How do I joint test a multi-level categorical effect in ipython using statsmodels? - ipython

Question

I am using the Ordinary Least Squares (ols) function in statsmodels in ipython to fit a linear model where one covariate (City) is a multi-level categorical effect:
result=smf.ols(formula="Y ~ C(City) + X*C(Group)",data=s).fit();
(X is continuous, Group is a binary categorical variable).
When I do results.summary(), I get one row per level of City, however, what I would like to know is the overall significance of the 'City' covariate (i.e., compare Y~C(City)+X*C(Group) with the partial model Y~X*C(Group)).
Is there a way of doing it?
thanks in advance

Answer 1

Thank you user333700!
Here's an elaboration of your hint. I generate data with a 3-level categorical variable, use statsmodels to fit a model, and then test all levels of the categorical variable jointly:
# 1. generate data
def rnorm(n,u,s):
return np.random.standard_normal(n)*s+u
a=rnorm(100,-1,1);
b=rnorm(100,0,1);
c=rnorm(100,+1,1);
n=rnorm(300,0,1); # some noise
y=np.concatenate((a,b,c))+n
g=np.zeros(300);
g[0:100]=1
g[100:200]=2
g[200:300]=3
df=pd.DataFrame({'Y':y,'G':g,'N':n});
# 2. fit model
r=smf.ols(formula="Y ~ N + C(G)",data=df).fit();
r.summary()
# 3. joint test
print r.params
A=np.identity(len(r.params)) # identity matrix with size = number of params
GroupTest=A[1:3,:] # for the categorical var., keep the corresponding rows of A
CovTest=A[3,:] # row for the continuous var.
print "Group effect test",r.f_test(GroupTest).fvalue
print "Covariate effect test",r.f_test(CovTest).fvalue
The result should be something like this:
Intercept -1.188975
C(G)[T.2.0] 1.315898
C(G)[T.3.0] 2.137431
N 0.922038
dtype: float64
Group effect test [[ 120.86097747]]
Covariate effect test [[ 259.34155851]]

Answer 2

brief answer
you can use anova_lm (type 3) directly or use f_test or wald_test and either construct the constraint matrix or provide the constraints of the hypothesis in the form of a sequence of formulas.
http://statsmodels.sourceforge.net/devel/anova.html
http://statsmodels.sourceforge.net/devel/generated/statsmodels.regression.linear_model.RegressionResults.f_test.html