Convert Diagonal Cohort-Based Metrics to a Clean Wide Table in Pandas with Age at Commencement and MultiIndex Columns

Learn how to reshape diagonal cohort-based metrics in Pandas by melting, deriving Age at commencement, and pivoting to MultiIndex columns for simpler analytics.

When cohort-based metrics are stored diagonally across multiple year columns, any downstream computation becomes awkward. You end up chasing offsets across columns to align cohorts, ages, and years. A much simpler path is to convert that diagonal layout into a vertical table and then reshape it into a wide form with hierarchical headers that reflect Cohort and Age at commencement. That way, extracting a whole logical column is a single operation instead of a set of offset calculations.

Problem setup: diagonal layout is hard to work with

The source data keeps values in Year 1…Year N columns, and the diagonal structure reflects how a person’s age increases across years. In plain terms, an 18-year-old in Year 1 becomes 19 in Year 2, 20 in Year 3, and so on. With multiple cohorts, the diagonal pattern repeats, which quickly becomes tedious to index by offsets.

import pandas as pd
seed_data = {
    'Cohort': [1]*4 + [2]*4,
    'age': [18, 19, 20, 21]*2,
    'Year 1': [1, 2, 3, 4, 1.5, 2.5, 3.5, 4.5],
    'year 2': [None, 1, 2, 3, None, 1.5, 2.5, 3.5],
    'year 3': [None, None, 1, 2, None, None, 1.5, 2.5],
    'year 4': [None, None, None, 1, None, None, None, 1.5]
}
tbl = pd.DataFrame(seed_data)
print(tbl)

This setup is representative: multiple cohorts, ages from entry and onward, and values distributed along the diagonal. Operating on this structure directly is inconvenient when you need tidy columns like Cohort, Age at commencement, and Year.

What’s actually going on

The key is to explicitly derive Age at commencement from the current row’s age and the year index. If Year is the nth period, then Age at commencement equals age − (n − 1). Once that value is available, you can pivot to a table with a clear MultiIndex on columns: first by Cohort, then by Age at commencement. The years become the index, and the values fall into their correct intersection. Any cells that have no corresponding diagonal value stay empty.

Solution: reshape, derive, pivot

The following snippet converts the diagonal metric to a wide table with hierarchical headers. It keeps Cohort and Age at commencement as the column hierarchy and lays out Year 1…Year N on the index. Missing values are rendered as empty strings, and integer-like values are printed without a decimal.

import pandas as pd
import numpy as np
src = {
    'Cohort': [1]*4 + [2]*4,
    'age': [18, 19, 20, 21]*2,
    'Year 1': [1, 2, 3, 4, 1.5, 2.5, 3.5, 4.5],
    'year 2': [None, 1, 2, 3, None, 1.5, 2.5, 3.5],
    'year 3': [None, None, 1, 2, None, None, 1.5, 2.5],
    'year 4': [None, None, None, 1, None, None, None, 1.5]
}
raw_df = pd.DataFrame(src)
unpvt = raw_df.melt(
    id_vars=['Cohort', 'age'],
    var_name='Period',
    value_name='metric'
)
unpvt['period_n'] = unpvt['Period'].str.extract(r'(\d+)').astype(int)
unpvt['start_age'] = unpvt['age'] - (unpvt['period_n'] - 1)
unpvt = unpvt.dropna(subset=['metric'])
wide_tbl = unpvt.pivot(
    index='period_n',
    columns=['Cohort', 'start_age'],
    values='metric'
)
wide_tbl = wide_tbl.sort_index(axis=1, level=[0, 1])
wide_tbl.index = [f'Year {i}' for i in wide_tbl.index]
def fmt_cell(val):
    if pd.isna(val):
        return ''
    if float(val).is_integer():
        return str(int(val))
    return str(val)
pretty_wide = wide_tbl.apply(lambda s: s.map(fmt_cell))
print(pretty_wide)

If you are processing large dataframes, a vectorized variant avoids per-cell Python calls for formatting and uses NumPy operations to format numbers and blanks. This pattern may be preferable for big inputs and is not ideal for very small ones.

import pandas as pd
import numpy as np
src2 = {
    'Cohort': [1]*4 + [2]*4,
    'age': [18, 19, 20, 21]*2,
    'Year 1': [1, 2, 3, 4, 1.5, 2.5, 3.5, 4.5],
    'year 2': [None, 1, 2, 3, None, 1.5, 2.5, 3.5],
    'year 3': [None, None, 1, 2, None, None, 1.5, 2.5],
    'year 4': [None, None, None, 1, None, None, None, 1.5]
}
raw2 = pd.DataFrame(src2)
flat = pd.melt(
    raw2,
    id_vars=['Cohort', 'age'],
    var_name='Period',
    value_name='metric'
)
flat['period_n'] = flat['Period'].str.extract(r'(\d+)').astype(np.uint8)
flat['start_age'] = flat['age'] - (flat['period_n'] - 1)
flat.dropna(subset=['metric'], inplace=True)
wide2 = flat.pivot_table(
    index='period_n',
    columns=['Cohort', 'start_age'],
    values='metric',
    aggfunc='first'
)
wide2.sort_index(axis=1, level=[0, 1], inplace=True)
wide2.index = [f'Year {i}' for i in wide2.index]
arr = wide2.to_numpy()
ints_mask = np.isclose(arr % 1, 0, equal_nan=False)
rendered = np.where(np.isnan(arr), '', np.where(ints_mask, arr.astype(int).astype(str), arr.astype(str)))
pretty2 = pd.DataFrame(rendered, index=wide2.index, columns=wide2.columns)
print(pretty2)

Reading the result correctly

In the reshaped output, columns form a MultiIndex of Cohort followed by Age at commencement. Each row is a Year k, and the cell shows the metric for that cohort and starting age in that year. If you see a value under Age at commencement 18 for Year 2, that reflects records whose current age is 19 in Year 2 but whose derived starting age is 18. The transformation places values strictly by that derivation.

Why this transformation matters

Once the table is organized by Cohort and Age at commencement, you no longer need offsets to find the correct values. You can select contiguous columns for a cohort-age slice, aggregate, or join with external inputs without diagonal math. This layout also avoids accidental misalignment when the number of cohorts or years changes over time.

Takeaways

Keep the diagonal source, but compute Age at commencement explicitly from the year number. Melt to long form, derive the year index, drop nulls, and pivot to a MultiIndex on columns. Sort columns for a stable order and, if presentation matters, format integers cleanly and show blanks for missing values. For large frames, lean on the vectorized path to keep runtime predictable. With this structure in place, cohort analytics become simpler, safer, and easier to scale.