balance: transformations and formulas¶

This tutorial focuses on the ways transformations, formulas and penalty can be included in your pre-processing of the coveriates before adjusting for them.

Example dataset - preparing the objects¶

The following is a toy simulated dataset.

For a more basic walkthrough of the elements in the next code block, please take a look at the tutorial: balance Quickstart: Analyzing and adjusting the bias on a simulated toy dataset

In [1]:
from balance import load_data
target_df, sample_df = load_data()
from balance import Sample
sample = Sample.from_frame(sample_df, outcome_columns=["happiness"])
target = Sample.from_frame(target_df, outcome_columns=["happiness"])
sample_with_target = sample.set_target(target)
sample_with_target

INFO (2025-05-23 17:45:10,813) [__init__/<module> (line 54)]: Using balance version 0.10.0

WARNING (2025-05-23 17:45:11,000) [util/guess_id_column (line 113)]: Guessed id column name id for the data

WARNING (2025-05-23 17:45:11,009) [sample_class/from_frame (line 261)]: No weights passed. Adding a 'weight' column and setting all values to 1

WARNING (2025-05-23 17:45:11,017) [util/guess_id_column (line 113)]: Guessed id column name id for the data

WARNING (2025-05-23 17:45:11,030) [sample_class/from_frame (line 261)]: No weights passed. Adding a 'weight' column and setting all values to 1
Out[1]:
(balance.sample_class.Sample)

        balance Sample object with target set
        1000 observations x 3 variables: gender,age_group,income
        id_column: id, weight_column: weight,
        outcome_columns: happiness
        
            target:
                 
	        balance Sample object
	        10000 observations x 3 variables: gender,age_group,income
	        id_column: id, weight_column: weight,
	        outcome_columns: happiness
	        
            3 common variables: gender,age_group,income

Transformations¶

Basic usage: manipulating existing variables¶

When trying to understand what an adjustment does, we can look at the model_coef items collected from the diagnostics method.

In [2]:
adjusted = sample_with_target.adjust(
    # method="ipw", # default method
    # transformations=None,
    # formula=None,
    # penalty_factor=None, # all 1s
    # max_de=None,
)
adj_diag = adjusted.diagnostics()
adj_diag.query("metric == 'model_coef'")

INFO (2025-05-23 17:45:11,048) [ipw/ipw (line 399)]: Starting ipw function

INFO (2025-05-23 17:45:11,051) [adjustment/apply_transformations (line 305)]: Adding the variables: []

INFO (2025-05-23 17:45:11,052) [adjustment/apply_transformations (line 306)]: Transforming the variables: ['gender', 'age_group', 'income']

INFO (2025-05-23 17:45:11,062) [adjustment/apply_transformations (line 343)]: Final variables in output: ['gender', 'age_group', 'income']

INFO (2025-05-23 17:45:11,068) [ipw/ipw (line 433)]: Building model matrix

INFO (2025-05-23 17:45:11,163) [ipw/ipw (line 455)]: The formula used to build the model matrix: ['income + gender + age_group + _is_na_gender']

INFO (2025-05-23 17:45:11,164) [ipw/ipw (line 458)]: The number of columns in the model matrix: 16

INFO (2025-05-23 17:45:11,165) [ipw/ipw (line 459)]: The number of rows in the model matrix: 11000

INFO (2025-05-23 17:45:27,752) [ipw/ipw (line 578)]: Done with sklearn

INFO (2025-05-23 17:45:27,753) [ipw/ipw (line 584)]: max_de: None

INFO (2025-05-23 17:45:27,754) [ipw/ipw (line 605)]: Starting model selection

INFO (2025-05-23 17:45:27,757) [ipw/ipw (line 638)]: Chosen lambda: 0.041158338186664825

INFO (2025-05-23 17:45:27,757) [ipw/ipw (line 654)]: Proportion null deviance explained 0.17265121909892267

INFO (2025-05-23 17:45:27,762) [sample_class/diagnostics (line 839)]: Starting computation of diagnostics of the fitting

INFO (2025-05-23 17:45:28,029) [sample_class/diagnostics (line 1049)]: Done computing diagnostics
Out[2]:
metric val var
44 model_coef 0.142821 intercept
45 model_coef 0.043803 _is_na_gender[T.True]
46 model_coef -0.203801 age_group[T.25-34]
47 model_coef -0.428742 age_group[T.35-44]
48 model_coef -0.529629 age_group[T.45+]
49 model_coef 0.332477 gender[T.Male]
50 model_coef 0.043803 gender[T._NA]
51 model_coef 0.168359 income[Interval(-0.0009997440000000001, 0.44, ...
52 model_coef 0.152978 income[Interval(0.44, 1.664, closed='right')]
53 model_coef 0.11004 income[Interval(1.664, 3.472, closed='right')]
54 model_coef -0.042502 income[Interval(11.312, 15.139, closed='right')]
55 model_coef -0.162192 income[Interval(15.139, 20.567, closed='right')]
56 model_coef -0.212078 income[Interval(20.567, 29.504, closed='right')]
57 model_coef -0.358711 income[Interval(29.504, 128.536, closed='right')]
58 model_coef 0.092556 income[Interval(3.472, 5.663, closed='right')]
59 model_coef 0.071799 income[Interval(5.663, 8.211, closed='right')]
60 model_coef 0.00469 income[Interval(8.211, 11.312, closed='right')]

As we can see from the glm coefficients, the age and gender groups got an extra NA column. And the income variable is bucketed into 10 buckets.

We can change these defaults by deciding on the specific transformation we want.

Let's start with NO transformations.

The transformation argument accepts either a dict or None. None indicates no transformations.

In [3]:
adjusted = sample_with_target.adjust(
    # method="ipw",
    transformations=None,
    # formula=formula,
    # penalty_factor=penalty_factor,
    # max_de=None,
)
adj_diag = adjusted.diagnostics()
adj_diag.query("metric == 'model_coef'")

INFO (2025-05-23 17:45:28,045) [ipw/ipw (line 399)]: Starting ipw function

INFO (2025-05-23 17:45:28,046) [ipw/ipw (line 433)]: Building model matrix

INFO (2025-05-23 17:45:28,112) [ipw/ipw (line 455)]: The formula used to build the model matrix: ['income + gender + age_group + _is_na_gender']

INFO (2025-05-23 17:45:28,113) [ipw/ipw (line 458)]: The number of columns in the model matrix: 8

INFO (2025-05-23 17:45:28,113) [ipw/ipw (line 459)]: The number of rows in the model matrix: 11000

INFO (2025-05-23 17:45:43,481) [ipw/ipw (line 578)]: Done with sklearn

INFO (2025-05-23 17:45:43,482) [ipw/ipw (line 584)]: max_de: None

INFO (2025-05-23 17:45:43,482) [ipw/ipw (line 605)]: Starting model selection

INFO (2025-05-23 17:45:43,485) [ipw/ipw (line 638)]: Chosen lambda: 0.0368353720078807

INFO (2025-05-23 17:45:43,486) [ipw/ipw (line 654)]: Proportion null deviance explained 0.17353587606008936

INFO (2025-05-23 17:45:43,490) [sample_class/diagnostics (line 839)]: Starting computation of diagnostics of the fitting

INFO (2025-05-23 17:45:43,754) [sample_class/diagnostics (line 1049)]: Done computing diagnostics
Out[3]:
metric val var
44 model_coef 0.998089 intercept
45 model_coef 0.000043 _is_na_gender[T.True]
46 model_coef -0.212989 age_group[T.25-34]
47 model_coef -0.440492 age_group[T.35-44]
48 model_coef -0.545653 age_group[T.45+]
49 model_coef -0.188196 gender[Female]
50 model_coef 0.18171 gender[Male]
51 model_coef 0.000043 gender[_NA]
52 model_coef -0.570551 income

In this setting, income was treated as a numeric variable, with no transformations (e.g.: bucketing) on it. Regardless of the transformations, the model matrix made sure to turn the gender and age_group into dummy variables (including a column for NA).

Next we can fit a simple transformation.

Let's say we wanted to bucket age_groups groups that are smaller than 25% of the data, and use different bucketing on income, here is how we'd do it:

In [4]:
from balance.util import fct_lump, quantize

transformations = {
    "age_group": lambda x: fct_lump(x, 0.25),
    "gender": lambda x: x,
    "income": lambda x: quantize(x.fillna(x.mean()), q=3),
}

adjusted = sample_with_target.adjust(
    # method="ipw",
    transformations=transformations,
    # formula=formula,
    # penalty_factor=penalty_factor,
    # max_de=None,
)
adj_diag = adjusted.diagnostics()
adj_diag.query("metric == 'model_coef'")

INFO (2025-05-23 17:45:43,769) [ipw/ipw (line 399)]: Starting ipw function

INFO (2025-05-23 17:45:43,772) [adjustment/apply_transformations (line 305)]: Adding the variables: []

INFO (2025-05-23 17:45:43,773) [adjustment/apply_transformations (line 306)]: Transforming the variables: ['age_group', 'gender', 'income']

INFO (2025-05-23 17:45:43,779) [adjustment/apply_transformations (line 343)]: Final variables in output: ['age_group', 'gender', 'income']

INFO (2025-05-23 17:45:43,785) [ipw/ipw (line 433)]: Building model matrix

INFO (2025-05-23 17:45:43,880) [ipw/ipw (line 455)]: The formula used to build the model matrix: ['income + gender + age_group + _is_na_gender']

INFO (2025-05-23 17:45:43,881) [ipw/ipw (line 458)]: The number of columns in the model matrix: 8

INFO (2025-05-23 17:45:43,881) [ipw/ipw (line 459)]: The number of rows in the model matrix: 11000

INFO (2025-05-23 17:45:57,649) [ipw/ipw (line 578)]: Done with sklearn

INFO (2025-05-23 17:45:57,650) [ipw/ipw (line 584)]: max_de: None

INFO (2025-05-23 17:45:57,651) [ipw/ipw (line 605)]: Starting model selection

INFO (2025-05-23 17:45:57,653) [ipw/ipw (line 638)]: Chosen lambda: 0.11811067639400605

INFO (2025-05-23 17:45:57,654) [ipw/ipw (line 654)]: Proportion null deviance explained 0.09420328935831213

WARNING (2025-05-23 17:45:57,656) [ipw/ipw (line 662)]: The propensity model has low fraction null deviance explained (0.09420328935831213). Results may not be accurate

INFO (2025-05-23 17:45:57,659) [sample_class/diagnostics (line 839)]: Starting computation of diagnostics of the fitting

INFO (2025-05-23 17:45:57,925) [sample_class/diagnostics (line 1049)]: Done computing diagnostics
Out[4]:
metric val var
44 model_coef -0.327112 intercept
45 model_coef 0.031737 _is_na_gender[T.True]
46 model_coef -0.181989 age_group[T.35-44]
47 model_coef 0.098871 age_group[T._lumped_other]
48 model_coef 0.241586 gender[T.Male]
49 model_coef 0.031737 gender[T._NA]
50 model_coef 0.19926 income[Interval(-0.0009997440000000001, 4.194,...
51 model_coef -0.283084 income[Interval(13.693, 128.536, closed='right')]
52 model_coef 0.048146 income[Interval(4.194, 13.693, closed='right')]

As we can see - we managed to change the bucket sizes of income to have only 3 buckets, and we lumped the age_group to two groups (and collapsed together "small" buckets into the _lumped_other bucket).

Lastly, notice that if we omit a variable from transformations, it will not be available for the model construction (This behavior might change in the future).

In [5]:
transformations = {
    # "age_group": lambda x: fct_lump(x, 0.25),
    "gender": lambda x: x,
    # "income": lambda x: quantize(x.fillna(x.mean()), q=3),
}

adjusted = sample_with_target.adjust(
    # method="ipw",
    transformations=transformations,
    # formula=formula,
    # penalty_factor=penalty_factor,
    # max_de=None,
)
adj_diag = adjusted.diagnostics()
adj_diag.query("metric == 'model_coef'")

INFO (2025-05-23 17:45:57,939) [ipw/ipw (line 399)]: Starting ipw function

INFO (2025-05-23 17:45:57,942) [adjustment/apply_transformations (line 305)]: Adding the variables: []

INFO (2025-05-23 17:45:57,943) [adjustment/apply_transformations (line 306)]: Transforming the variables: ['gender']

WARNING (2025-05-23 17:45:57,944) [adjustment/apply_transformations (line 340)]: Dropping the variables: ['income', 'age_group']

INFO (2025-05-23 17:45:57,944) [adjustment/apply_transformations (line 343)]: Final variables in output: ['gender']

INFO (2025-05-23 17:45:57,947) [ipw/ipw (line 433)]: Building model matrix

INFO (2025-05-23 17:45:57,983) [ipw/ipw (line 455)]: The formula used to build the model matrix: ['gender + _is_na_gender']

INFO (2025-05-23 17:45:57,984) [ipw/ipw (line 458)]: The number of columns in the model matrix: 4

INFO (2025-05-23 17:45:57,984) [ipw/ipw (line 459)]: The number of rows in the model matrix: 11000

INFO (2025-05-23 17:46:06,699) [ipw/ipw (line 578)]: Done with sklearn

INFO (2025-05-23 17:46:06,699) [ipw/ipw (line 584)]: max_de: None

INFO (2025-05-23 17:46:06,700) [ipw/ipw (line 605)]: Starting model selection

INFO (2025-05-23 17:46:06,703) [ipw/ipw (line 638)]: Chosen lambda: 0.20570886693214954

INFO (2025-05-23 17:46:06,704) [ipw/ipw (line 654)]: Proportion null deviance explained 0.0264854344569313

WARNING (2025-05-23 17:46:06,705) [ipw/ipw (line 662)]: The propensity model has low fraction null deviance explained (0.0264854344569313). Results may not be accurate

INFO (2025-05-23 17:46:06,709) [sample_class/diagnostics (line 839)]: Starting computation of diagnostics of the fitting

INFO (2025-05-23 17:46:06,976) [sample_class/diagnostics (line 1049)]: Done computing diagnostics
Out[5]:
metric val var
44 model_coef -0.035465 intercept
45 model_coef 0.001051 _is_na_gender[T.True]
46 model_coef -0.141695 gender[Female]
47 model_coef 0.136225 gender[Male]
48 model_coef 0.001051 gender[_NA]

As we can see, only gender was included in the model.

In [6]:
# TODO: add more examples about how add_na works
# TODO: add more examples about rare values in categorical variables and how they are grouped together.

Creating new variables¶

In the next example we will create several new transformations of income.

The info gives information on which variables were added, which were transformed, and what is the final variables in the output.

The x in the lambda function can have one of two meanings:

  1. When the keys in the dict match the exact names of the variables in the DataFrame (e.g.: "income"), then the lambda function treats x as the pandas.Series of that variable.
  2. If the name of the key does NOT exist in the DataFrame (e.g.: "income_squared"), then x will become the DataFrame of the data.
In [7]:
from balance.util import fct_lump, quantize

transformations = {
    "age_group": lambda x: x,
    "gender": lambda x: x,
    "income": lambda x: x,
    "income_squared": lambda x: x.income**2,
    "income_buckets": lambda x: quantize(x.income.fillna(x.income.mean()), q=3),
}

adjusted = sample_with_target.adjust(
    # method="ipw",
    transformations=transformations,
    # formula=formula,
    # penalty_factor=penalty_factor,
    # max_de=None,
)
adj_diag = adjusted.diagnostics()
adj_diag.query("metric == 'model_coef'")

INFO (2025-05-23 17:46:06,995) [ipw/ipw (line 399)]: Starting ipw function

INFO (2025-05-23 17:46:06,998) [adjustment/apply_transformations (line 305)]: Adding the variables: ['income_squared', 'income_buckets']

INFO (2025-05-23 17:46:06,998) [adjustment/apply_transformations (line 306)]: Transforming the variables: ['age_group', 'gender', 'income']

INFO (2025-05-23 17:46:07,004) [adjustment/apply_transformations (line 343)]: Final variables in output: ['income_squared', 'income_buckets', 'age_group', 'gender', 'income']

INFO (2025-05-23 17:46:07,015) [ipw/ipw (line 433)]: Building model matrix

INFO (2025-05-23 17:46:07,114) [ipw/ipw (line 455)]: The formula used to build the model matrix: ['income_squared + income_buckets + income + gender + age_group + _is_na_gender']

INFO (2025-05-23 17:46:07,115) [ipw/ipw (line 458)]: The number of columns in the model matrix: 11

INFO (2025-05-23 17:46:07,116) [ipw/ipw (line 459)]: The number of rows in the model matrix: 11000

INFO (2025-05-23 17:46:28,823) [ipw/ipw (line 578)]: Done with sklearn

INFO (2025-05-23 17:46:28,824) [ipw/ipw (line 584)]: max_de: None

INFO (2025-05-23 17:46:28,825) [ipw/ipw (line 605)]: Starting model selection

INFO (2025-05-23 17:46:28,827) [ipw/ipw (line 638)]: Chosen lambda: 0.043506507030756265

INFO (2025-05-23 17:46:28,828) [ipw/ipw (line 654)]: Proportion null deviance explained 0.17223252304635372

INFO (2025-05-23 17:46:28,832) [sample_class/diagnostics (line 839)]: Starting computation of diagnostics of the fitting

INFO (2025-05-23 17:46:29,097) [sample_class/diagnostics (line 1049)]: Done computing diagnostics
Out[7]:
metric val var
44 model_coef 0.41745 intercept
45 model_coef 0.044654 _is_na_gender[T.True]
46 model_coef -0.194436 age_group[T.25-34]
47 model_coef -0.421207 age_group[T.35-44]
48 model_coef -0.521732 age_group[T.45+]
49 model_coef 0.325806 gender[T.Male]
50 model_coef 0.044654 gender[T._NA]
51 model_coef -0.26602 income
52 model_coef 0.113306 income_buckets[Interval(-0.0009997440000000001...
53 model_coef -0.166366 income_buckets[Interval(13.693, 128.536, close...
54 model_coef 0.032296 income_buckets[Interval(4.194, 13.693, closed=...
55 model_coef -0.185931 income_squared

Formula¶

The formula can accept a list of strings indicating how to combine the transformed variables together. It follows the formula notation from patsy.

For example, we can have an interaction between age_group and gender:

In [8]:
from balance.util import fct_lump_by, quantize

transformations = {
    "age_group": lambda x: x,
    "gender": lambda x: x,
    "income": lambda x: quantize(x.fillna(x.mean()), q=20),
}
formula = ["age_group * gender"]
# the penalty is per elemnt in the list of formula:
# penalty_factor = [0.1, 0.1, 0.1]

adjusted = sample_with_target.adjust(
    method="ipw",
    transformations=transformations,
    formula=formula,
    # penalty_factor=penalty_factor,
    # max_de=None,
)

adj_diag = adjusted.diagnostics()
adj_diag.query("metric == 'model_coef'")

INFO (2025-05-23 17:46:29,112) [ipw/ipw (line 399)]: Starting ipw function

INFO (2025-05-23 17:46:29,115) [adjustment/apply_transformations (line 305)]: Adding the variables: []

INFO (2025-05-23 17:46:29,115) [adjustment/apply_transformations (line 306)]: Transforming the variables: ['age_group', 'gender', 'income']

INFO (2025-05-23 17:46:29,120) [adjustment/apply_transformations (line 343)]: Final variables in output: ['age_group', 'gender', 'income']

INFO (2025-05-23 17:46:29,127) [ipw/ipw (line 433)]: Building model matrix

INFO (2025-05-23 17:46:29,190) [ipw/ipw (line 455)]: The formula used to build the model matrix: ['age_group * gender']

INFO (2025-05-23 17:46:29,191) [ipw/ipw (line 458)]: The number of columns in the model matrix: 12

INFO (2025-05-23 17:46:29,192) [ipw/ipw (line 459)]: The number of rows in the model matrix: 11000

INFO (2025-05-23 17:46:46,900) [ipw/ipw (line 578)]: Done with sklearn

INFO (2025-05-23 17:46:46,901) [ipw/ipw (line 584)]: max_de: None

INFO (2025-05-23 17:46:46,902) [ipw/ipw (line 605)]: Starting model selection

INFO (2025-05-23 17:46:46,905) [ipw/ipw (line 638)]: Chosen lambda: 0.0894967426547247

INFO (2025-05-23 17:46:46,906) [ipw/ipw (line 654)]: Proportion null deviance explained 0.11496302030801142

INFO (2025-05-23 17:46:46,910) [sample_class/diagnostics (line 839)]: Starting computation of diagnostics of the fitting

INFO (2025-05-23 17:46:47,178) [sample_class/diagnostics (line 1049)]: Done computing diagnostics
Out[8]:
metric val var
44 model_coef -0.348132 intercept
45 model_coef 0.334726 age_group[18-24]
46 model_coef 0.005414 age_group[25-34]
47 model_coef -0.160449 age_group[35-44]
48 model_coef -0.280501 age_group[45+]
49 model_coef 0.032004 age_group[T.25-34]:gender[T.Male]
50 model_coef 0.016476 age_group[T.25-34]:gender[T._NA]
51 model_coef -0.037461 age_group[T.35-44]:gender[T.Male]
52 model_coef -0.046181 age_group[T.35-44]:gender[T._NA]
53 model_coef -0.031939 age_group[T.45+]:gender[T.Male]
54 model_coef -0.042359 age_group[T.45+]:gender[T._NA]
55 model_coef 0.271811 gender[T.Male]
56 model_coef 0.06233 gender[T._NA]

As we can see, the formula makes it so that we have combinations of age_group and gender, as well as a main effects of age_group and gender. Since income was not in the formula, it is not included in the model.

Formula and penalty_factor¶

The formula can be provided as several strings, and then the penalty factor can indicate how much the model should focus to adjust to that element of the formula. Larger penalty factors means that element will be less corrected.

The next two examples shows how in one case we focus on correcting for income, and in the second case we focus to correct for age and gender.

In [9]:
transformations = {
    "age_group": lambda x: x,
    "gender": lambda x: x,
    "income": lambda x: x,
}
formula = ["age_group + gender", "income"]
# the penalty is per elemnt in the list of formula:
penalty_factor = [10, 0.1]

adjusted = sample_with_target.adjust(
    method="ipw",
    transformations=transformations,
    formula=formula,
    penalty_factor=penalty_factor,
    # max_de=None,
)

adj_diag = adjusted.diagnostics()
adj_diag.query("metric == 'model_coef'")

INFO (2025-05-23 17:46:47,194) [ipw/ipw (line 399)]: Starting ipw function

INFO (2025-05-23 17:46:47,197) [adjustment/apply_transformations (line 305)]: Adding the variables: []

INFO (2025-05-23 17:46:47,198) [adjustment/apply_transformations (line 306)]: Transforming the variables: ['age_group', 'gender', 'income']

INFO (2025-05-23 17:46:47,199) [adjustment/apply_transformations (line 343)]: Final variables in output: ['age_group', 'gender', 'income']

INFO (2025-05-23 17:46:47,205) [ipw/ipw (line 433)]: Building model matrix

INFO (2025-05-23 17:46:47,271) [ipw/ipw (line 455)]: The formula used to build the model matrix: ['age_group + gender', 'income']

INFO (2025-05-23 17:46:47,272) [ipw/ipw (line 458)]: The number of columns in the model matrix: 7

INFO (2025-05-23 17:46:47,273) [ipw/ipw (line 459)]: The number of rows in the model matrix: 11000

INFO (2025-05-23 17:47:15,552) [ipw/ipw (line 578)]: Done with sklearn

INFO (2025-05-23 17:47:15,553) [ipw/ipw (line 584)]: max_de: None

INFO (2025-05-23 17:47:15,553) [ipw/ipw (line 605)]: Starting model selection

INFO (2025-05-23 17:47:15,556) [ipw/ipw (line 638)]: Chosen lambda: 0.0009460271806598614

INFO (2025-05-23 17:47:15,557) [ipw/ipw (line 654)]: Proportion null deviance explained 0.17289162681789683

INFO (2025-05-23 17:47:15,561) [sample_class/diagnostics (line 839)]: Starting computation of diagnostics of the fitting

INFO (2025-05-23 17:47:15,829) [sample_class/diagnostics (line 1049)]: Done computing diagnostics
Out[9]:
metric val var
44 model_coef 0.243384 intercept
45 model_coef 3.238671 age_group[18-24]
46 model_coef 0.394707 age_group[25-34]
47 model_coef -1.759083 age_group[35-44]
48 model_coef -2.919449 age_group[45+]
49 model_coef 2.599977 gender[T.Male]
50 model_coef 0.487265 gender[T._NA]
51 model_coef -0.073744 income

The above example corrected more to income. As we can see, age and gender got 0 correction (since their penalty was so high). Let's now over correct for age and gender:

In [10]:
transformations = {
    "age_group": lambda x: x,
    "gender": lambda x: x,
    "income": lambda x: x,
}
formula = ["age_group + gender", "income"]
# the penalty is per elemnt in the list of formula:
penalty_factor = [0.1, 10]  # this is flipped

adjusted = sample_with_target.adjust(
    method="ipw",
    transformations=transformations,
    formula=formula,
    penalty_factor=penalty_factor,
    # max_de=None,
)

adj_diag = adjusted.diagnostics()
adj_diag.query("metric == 'model_coef'")

INFO (2025-05-23 17:47:15,845) [ipw/ipw (line 399)]: Starting ipw function

INFO (2025-05-23 17:47:15,848) [adjustment/apply_transformations (line 305)]: Adding the variables: []

INFO (2025-05-23 17:47:15,849) [adjustment/apply_transformations (line 306)]: Transforming the variables: ['age_group', 'gender', 'income']

INFO (2025-05-23 17:47:15,850) [adjustment/apply_transformations (line 343)]: Final variables in output: ['age_group', 'gender', 'income']

INFO (2025-05-23 17:47:15,856) [ipw/ipw (line 433)]: Building model matrix

INFO (2025-05-23 17:47:15,922) [ipw/ipw (line 455)]: The formula used to build the model matrix: ['age_group + gender', 'income']

INFO (2025-05-23 17:47:15,923) [ipw/ipw (line 458)]: The number of columns in the model matrix: 7

INFO (2025-05-23 17:47:15,924) [ipw/ipw (line 459)]: The number of rows in the model matrix: 11000

INFO (2025-05-23 17:47:42,270) [ipw/ipw (line 578)]: Done with sklearn

INFO (2025-05-23 17:47:42,270) [ipw/ipw (line 584)]: max_de: None

INFO (2025-05-23 17:47:42,271) [ipw/ipw (line 605)]: Starting model selection

INFO (2025-05-23 17:47:42,274) [ipw/ipw (line 638)]: Chosen lambda: 0.0012484913627071772

INFO (2025-05-23 17:47:42,275) [ipw/ipw (line 654)]: Proportion null deviance explained 0.17058848391571657

INFO (2025-05-23 17:47:42,279) [sample_class/diagnostics (line 839)]: Starting computation of diagnostics of the fitting

INFO (2025-05-23 17:47:42,537) [sample_class/diagnostics (line 1049)]: Done computing diagnostics
Out[10]:
metric val var
44 model_coef -0.436751 intercept
45 model_coef 0.053355 age_group[18-24]
46 model_coef 0.014525 age_group[25-34]
47 model_coef -0.014981 age_group[35-44]
48 model_coef -0.037504 age_group[45+]
49 model_coef 0.041851 gender[T.Male]
50 model_coef 0.011851 gender[T._NA]
51 model_coef -3.824697 income

In the above case, income basically got 0 correction.

We can add two versions of income, and give each of them a higher penalty than the age and gender:

In [11]:
from balance.util import fct_lump_by, quantize

transformations = {
    "age_group": lambda x: x,
    "gender": lambda x: x,
    "income": lambda x: x,
    "income_buckets": lambda x: quantize(x.income.fillna(x.income.mean()), q=4),
}
formula = ["age_group + gender", "income", "income_buckets"]
# the penalty is per elemnt in the list of formula:
penalty_factor = [1, 2, 2]

adjusted = sample_with_target.adjust(
    method="ipw",
    transformations=transformations,
    formula=formula,
    penalty_factor=penalty_factor,
    # max_de=None,
)

adj_diag = adjusted.diagnostics()
adj_diag.query("metric == 'model_coef'")

INFO (2025-05-23 17:47:42,552) [ipw/ipw (line 399)]: Starting ipw function

INFO (2025-05-23 17:47:42,555) [adjustment/apply_transformations (line 305)]: Adding the variables: ['income_buckets']

INFO (2025-05-23 17:47:42,556) [adjustment/apply_transformations (line 306)]: Transforming the variables: ['age_group', 'gender', 'income']

INFO (2025-05-23 17:47:42,561) [adjustment/apply_transformations (line 343)]: Final variables in output: ['income_buckets', 'age_group', 'gender', 'income']

INFO (2025-05-23 17:47:42,569) [ipw/ipw (line 433)]: Building model matrix

INFO (2025-05-23 17:47:42,665) [ipw/ipw (line 455)]: The formula used to build the model matrix: ['age_group + gender', 'income', 'income_buckets']

INFO (2025-05-23 17:47:42,666) [ipw/ipw (line 458)]: The number of columns in the model matrix: 11

INFO (2025-05-23 17:47:42,667) [ipw/ipw (line 459)]: The number of rows in the model matrix: 11000

INFO (2025-05-23 17:48:02,153) [ipw/ipw (line 578)]: Done with sklearn

INFO (2025-05-23 17:48:02,154) [ipw/ipw (line 584)]: max_de: None

INFO (2025-05-23 17:48:02,154) [ipw/ipw (line 605)]: Starting model selection

INFO (2025-05-23 17:48:02,157) [ipw/ipw (line 638)]: Chosen lambda: 0.043506507030756265

INFO (2025-05-23 17:48:02,158) [ipw/ipw (line 654)]: Proportion null deviance explained 0.17297124065566938

INFO (2025-05-23 17:48:02,162) [sample_class/diagnostics (line 839)]: Starting computation of diagnostics of the fitting

INFO (2025-05-23 17:48:02,424) [sample_class/diagnostics (line 1049)]: Done computing diagnostics
Out[11]:
metric val var
44 model_coef -0.286191 intercept
45 model_coef 0.378645 age_group[18-24]
46 model_coef 0.047595 age_group[25-34]
47 model_coef -0.199745 age_group[35-44]
48 model_coef -0.350982 age_group[45+]
49 model_coef 0.321907 gender[T.Male]
50 model_coef 0.074456 gender[T._NA]
51 model_coef -0.418356 income
52 model_coef 0.216575 income_buckets[Interval(-0.0009997440000000001...
53 model_coef -0.366924 income_buckets[Interval(17.694, 128.536, close...
54 model_coef 0.12985 income_buckets[Interval(2.53, 8.211, closed='r...
55 model_coef -0.05101 income_buckets[Interval(8.211, 17.694, closed=...

Another way is to create a formula for several variations of each variable, and give each a penalty of 1. For example:

In [12]:
from balance.util import fct_lump_by, quantize

transformations = {
    "age_group": lambda x: x,
    "gender": lambda x: x,
    "income": lambda x: x,
    "income_buckets": lambda x: quantize(x.income.fillna(x.income.mean()), q=4),
}
formula = ["age_group", "gender", "income + income_buckets"]
# the penalty is per elemnt in the list of formula:
penalty_factor = [1, 1, 1]

adjusted = sample_with_target.adjust(
    method="ipw",
    transformations=transformations,
    formula=formula,
    penalty_factor=penalty_factor,
    # max_de=None,
)

adj_diag = adjusted.diagnostics()
adj_diag.query("metric == 'model_coef'")

INFO (2025-05-23 17:48:02,440) [ipw/ipw (line 399)]: Starting ipw function

INFO (2025-05-23 17:48:02,443) [adjustment/apply_transformations (line 305)]: Adding the variables: ['income_buckets']

INFO (2025-05-23 17:48:02,443) [adjustment/apply_transformations (line 306)]: Transforming the variables: ['age_group', 'gender', 'income']

INFO (2025-05-23 17:48:02,448) [adjustment/apply_transformations (line 343)]: Final variables in output: ['income_buckets', 'age_group', 'gender', 'income']

INFO (2025-05-23 17:48:02,457) [ipw/ipw (line 433)]: Building model matrix

INFO (2025-05-23 17:48:02,556) [ipw/ipw (line 455)]: The formula used to build the model matrix: ['age_group', 'gender', 'income + income_buckets']

INFO (2025-05-23 17:48:02,556) [ipw/ipw (line 458)]: The number of columns in the model matrix: 12

INFO (2025-05-23 17:48:02,557) [ipw/ipw (line 459)]: The number of rows in the model matrix: 11000

INFO (2025-05-23 17:48:18,218) [ipw/ipw (line 578)]: Done with sklearn

INFO (2025-05-23 17:48:18,218) [ipw/ipw (line 584)]: max_de: None

INFO (2025-05-23 17:48:18,219) [ipw/ipw (line 605)]: Starting model selection

INFO (2025-05-23 17:48:18,221) [ipw/ipw (line 638)]: Chosen lambda: 0.0894967426547247

INFO (2025-05-23 17:48:18,222) [ipw/ipw (line 654)]: Proportion null deviance explained 0.17297566853458446

INFO (2025-05-23 17:48:18,226) [sample_class/diagnostics (line 839)]: Starting computation of diagnostics of the fitting

INFO (2025-05-23 17:48:18,486) [sample_class/diagnostics (line 1049)]: Done computing diagnostics
Out[12]:
metric val var
44 model_coef 0.084942 intercept
45 model_coef 0.327596 age_group[18-24]
46 model_coef 0.039282 age_group[25-34]
47 model_coef -0.176394 age_group[35-44]
48 model_coef -0.296639 age_group[45+]
49 model_coef -0.163857 gender[Female]
50 model_coef 0.158443 gender[Male]
51 model_coef -0.000375 gender[_NA]
52 model_coef -0.258364 income
53 model_coef 0.122028 income_buckets[Interval(-0.0009997440000000001...
54 model_coef -0.213971 income_buckets[Interval(17.694, 128.536, close...
55 model_coef 0.076064 income_buckets[Interval(2.53, 8.211, closed='r...
56 model_coef -0.025416 income_buckets[Interval(8.211, 17.694, closed=...

The impact of transformations and formulas¶

ipw¶

Using the above can have an impact on the final design effect, ASMD, and outcome. Here are several simple examples.

In [13]:
# Defaults from the package

adjusted = sample_with_target.adjust(
    # max_de=None,
)

print(adjusted.summary())
print(adjusted.outcomes().summary())
adjusted.covars().plot(library = "seaborn", dist_type = "kde")

INFO (2025-05-23 17:48:18,501) [ipw/ipw (line 399)]: Starting ipw function

INFO (2025-05-23 17:48:18,503) [adjustment/apply_transformations (line 305)]: Adding the variables: []

INFO (2025-05-23 17:48:18,504) [adjustment/apply_transformations (line 306)]: Transforming the variables: ['gender', 'age_group', 'income']

INFO (2025-05-23 17:48:18,513) [adjustment/apply_transformations (line 343)]: Final variables in output: ['gender', 'age_group', 'income']

INFO (2025-05-23 17:48:18,519) [ipw/ipw (line 433)]: Building model matrix

INFO (2025-05-23 17:48:18,613) [ipw/ipw (line 455)]: The formula used to build the model matrix: ['income + gender + age_group + _is_na_gender']

INFO (2025-05-23 17:48:18,613) [ipw/ipw (line 458)]: The number of columns in the model matrix: 16

INFO (2025-05-23 17:48:18,614) [ipw/ipw (line 459)]: The number of rows in the model matrix: 11000

INFO (2025-05-23 17:48:35,084) [ipw/ipw (line 578)]: Done with sklearn

INFO (2025-05-23 17:48:35,085) [ipw/ipw (line 584)]: max_de: None

INFO (2025-05-23 17:48:35,086) [ipw/ipw (line 605)]: Starting model selection

INFO (2025-05-23 17:48:35,089) [ipw/ipw (line 638)]: Chosen lambda: 0.041158338186664825

INFO (2025-05-23 17:48:35,090) [ipw/ipw (line 654)]: Proportion null deviance explained 0.17265121909892267

Covar ASMD reduction: 63.4%, design effect: 1.880
Covar ASMD (7 variables): 0.327 -> 0.119
Model performance: Model proportion deviance explained: 0.173
1 outcomes: ['happiness']
Mean outcomes (with 95% confidence intervals):
source       self  target  unadjusted           self_ci         target_ci     unadjusted_ci
happiness  53.297  56.278      48.559  (52.097, 54.496)  (55.961, 56.595)  (47.669, 49.449)

Response rates (relative to number of respondents in sample):
   happiness
n     1000.0
%      100.0
Response rates (relative to notnull rows in the target):
    happiness
n     1000.0
%       10.0
Response rates (in the target):
    happiness
n    10000.0
%      100.0
No description has been provided for this image
In [14]:
# No transformations at all

# transformations = None is just like using:
# transformations = {
#     "age_group": lambda x: x,
#     "gender": lambda x: x,
#     "income": lambda x: x,
# }

adjusted = sample_with_target.adjust(
    method="ipw",
    transformations=None,
    # formula=formula,
    # penalty_factor=penalty_factor,
    # max_de=None,
)

print(adjusted.summary())
print(adjusted.outcomes().summary())
adjusted.covars().plot(library = "seaborn", dist_type = "kde")

# slightly smaller design effect, slightly better ASMD reduction.

INFO (2025-05-23 17:48:36,070) [ipw/ipw (line 399)]: Starting ipw function

INFO (2025-05-23 17:48:36,072) [ipw/ipw (line 433)]: Building model matrix

INFO (2025-05-23 17:48:36,138) [ipw/ipw (line 455)]: The formula used to build the model matrix: ['income + gender + age_group + _is_na_gender']

INFO (2025-05-23 17:48:36,138) [ipw/ipw (line 458)]: The number of columns in the model matrix: 8

INFO (2025-05-23 17:48:36,139) [ipw/ipw (line 459)]: The number of rows in the model matrix: 11000

INFO (2025-05-23 17:48:51,509) [ipw/ipw (line 578)]: Done with sklearn

INFO (2025-05-23 17:48:51,510) [ipw/ipw (line 584)]: max_de: None

INFO (2025-05-23 17:48:51,511) [ipw/ipw (line 605)]: Starting model selection

INFO (2025-05-23 17:48:51,513) [ipw/ipw (line 638)]: Chosen lambda: 0.0368353720078807

INFO (2025-05-23 17:48:51,514) [ipw/ipw (line 654)]: Proportion null deviance explained 0.17353587606008936

Covar ASMD reduction: 68.5%, design effect: 2.087
Covar ASMD (7 variables): 0.327 -> 0.103
Model performance: Model proportion deviance explained: 0.174
1 outcomes: ['happiness']
Mean outcomes (with 95% confidence intervals):
source       self  target  unadjusted           self_ci         target_ci     unadjusted_ci
happiness  53.731  56.278      48.559  (52.513, 54.949)  (55.961, 56.595)  (47.669, 49.449)

Response rates (relative to number of respondents in sample):
   happiness
n     1000.0
%      100.0
Response rates (relative to notnull rows in the target):
    happiness
n     1000.0
%       10.0
Response rates (in the target):
    happiness
n    10000.0
%      100.0
No description has been provided for this image
In [15]:
# No transformations at all
transformations = None
# But passing a squared term of income to the formula:
formula = ["age_group + gender + income + income**2"]
# the penalty is per elemnt in the list of formula:
# penalty_factor = [1]

adjusted = sample_with_target.adjust(
    method="ipw",
    transformations=transformations,
    formula=formula,
    # penalty_factor=penalty_factor,
    # max_de=None,
)

print(adjusted.summary())
print(adjusted.outcomes().summary())
adjusted.covars().plot(library = "seaborn", dist_type = "kde")

# Adding income**2 to the formula led to lower Deff but also lower ASMD reduction.

INFO (2025-05-23 17:48:52,487) [ipw/ipw (line 399)]: Starting ipw function

INFO (2025-05-23 17:48:52,489) [ipw/ipw (line 433)]: Building model matrix

INFO (2025-05-23 17:48:52,555) [ipw/ipw (line 455)]: The formula used to build the model matrix: ['age_group + gender + income + income**2']

INFO (2025-05-23 17:48:52,556) [ipw/ipw (line 458)]: The number of columns in the model matrix: 7

INFO (2025-05-23 17:48:52,556) [ipw/ipw (line 459)]: The number of rows in the model matrix: 11000

INFO (2025-05-23 17:49:07,262) [ipw/ipw (line 578)]: Done with sklearn

INFO (2025-05-23 17:49:07,263) [ipw/ipw (line 584)]: max_de: None

INFO (2025-05-23 17:49:07,264) [ipw/ipw (line 605)]: Starting model selection

INFO (2025-05-23 17:49:07,267) [ipw/ipw (line 638)]: Chosen lambda: 0.0574164245593571

INFO (2025-05-23 17:49:07,267) [ipw/ipw (line 654)]: Proportion null deviance explained 0.17296221715396187

Covar ASMD reduction: 60.7%, design effect: 1.925
Covar ASMD (7 variables): 0.327 -> 0.128
Model performance: Model proportion deviance explained: 0.173
1 outcomes: ['happiness']
Mean outcomes (with 95% confidence intervals):
source       self  target  unadjusted           self_ci         target_ci     unadjusted_ci
happiness  53.258  56.278      48.559  (52.072, 54.445)  (55.961, 56.595)  (47.669, 49.449)

Response rates (relative to number of respondents in sample):
   happiness
n     1000.0
%      100.0
Response rates (relative to notnull rows in the target):
    happiness
n     1000.0
%       10.0
Response rates (in the target):
    happiness
n    10000.0
%      100.0
No description has been provided for this image
In [16]:
transformations = {
    "age_group": lambda x: x,
    "gender": lambda x: x,
    "income": lambda x: x,
    "income_buckets": lambda x: quantize(x.income.fillna(x.income.mean()), q=20),
}
formula = ["age_group + gender", "income_buckets"]
# the penalty is per elemnt in the list of formula:
penalty_factor = [1, 0.1]

adjusted = sample_with_target.adjust(
    method="ipw",
    transformations=transformations,
    formula=formula,
    penalty_factor=penalty_factor,
    # max_de=None,
)

print(adjusted.summary())
print(adjusted.outcomes().summary())
adjusted.covars().plot(library = "seaborn", dist_type = "kde")

# By adding income_buckets and using it instead of income, as well as putting more weight in it in terms of penalty
# we managed to correct income quite well, but at the expense of age and gender.

INFO (2025-05-23 17:49:08,300) [ipw/ipw (line 399)]: Starting ipw function

INFO (2025-05-23 17:49:08,303) [adjustment/apply_transformations (line 305)]: Adding the variables: ['income_buckets']

INFO (2025-05-23 17:49:08,304) [adjustment/apply_transformations (line 306)]: Transforming the variables: ['age_group', 'gender', 'income']

INFO (2025-05-23 17:49:08,310) [adjustment/apply_transformations (line 343)]: Final variables in output: ['income_buckets', 'age_group', 'gender', 'income']

INFO (2025-05-23 17:49:08,318) [ipw/ipw (line 433)]: Building model matrix

INFO (2025-05-23 17:49:08,415) [ipw/ipw (line 455)]: The formula used to build the model matrix: ['age_group + gender', 'income_buckets']

INFO (2025-05-23 17:49:08,416) [ipw/ipw (line 458)]: The number of columns in the model matrix: 26

INFO (2025-05-23 17:49:08,416) [ipw/ipw (line 459)]: The number of rows in the model matrix: 11000

INFO (2025-05-23 17:49:30,971) [ipw/ipw (line 578)]: Done with sklearn

INFO (2025-05-23 17:49:30,972) [ipw/ipw (line 584)]: max_de: None

INFO (2025-05-23 17:49:30,972) [ipw/ipw (line 605)]: Starting model selection

INFO (2025-05-23 17:49:30,975) [ipw/ipw (line 638)]: Chosen lambda: 0.09460271806598614

INFO (2025-05-23 17:49:30,976) [ipw/ipw (line 654)]: Proportion null deviance explained 0.17682033095496275

Covar ASMD reduction: 70.0%, design effect: 2.391
Covar ASMD (7 variables): 0.327 -> 0.098
Model performance: Model proportion deviance explained: 0.177
1 outcomes: ['happiness']
Mean outcomes (with 95% confidence intervals):
source       self  target  unadjusted          self_ci         target_ci     unadjusted_ci
happiness  52.289  56.278      48.559  (51.06, 53.519)  (55.961, 56.595)  (47.669, 49.449)

Response rates (relative to number of respondents in sample):
   happiness
n     1000.0
%      100.0
Response rates (relative to notnull rows in the target):
    happiness
n     1000.0
%       10.0
Response rates (in the target):
    happiness
n    10000.0
%      100.0
No description has been provided for this image
In [ ]:

CBPS¶

Let's see if we can improve on CBPS a bit.

In [17]:
# Defaults from the package

adjusted = sample_with_target.adjust(
    method = "cbps",
    # max_de=None,
)

print(adjusted.summary())
print(adjusted.outcomes().summary())
adjusted.covars().plot(library = "seaborn", dist_type = "kde")

# CBPS already corrects a lot. Let's see if we can make it correct a tiny bit more.

INFO (2025-05-23 17:49:31,914) [cbps/cbps (line 411)]: Starting cbps function

INFO (2025-05-23 17:49:31,917) [adjustment/apply_transformations (line 305)]: Adding the variables: []

INFO (2025-05-23 17:49:31,918) [adjustment/apply_transformations (line 306)]: Transforming the variables: ['gender', 'age_group', 'income']

INFO (2025-05-23 17:49:31,927) [adjustment/apply_transformations (line 343)]: Final variables in output: ['gender', 'age_group', 'income']

INFO (2025-05-23 17:49:32,027) [cbps/cbps (line 461)]: The formula used to build the model matrix: ['income + gender + age_group + _is_na_gender']

INFO (2025-05-23 17:49:32,028) [cbps/cbps (line 473)]: The number of columns in the model matrix: 16

INFO (2025-05-23 17:49:32,029) [cbps/cbps (line 474)]: The number of rows in the model matrix: 11000

INFO (2025-05-23 17:49:32,035) [cbps/cbps (line 543)]: Finding initial estimator for GMM optimization

INFO (2025-05-23 17:49:32,090) [cbps/cbps (line 570)]: Finding initial estimator for GMM optimization that minimizes the balance loss

INFO (2025-05-23 17:49:32,371) [cbps/cbps (line 605)]: Running GMM optimization

INFO (2025-05-23 17:49:32,811) [cbps/cbps (line 734)]: Done cbps function

Covar ASMD reduction: 77.4%, design effect: 2.754
Covar ASMD (7 variables): 0.327 -> 0.074

1 outcomes: ['happiness']
Mean outcomes (with 95% confidence intervals):
source       self  target  unadjusted          self_ci         target_ci     unadjusted_ci
happiness  54.366  56.278      48.559  (53.003, 55.73)  (55.961, 56.595)  (47.669, 49.449)

Response rates (relative to number of respondents in sample):
   happiness
n     1000.0
%      100.0
Response rates (relative to notnull rows in the target):
    happiness
n     1000.0
%       10.0
Response rates (in the target):
    happiness
n    10000.0
%      100.0
No description has been provided for this image
In [18]:
import numpy as np

# No transformations at all
transformations = {
    "age_group": lambda x: x,
    "gender": lambda x: x,
    # "income": lambda x: x,
    "income_log": lambda x: np.log(x.income.fillna(x.income.mean())),
    "income_buckets": lambda x: quantize(x.income.fillna(x.income.mean()), q=5),
}
formula = ["age_group + gender + income_log * income_buckets"]

adjusted = sample_with_target.adjust(
    method="cbps",
    transformations=transformations,
    formula=formula,
    # penalty_factor=penalty_factor, # CBPS seems to ignore the penalty factor.
    # max_de=None,
)

print(adjusted.summary())
print(adjusted.outcomes().summary())
adjusted.covars().plot(library="seaborn", dist_type="kde")

# Trying various transformations gives slightly different results (some effect on the outcome, Deff and ASMD) - but nothing too major here.

INFO (2025-05-23 17:49:33,782) [cbps/cbps (line 411)]: Starting cbps function

INFO (2025-05-23 17:49:33,785) [adjustment/apply_transformations (line 305)]: Adding the variables: ['income_log', 'income_buckets']

INFO (2025-05-23 17:49:33,786) [adjustment/apply_transformations (line 306)]: Transforming the variables: ['age_group', 'gender']

WARNING (2025-05-23 17:49:33,791) [adjustment/apply_transformations (line 340)]: Dropping the variables: ['income']

INFO (2025-05-23 17:49:33,792) [adjustment/apply_transformations (line 343)]: Final variables in output: ['income_log', 'income_buckets', 'age_group', 'gender']

INFO (2025-05-23 17:49:33,894) [cbps/cbps (line 461)]: The formula used to build the model matrix: ['age_group + gender + income_log * income_buckets']

INFO (2025-05-23 17:49:33,895) [cbps/cbps (line 473)]: The number of columns in the model matrix: 15

INFO (2025-05-23 17:49:33,896) [cbps/cbps (line 474)]: The number of rows in the model matrix: 11000

INFO (2025-05-23 17:49:33,901) [cbps/cbps (line 543)]: Finding initial estimator for GMM optimization

INFO (2025-05-23 17:49:34,003) [cbps/cbps (line 570)]: Finding initial estimator for GMM optimization that minimizes the balance loss

INFO (2025-05-23 17:49:34,326) [cbps/cbps (line 605)]: Running GMM optimization

INFO (2025-05-23 17:49:34,747) [cbps/cbps (line 734)]: Done cbps function

Covar ASMD reduction: 82.1%, design effect: 3.030
Covar ASMD (7 variables): 0.327 -> 0.059

1 outcomes: ['happiness']
Mean outcomes (with 95% confidence intervals):
source       self  target  unadjusted           self_ci         target_ci     unadjusted_ci
happiness  54.432  56.278      48.559  (53.042, 55.822)  (55.961, 56.595)  (47.669, 49.449)

Response rates (relative to number of respondents in sample):
   happiness
n     1000.0
%      100.0
Response rates (relative to notnull rows in the target):
    happiness
n     1000.0
%       10.0
Response rates (in the target):
    happiness
n    10000.0
%      100.0
No description has been provided for this image
In [19]:
# Sessions info
import session_info
session_info.show(html=False, dependencies=True)

-----
balance             0.10.0
numpy               1.26.4
pandas              2.0.3
session_info        v1.0.1
-----
PIL                         11.2.1
anyio                       NA
arrow                       1.3.0
asttokens                   NA
attr                        25.3.0
attrs                       25.3.0
babel                       2.17.0
certifi                     2025.04.26
charset_normalizer          3.4.2
comm                        0.2.2
cycler                      0.12.1
cython_runtime              NA
dateutil                    2.9.0.post0
debugpy                     1.8.14
decorator                   5.2.1
defusedxml                  0.7.1
exceptiongroup              1.3.0
executing                   2.2.0
fastjsonschema              NA
fqdn                        NA
idna                        3.10
importlib_metadata          NA
importlib_resources         NA
ipfn                        NA
ipykernel                   6.29.5
isoduration                 NA
jedi                        0.19.2
jinja2                      3.1.6
joblib                      1.5.1
json5                       0.12.0
jsonpointer                 3.0.0
jsonschema                  4.23.0
jsonschema_specifications   NA
jupyter_events              0.12.0
jupyter_server              2.16.0
jupyterlab_server           2.27.3
kiwisolver                  1.4.7
markupsafe                  3.0.2
matplotlib                  3.9.4
matplotlib_inline           0.1.7
mpl_toolkits                NA
narwhals                    1.40.0
nbformat                    5.10.4
overrides                   NA
packaging                   25.0
parso                       0.8.4
patsy                       1.0.1
pexpect                     4.9.0
platformdirs                4.3.8
plotly                      6.1.1
prometheus_client           NA
prompt_toolkit              3.0.51
psutil                      7.0.0
ptyprocess                  0.7.0
pure_eval                   0.2.3
pydev_ipython               NA
pydevconsole                NA
pydevd                      3.2.3
pydevd_file_utils           NA
pydevd_plugins              NA
pydevd_tracing              NA
pygments                    2.19.1
pyparsing                   3.2.3
pythonjsonlogger            NA
pytz                        2025.2
referencing                 NA
requests                    2.32.3
rfc3339_validator           0.1.4
rfc3986_validator           0.1.1
rpds                        NA
scipy                       1.10.1
seaborn                     0.13.2
send2trash                  NA
six                         1.17.0
sklearn                     1.2.2
sniffio                     1.3.1
sphinxcontrib               NA
stack_data                  0.6.3
statsmodels                 0.14.4
threadpoolctl               3.6.0
tornado                     6.5.1
traitlets                   5.14.3
typing_extensions           NA
uri_template                NA
urllib3                     2.4.0
wcwidth                     0.2.13
webcolors                   NA
websocket                   1.8.0
yaml                        6.0.2
zipp                        NA
zmq                         26.4.0
zoneinfo                    NA
-----
IPython             8.18.1
jupyter_client      8.6.3
jupyter_core        5.7.2
jupyterlab          4.4.2
notebook            7.4.2
-----
Python 3.9.22 (main, Apr  8 2025, 21:45:32) [GCC 13.3.0]
Linux-6.11.0-1014-azure-x86_64-with-glibc2.39
-----
Session information updated at 2025-05-23 17:49

/opt/hostedtoolcache/Python/3.9.22/x64/lib/python3.9/site-packages/session_info/main.py:213: UserWarning:

The '__version__' attribute is deprecated and will be removed in MarkupSafe 3.1. Use feature detection, or `importlib.metadata.version("markupsafe")`, instead.