Computing Autocorrelations in Single-Case Experimental Design — SCIA - Single Case Intervention Analysis with Python

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# Computing Autocorrelations in Single-Case Experimental Design

The `autocorr` function calculates autocorrelation values for different phases and overall in a single-case dataset. It helps in analyzing the dependency between observations across time.

## Analyzing Temporal Dependencies with `autocorr`

The `autocorr` function computes autocorrelations within each phase and across all phases in a dataset. This is useful for understanding whether measurements at one time point influence future values.

### Required Arguments:

- `data`: A Pandas DataFrame containing SCED data.

### Optional Arguments:

- `dvar`: The column name of the dependent variable (default `"values"`).

- `pvar`: The column name of the phase variable (default `"phase"`).

- `mvar`: The column name representing measurement time (default `"mt"`).

- `lag_max`: The maximum lag for which autocorrelations should be computed (default `3`).

The function processes each case separately and computes autocorrelations within each phase and across all observations.

    import scia as sc

    📖 scia 1.101.0.dev6 - For Documentation, visit: https://ahsankhodami.github.io/scia/intro.html

### Example 1: Computing Autocorrelations in a Dataset

This example calculates autocorrelations up to a lag of 3 for each phase and overall.

    import pandas as pd
    import numpy as np

    # Create a sample dataset
    df = pd.DataFrame({
        "case": ["A", "A", "A", "A", "A", "B", "B", "B", "B", "B"],
        "phase": ["Baseline", "Baseline", "Baseline", "Intervention", "Intervention",
                  "Baseline", "Baseline", "Intervention", "Intervention", "Intervention"],
        "values": [5, 6, 7, 8, 10, 3, 4, 6, 8, 9],
        "mt": [1, 2, 3, 4, 5, 1, 2, 3, 4, 5]
    })

    # Compute autocorrelations
    df_ac = sc.autocorr(df, lag_max=3)
    print(df_ac)

      Case         Phase     Lag 1     Lag 2     Lag 3
    0    A      Baseline  0.000000 -0.500000       NaN
    1    A  Intervention -0.500000       NaN       NaN
    2    A           all  0.335135 -0.072973 -0.345946
    3    B      Baseline -0.500000       NaN       NaN
    4    B  Intervention -0.023810 -0.476190       NaN
    5    B           all  0.461538 -0.153846 -0.461538

### Example 2: Computing Autocorrelations with a Higher Lag

Setting `lag_max=5` allows computing autocorrelations for more time points.

    df_ac = sc.autocorr(df, lag_max=5)
    print(df_ac)

      Case         Phase     Lag 1     Lag 2     Lag 3     Lag 4  Lag 5
    0    A      Baseline  0.000000 -0.500000       NaN       NaN    NaN
    1    A  Intervention -0.500000       NaN       NaN       NaN    NaN
    2    A           all  0.335135 -0.072973 -0.345946 -0.416216    NaN
    3    B      Baseline -0.500000       NaN       NaN       NaN    NaN
    4    B  Intervention -0.023810 -0.476190       NaN       NaN    NaN
    5    B           all  0.461538 -0.153846 -0.461538 -0.346154    NaN