Weekday as dummy / factor variable in a linear regression model using statsmodels
Question
The question:
How can I add a dummy / factor variable to a model using sm.OLS() ?
The details:
Data sample structure:
Date A B weekday
2013-05-04 25.03 88.51 Saturday
2013-05-05 52.98 67.99 Sunday
2013-05-06 39.93 75.19 Monday
2013-05-07 47.31 86.99 Tuesday
2013-05-08 19.61 87.94 Wednesday
2013-05-09 39.51 83.10 Thursday
2013-05-10 21.22 62.16 Friday
2013-05-11 19.04 58.79 Saturday
2013-05-12 18.53 75.27 Sunday
2013-05-13 11.90 75.43 Monday
2013-05-14 47.64 64.76 Tuesday
2013-05-15 27.47 91.65 Wednesday
2013-05-16 11.20 59.83 Thursday
2013-05-17 25.10 67.47 Friday
2013-05-18 19.89 64.70 Saturday
2013-05-19 38.91 76.68 Sunday
2013-05-20 42.11 94.36 Monday
2013-05-21 7.845 73.67 Tuesday
2013-05-22 35.45 76.67 Wednesday
2013-05-23 29.43 79.05 Thursday
2013-05-24 33.51 78.53 Friday
2013-05-25 13.58 59.26 Saturday
2013-05-26 37.38 68.59 Sunday
2013-05-27 37.09 67.79 Monday
2013-05-28 21.70 70.54 Tuesday
2013-05-29 11.85 60.00 Wednesday
The following creates a linear regression model of B on A using sm.ols() (including a constant term using sm.add_constant() )
Complete code with data sample for regression analysis using statsmodels:
# imports
import pandas as pd
import statsmodels.api as sm
# same data as described above
data = {'Date': {0: '2013-05-04',
1: '2013-05-05',
2: '2013-05-06',
3: '2013-05-07',
4: '2013-05-08',
5: '2013-05-09',
6: '2013-05-10',
7: '2013-05-11',
8: '2013-05-12',
9: '2013-05-13',
10: '2013-05-14',
11: '2013-05-15',
12: '2013-05-16',
13: '2013-05-17',
14: '2013-05-18',
15: '2013-05-19',
16: '2013-05-20',
17: '2013-05-21',
18: '2013-05-22',
19: '2013-05-23',
20: '2013-05-24',
21: '2013-05-25',
22: '2013-05-26',
23: '2013-05-27',
24: '2013-05-28',
25: '2013-05-29'},
'A': {0: 25.03,
1: 52.98,
2: 39.93,
3: 47.31,
4: 19.61,
5: 39.51,
6: 21.22,
7: 19.04,
8: 18.53,
9: 11.9,
10: 47.64,
11: 27.47,
12: 11.2,
13: 25.1,
14: 19.89,
15: 38.91,
16: 42.11,
17: 7.845,
18: 35.45,
19: 29.43,
20: 33.51,
21: 13.58,
22: 37.38,
23: 37.09,
24: 21.7,
25: 11.85},
'B': {0: 88.51,
1: 67.99,
2: 75.19,
3: 86.99,
4: 87.94,
5: 83.1,
6: 62.16,
7: 58.79,
8: 75.27,
9: 75.43,
10: 64.76,
11: 91.65,
12: 59.83,
13: 67.47,
14: 64.7,
15: 76.68,
16: 94.36,
17: 73.67,
18: 76.67,
19: 79.05,
20: 78.53,
21: 59.26,
22: 68.59,
23: 67.79,
24: 70.54,
25: 60.0},
'weekday': {0: 'Saturday',
1: 'Sunday',
2: 'Monday',
3: 'Tuesday',
4: 'Wednesday',
5: 'Thursday',
6: 'Friday',
7: 'Saturday',
8: 'Sunday',
9: 'Monday',
10: 'Tuesday',
11: 'Wednesday',
12: 'Thursday',
13: 'Friday',
14: 'Saturday',
15: 'Sunday',
16: 'Monday',
17: 'Tuesday',
18: 'Wednesday',
19: 'Thursday',
20: 'Friday',
21: 'Saturday',
22: 'Sunday',
23: 'Monday',
24: 'Tuesday',
25: 'Wednesday'}}
df = pd.DataFrame(data)
df = df.set_index(['Date'])
df['weekday'] = df['weekday'].astype(object)
independent = df['B'].to_frame()
x = sm.add_constant(independent)
model = sm.OLS(df['A'], x).fit()
model.summary()
Output (shortened):
coef std err t P>|t| [95.0% Conf. Int.]
------------------------------------------------------------------------------
const -1.4328 17.355 -0.083 0.935 -37.252 34.386
B 0.4034 0.233 1.729 0.097 -0.078 0.885
==============================================================================
Now I'd like to add weekday as an explanatory factor variable. I was hoping it would be as easy as changing the data type in the dataframe, but unfortunately that doesn't seem to work although the column was accepted by the x = sm.add_constant(independent) part.
import pandas as pd
import statsmodels.api as sm
df = pd.read_clipboard(sep='\\s+')
df = df.set_index(['Date'])
df['weekday'] = df['weekday'].astype(object)
independent = df[['B', 'weekday']]
x = sm.add_constant(independent)
model = sm.OLS(df['A'], x).fit()
model.summary()
When you come to the model = sm.OLS(df['A'], x).fit() part, a value error is raised:
ValueError: Pandas data cast to numpy dtype of object. Check input data with np.asarray(data).
Any other suggestions?
1 answers
solution1
3 ACCPTED 2018-05-03 19:33:27
You can use pandas categorical to create the dummy variables, or, simpler, use the formula interface where patsy transforms all non-numeric columns to the dummy variables, or other factor encoding.
Using the formula interface in this case (same as lower case ols in statsmodels.formula.api) shows the result below. Patsy sorts levels of the categorical variable alphabetically. 'Friday' is missing in the list of variables and has been selected as reference category.
>>> res = sm.OLS.from_formula('A ~ B + weekday', df).fit()
>>> print(res.summary())
OLS Regression Results
==============================================================================
Dep. Variable: A R-squared: 0.301
Model: OLS Adj. R-squared: 0.029
Method: Least Squares F-statistic: 1.105
Date: Thu, 03 May 2018 Prob (F-statistic): 0.401
Time: 15:26:02 Log-Likelihood: -97.898
No. Observations: 26 AIC: 211.8
Df Residuals: 18 BIC: 221.9
Df Model: 7
Covariance Type: nonrobust
========================================================================================
coef std err t P>|t| [0.025 0.975]
----------------------------------------------------------------------------------------
Intercept -1.4717 19.343 -0.076 0.940 -42.110 39.167
weekday[T.Monday] 2.5837 9.857 0.262 0.796 -18.124 23.291
weekday[T.Saturday] -6.5889 9.599 -0.686 0.501 -26.755 13.577
weekday[T.Sunday] 9.2287 9.616 0.960 0.350 -10.975 29.432
weekday[T.Thursday] -1.7610 10.321 -0.171 0.866 -23.445 19.923
weekday[T.Tuesday] 2.6507 9.664 0.274 0.787 -17.652 22.953
weekday[T.Wendesday] -6.9320 9.911 -0.699 0.493 -27.754 13.890
B 0.4047 0.258 1.566 0.135 -0.138 0.948
==============================================================================
Omnibus: 1.039 Durbin-Watson: 2.313
Prob(Omnibus): 0.595 Jarque-Bera (JB): 0.532
Skew: -0.350 Prob(JB): 0.766
Kurtosis: 3.007 Cond. No. 638.
==============================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
See patsy documentation for options for categorical encodings http://patsy.readthedocs.io/en/latest/categorical-coding.html
For example, the reference coding can be specified explicitly as in this formula
"A ~ B + C(weekday, Treatment('Sunday'))"
http://patsy.readthedocs.io/en/latest/API-reference.html#patsy.Treatment
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