Variables with VIF above this threshold will be removed.
        Defaults to 10.0.
    settings : dict, optional
        Settings dictionary containing field classifications, if needed for VIF computation.
        Defaults to None.

    Returns
    -------
    dict
        Dictionary with two keys:

        - "initial": pandas.DataFrame of VIF values before dropping variables.
        - "final": pandas.DataFrame of VIF values after recursively dropping high-VIF variables.

    Raises
    ------
    ValueError
        If no columns remain for VIF calculation.
    """
    X = X.copy()
    X = X.astype(np.float64)

    # Get boolean and categorical variables from settings if provided
    bool_fields = get_fields_boolean(settings, X)
    cat_fields = get_fields_categorical(settings, X, include_boolean=False)
    exclude_vars = bool_fields + cat_fields

    # Remove boolean and categorical variables
    X = X.drop(
        columns=[col for col in X.columns if col in exclude_vars], errors="ignore"
    )

    # Drop constant columns (VIF cannot be calculated for constant columns)
    X = X.loc[:, X.nunique() > 1]  # Keep only columns with more than one unique value

    # If no columns are left after removing constant columns or dropping NaN values, raise an error
    if X.shape[1] == 0:
        raise ValueError(
            "All columns are constant or have missing values; VIF cannot be computed."
        )
    first_run = None
    while True:
        vif_data = calc_vif(X)
        if first_run is None:
            first_run = vif_data
        if vif_data["vif"].max() > threshold:
            max_vif_idx = vif_data["vif"].idxmax()
            X = X.drop(X.columns[max_vif_idx], axis=1)
        else:
            break
    return {"initial": first_run, "final": vif_data}

plot_correlation

plot_correlation(corr, title='Correlation of Variables')

Plot a heatmap of a correlation matrix.

Parameters:

Name	Type	Description	Default
corr	DataFrame	Correlation matrix as a DataFrame.	required
title	str	Title of the plot. Defaults to "Correlation of Variables".	'Correlation of Variables'

Source code in openavmkit/utilities/stats.py

def plot_correlation(corr: pd.DataFrame, title: str = "Correlation of Variables") -> None:
    """
    Plot a heatmap of a correlation matrix.

    Parameters
    ----------
    corr : pandas.DataFrame
        Correlation matrix as a DataFrame.
    title : str, optional
        Title of the plot. Defaults to "Correlation of Variables".
    """

    cmap = sns.diverging_palette(220, 10, as_cmap=True)
    cmap = cmap.reversed()

    plt.figure(figsize=(10, 8))

    # Create the heatmap with the correct labels
    sns.heatmap(
        corr,
        annot=True,
        fmt=".1f",
        cbar=True,
        cmap=cmap,
        vmax=1.0,
        vmin=-1.0,
        xticklabels=corr.columns.tolist(),  # explicitly set the xticklabels
        yticklabels=corr.index.tolist(),  # explicitly set the yticklabels
        annot_kws={"size": 8},  # adjust font size if needed
    )

    plt.title(title)
    plt.xticks(rotation=45, ha="right")  # rotate x labels if needed
    plt.yticks(rotation=0)  # keep y labels horizontal
    plt.tight_layout(pad=2)
    plt.show()

quick_median_chd_pl

quick_median_chd_pl(df, field_value, field_cluster)

Calculate the median CHD for groups in a Polars DataFrame.

This function filters out missing values for the given value field, groups the data by the specified cluster field, computes COD for each group, and returns the median COD value.

Parameters:

Name	Type	Description	Default
df	DataFrame	Input Polars DataFrame.	required
field_value	str	Name of the field containing values for COD calculation.	required
field_cluster	str	Name of the field to group by for computing COD.	required

Returns:

Type	Description
float	The median COD value across all groups.

Source code in openavmkit/utilities/stats.py

def quick_median_chd_pl(
    df: pl.DataFrame, field_value: str, field_cluster: str
) -> float:
    """
    Calculate the median CHD for groups in a Polars DataFrame.

    This function filters out missing values for the given value field, groups the data
    by the specified cluster field, computes COD for each group, and returns the median
    COD value.

    Parameters
    ----------
    df : pl.DataFrame
        Input Polars DataFrame.
    field_value : str
        Name of the field containing values for COD calculation.
    field_cluster : str
        Name of the field to group by for computing COD.

    Returns
    -------
    float
        The median COD value across all groups.
    """
    # Filter out rows with missing values for field_value.
    df = df.filter(~pd.isna(df[field_value]))
    df = df.filter(df[field_value].gt(0))

    chds = df.group_by(field_cluster).agg(pl.col(field_value).alias("values"))

    # Apply the calc_cod function to each group (the list of values)
    chd_values = np.array([calc_cod(group.to_numpy()) for group in chds["values"]])

    # Calculate the median of the CHD values
    median_chd = float(np.median(chd_values))
    return median_chd

trim_outliers

trim_outliers(values, lower_quantile=0.25, upper_quantile=0.75)

Trim outliers from an array of values based on quantile thresholds.

Parameters:

Name	Type	Description	Default
values	ndarray	Input array of numeric values.	required
lower_quantile	float	Lower quantile bound. Values below this quantile will be removed. Defaults to 0.25.	0.25
upper_quantile	float	Upper quantile bound. Values above this quantile will be removed. Defaults to 0.75.	0.75

Returns:

Type	Description
ndarray	Array with values outside the specified quantile bounds removed.

Source code in openavmkit/utilities/stats.py

def trim_outliers(
    values: np.ndarray,
    lower_quantile: float = 0.25,
    upper_quantile: float = 0.75
) -> np.ndarray:
    """
    Trim outliers from an array of values based on quantile thresholds.

    Parameters
    ----------
    values : np.ndarray
        Input array of numeric values.
    lower_quantile : float, optional
        Lower quantile bound. Values below this quantile will be removed. Defaults to 0.25.
    upper_quantile : float, optional
        Upper quantile bound. Values above this quantile will be removed. Defaults to 0.75.

    Returns
    -------
    np.ndarray
        Array with values outside the specified quantile bounds removed.
    """
    if len(values) == 0:
        return values
    lower_bound = np.quantile(values, lower_quantile)
    upper_bound = np.quantile(values, upper_quantile)
    return values[(values >= lower_bound) & (values <= upper_bound)]

trim_outliers_mask

trim_outliers_mask(values, lower_quantile=0.25, upper_quantile=0.75)

Generate a boolean mask for values within specified quantile bounds.

Parameters:

Name	Type	Description	Default
values	ndarray	Input array of numeric values.	required
lower_quantile	float	Lower quantile bound. Values below this quantile are masked out. Defaults to 0.25.	0.25
upper_quantile	float	Upper quantile bound. Values above this quantile are masked out. Defaults to 0.75.	0.75

Returns:

Type	Description
ndarray	Boolean array where True indicates values within the quantile bounds.

Source code in openavmkit/utilities/stats.py

def trim_outliers_mask(
    values: np.ndarray,
    lower_quantile: float = 0.25,
    upper_quantile: float = 0.75
) -> np.ndarray:
    """
    Generate a boolean mask for values within specified quantile bounds.

    Parameters
    ----------
    values : np.ndarray
        Input array of numeric values.
    lower_quantile : float, optional
        Lower quantile bound. Values below this quantile are masked out. Defaults to 0.25.
    upper_quantile : float, optional
        Upper quantile bound. Values above this quantile are masked out. Defaults to 0.75.

    Returns
    -------
    np.ndarray
        Boolean array where `True` indicates values within the quantile bounds.
    """
    if len(values) == 0:
        return values
    lower_bound = np.quantile(values, lower_quantile)
    upper_bound = np.quantile(values, upper_quantile)
    return (values >= lower_bound) & (values <= upper_bound)