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Linearity in Parameters: Ramsey RESET Test in Python

Last Update: February 21, 2022

Linearity in Parameters: Ramsey RESET Test in Python can be done using statsmodels package linear_reset function found within statsmodels.stats.diagnostic module for evaluating whether linear regression fitted values non-linear combinations explain dependent variable. Main parameters within linear_reset function are res with original model results, power with augmented model added independent variables powers, test_type with original model fitted values, independent variables or independent variables first principal component as augmented model added independent variables and use_f with logical value on whether an F-test or chi-square test should be done.

As example, we can do Ramsey RESET test on multiple linear regression of house price explained by its lot size and number of bedrooms using data included within AER R package HousePrices object [1].

First, we import statmodels package for data downloading, multiple linear regression fitting and Ramsey RESET test [2].

In [1]:
import statsmodels.api as sm
import statsmodels.formula.api as smf
import statsmodels.stats.diagnostic as smd

Second, we create houseprices data object using get_rdataset function and display first five rows and three columns of data using print function and head data frame method to view its structure.

In [2]:
houseprices = sm.datasets.get_rdataset(dataname="HousePrices", package="AER", cache=True).data
print(houseprices.iloc[:, 0:3].head())
Out [2]:
     price  lotsize  bedrooms
0  42000.0     5850         3
1  38500.0     4000         2
2  49500.0     3060         3
3  60500.0     6650         3
4  61000.0     6360         2

Third, we fit model with ols function using variables within houseprices data object and store results within mlr object. Within ols function, parameter formula = “price ~ lotsize + bedrooms” fits model where house price is explained by its lot size and number of bedrooms.

In [3]:
mlr = smf.ols(formula="price ~ lotsize + bedrooms", data=houseprices).fit()

Fourth, as example again, we do Ramsey RESET test using linear_reset function, store results in resettest object and print it. Within linear_reset function, parameters res=mlr includes original model results, power=2 adds squared independent variable to augmented model, test_type="fitted" adds original model fitted values as augmented model independent variable and use_f=True does F-test. Notice that linear_reset function parameters power=2, test_type="fitted" and use_f=True were only included as educational examples which can be modified according to your needs.

In [4]:
resettest = smd.linear_reset(res=mlr, power=2, test_type="fitted", use_f=True)
Out [4]:
<F test: F=array([[10.63462745]]), p=0.0011796522160904715, df_denom=542, df_num=1>


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[1] Data Description: Sales prices of houses sold in the city of Windsor, Canada, during July, August and September, 1987.

Original Source: Anglin, P., and Gencay, R. (1996). Semiparametric Estimation of a Hedonic Price Function. Journal of Applied Econometrics, 11, 633–648.

[2] statsmodels Python package: Seabold, Skipper, and Josef Perktold. (2010). “statsmodels: Econometric and statistical modeling with python.” Proceedings of the 9th Python in Science Conference.

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