Brussels. Step 1.d Micro-level Water demand model¶
In [1]:
import datetime; print(datetime.datetime.now())
2018-03-26 02:13:23.269759
Notebook abstract
A simple micro-level water demand model.
A simple micro-level water demand model. Similar to the electricity demand model, the water demand model uses micro level consumption demand data for the construction of a table model. The table model describes simple rules for the construction of the proxy micro level sample data.
Prior water demand model¶
In [2]:
import statsmodels.api as sm
import pandas as pd
import numpy as np
from smum._scripts.micro import compute_categories, change_index
/usr/lib/python3.6/site-packages/statsmodels-0.8.0-py3.6-linux-x86_64.egg/statsmodels/compat/pandas.py:56: FutureWarning: The pandas.core.datetools module is deprecated and will be removed in a future version. Please use the pandas.tseries module instead.
from pandas.core import datetools
Dataset¶
The data used for the construction of the household water demand model is downscale from municipal-level data-sets from the Wallonie region.
This data to construct a water demand model a function of: 1. Building construction type (classified as house or apartment) 2. Building construction year 3. Head of household gender 4. Household size 5. Household income level
In [3]:
water_data = pd.read_csv('data/downscaled_data_be.csv', index_col=0)
water_data.loc[
water_data.ConstructionType != 'appartements',
'ConstructionType'] = 'House'
formula = "Water ~ Age + ConstructionType + ConstructionYear + HHSize + Income"
In [4]:
water_data.head()
Out[4]:
| Age | ConstructionType | ConstructionYear | Energy | Gender | HHSize | Income | Waste | Water | w | |
|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 70 | House | 1900 | 49 | femme | 2.61 | 28150.0 | 147.0 | 79 | 71.45 |
| 1 | 22 | House | 1977 | 49 | femme | 2.61 | 28150.0 | 147.0 | 79 | 71.45 |
| 2 | 28 | House | 1972 | 49 | femme | 2.61 | 28150.0 | 147.0 | 79 | 71.45 |
| 3 | 7 | House | 1900 | 49 | femme | 2.61 | 28150.0 | 147.0 | 79 | 71.45 |
| 4 | 33 | House | 1962 | 49 | homme | 2.61 | 28150.0 | 147.0 | 79 | 71.45 |
Regression model¶
A weighted multiple regression model is defined and run with help of the ‘statsmodels’ python library.
The model regression coefficients and their standard error are used as the water demand model.
In [5]:
model_water = sm.WLS.from_formula(formula, water_data, weights=water_data.w)
model_results_water = model_water.fit()
In [6]:
model_results_water.summary()
Out[6]:
| Dep. Variable: | Water | R-squared: | 0.360 |
|---|---|---|---|
| Model: | WLS | Adj. R-squared: | 0.360 |
| Method: | Least Squares | F-statistic: | 2519. |
| Date: | Mon, 26 Mar 2018 | Prob (F-statistic): | 0.00 |
| Time: | 02:13:26 | Log-Likelihood: | -75359. |
| No. Observations: | 22412 | AIC: | 1.507e+05 |
| Df Residuals: | 22406 | BIC: | 1.508e+05 |
| Df Model: | 5 | ||
| Covariance Type: | nonrobust |
| coef | std err | t | P>|t| | [0.025 | 0.975] | |
|---|---|---|---|---|---|---|
| Intercept | -5.2824 | 2.273 | -2.324 | 0.020 | -9.738 | -0.826 |
| ConstructionType[T.appartements] | 1.1517 | 0.112 | 10.307 | 0.000 | 0.933 | 1.371 |
| Age | 0.0005 | 0.002 | 0.305 | 0.760 | -0.003 | 0.004 |
| ConstructionYear | 0.0157 | 0.001 | 13.527 | 0.000 | 0.013 | 0.018 |
| HHSize | 10.3606 | 0.273 | 37.966 | 0.000 | 9.826 | 10.895 |
| Income | 0.0010 | 1.27e-05 | 75.207 | 0.000 | 0.001 | 0.001 |
| Omnibus: | 2964.935 | Durbin-Watson: | 0.038 |
|---|---|---|---|
| Prob(Omnibus): | 0.000 | Jarque-Bera (JB): | 7638.192 |
| Skew: | 0.748 | Prob(JB): | 0.00 |
| Kurtosis: | 5.438 | Cond. No. | 1.28e+06 |
In [7]:
params_water = change_index(model_results_water.params)
bse_water = change_index(model_results_water.bse)
water = pd.concat([params_water, bse_water], axis=1)
water.columns = ['co_mu', 'co_sd']
In [8]:
water.index = [
'Intercept', 'ConstructionType', 'Age',
'ConstructionYear', 'HHSize', 'Income',
]
In [9]:
water.loc[:, 'p'] = np.nan
water.loc[:,'mu'] = np.nan
water.loc[:,'sd'] = np.nan
water.loc['ConstructionType', 'dis'] = 'Bernoulli'
water.loc['Age', 'dis'] = 'Normal'
water.loc['ConstructionYear', 'dis'] = 'Poisson'
water.loc['HHSize', 'dis'] = 'Poisson'
water.loc['Income', 'dis'] = 'Gamma'
water.loc[:, 'ub'] = np.inf
water.loc[:, 'lb'] = 0
water.loc['Intercept', 'lb'] = -np.inf
water.loc['Age', 'ub'] = 85
water.loc['Age', 'lb'] = 20
water.loc['HHSize', 'ub'] = 8
water.loc['HHSize', 'lb'] = 1
water.loc['ConstructionYear', 'ub'] = 2035
water.loc['ConstructionYear', 'lb'] = 1800
water.loc['Intercept', 'p'] = water.loc['Intercept', 'co_mu']
water.loc['Intercept', 'dis'] = 'Deterministic'
water.loc['Intercept', 'co_mu'] = np.nan
water.loc['Intercept', 'co_sd'] = np.nan
In [10]:
water.index = ['w_'+i for i in water.index]
In [11]:
water.to_csv('data/table_water.csv')
In [12]:
water
Out[12]:
| co_mu | co_sd | p | mu | sd | dis | ub | lb | |
|---|---|---|---|---|---|---|---|---|
| w_Intercept | NaN | NaN | -5.282409 | NaN | NaN | Deterministic | inf | -inf |
| w_ConstructionType | 1.151750 | 0.111739 | NaN | NaN | NaN | Bernoulli | inf | 0.000000 |
| w_Age | 0.000516 | 0.001691 | NaN | NaN | NaN | Normal | 85.000000 | 20.000000 |
| w_ConstructionYear | 0.015676 | 0.001159 | NaN | NaN | NaN | Poisson | 2035.000000 | 1800.000000 |
| w_HHSize | 10.360614 | 0.272889 | NaN | NaN | NaN | Poisson | 8.000000 | 1.000000 |
| w_Income | 0.000957 | 0.000013 | NaN | NaN | NaN | Gamma | inf | 0.000000 |