def fit_backward_difference_coding(col, values, handle_missing, handle_unknown):
if handle_missing == 'value':
values = values[values > 0]
values_to_encode = values.get_values()
if len(values) < 2:
return pd.DataFrame(index=values_to_encode)
if handle_unknown == 'indicator':
values_to_encode = np.append(values_to_encode, -1)
backwards_difference_matrix = Diff().code_without_intercept(values_to_encode)
df = pd.DataFrame(data=backwards_difference_matrix.matrix, index=values_to_encode,
columns=[str(col) + '_%d' % (i, ) for i in range(len(backwards_difference_matrix.column_suffixes))])
if handle_unknown == 'return_nan':
df.loc[-1] = np.nan
elif handle_unknown == 'value':
df.loc[-1] = np.zeros(len(values_to_encode) - 1)
if handle_missing == 'return_nan':
df.loc[values.loc[np.nan]] = np.nan
elif handle_missing == 'value':
df.loc[-2] = np.zeros(len(values_to_encode) - 1)
return df
def fit_backward_difference_coding(values):
if len(values) < 2:
return pd.DataFrame()
backwards_difference_matrix = Diff().code_without_intercept(values)
df = pd.DataFrame(data=backwards_difference_matrix.matrix, columns=backwards_difference_matrix.column_suffixes)
df.index += 1
df.loc[0] = np.zeros(len(values) - 1)
return df
# This corresponds to a parameterization that forces all the coefficients
# to sum to zero. Notice that the intercept here is the grand mean where the
# grand mean is the mean of means of the dependent variable by each level.
hsb2.groupby('race')['write'].mean().mean()
# ### Backward Difference Coding
# In backward difference coding, the mean of the dependent variable for a
# level is compared with the mean of the dependent variable for the prior
# level. This type of coding may be useful for a nominal or an ordinal
# variable.
from patsy.contrasts import Diff
contrast = Diff().code_without_intercept(levels)
print(contrast.matrix)
mod = ols("write ~ C(race, Diff)", data=hsb2)
res = mod.fit()
print(res.summary())
# For example, here the coefficient on level 1 is the mean of `write` at
# level 2 compared with the mean at level 1. Ie.,
res.params["C(race, Diff)[D.1]"]
hsb2.groupby('race').mean()["write"][2] - hsb2.groupby(
'race').mean()["write"][1]
# ### Helmert Coding
def contrasting():
global c
if c:
#to account for multiple contrast variables
contrastvars = []
if "," in c:
contrastvars = c.split(",")
for i in range(len(contrastvars)):
contrastvars[i] = contrastvars[i].strip()
if " " in contrastvars[i]:
contrastvars[i] = contrastvars[i].replace(" ", "_")
if "/" in contrastvars[i]: #to account for URLs
splitted = contrastvars[i].split("/")
contrastvars[i] = splitted[len(splitted) - 1]
else:
splitted = c.split("/") #to account for URLs
c = splitted[len(splitted) - 1]
ind_vars_no_contrast_var = ''
index = 1
for i in range(len(full_model_variable_list)):
if "/" in full_model_variable_list[i]:
splitted = full_model_variable_list[i].split("/")
full_model_variable_list[i] = splitted[len(splitted) - 1]
if " " in full_model_variable_list[i]:
full_model_variable_list[i] = full_model_variable_list[
i].replace(" ", "_")
for var in full_model_variable_list:
if var != c and not (var in contrastvars):
if index == 1:
ind_vars_no_contrast_var = var
index += 1
else:
ind_vars_no_contrast_var = ind_vars_no_contrast_var + " + " + var
if len(contrastvars) > 0:
contraststring = ' + '.join(contrastvars)
else:
if " " in c:
c = c.replace(" ", "_")
contraststring = c
# With contrast (treatment coding)
print(
"\n\nTreatment (Dummy) Coding: Dummy coding compares each level of the categorical variable to a base reference level. The base reference level is the value of the intercept."
)
ctrst = Treatment(reference=0).code_without_intercept(levels)
mod = ols(dep_var + " ~ " + ind_vars_no_contrast_var + " + C(" +
contraststring + ", Treatment)",
data=df_final)
res = mod.fit()
print("With contrast (treatment coding)")
print(res.summary())
if (o is not None):
# concatenate data frames
f = open(o, "a")
f.write("\n" + full_model)
f.write(
"\n\n***********************************************************************************************************"
)
f.write(
"\n\n\n\nTreatment (Dummy) Coding: Dummy coding compares each level of the categorical variable to a base reference level. The base reference level is the value of the intercept."
)
f.write("With contrast (treatment coding)")
f.write(res.summary().as_text())
f.close()
# Defining the Simple class
def _name_levels(prefix, levels):
return ["[%s%s]" % (prefix, level) for level in levels]
class Simple(object):
def _simple_contrast(self, levels):
nlevels = len(levels)
contr = -1. / nlevels * np.ones((nlevels, nlevels - 1))
contr[1:][np.diag_indices(nlevels -
1)] = (nlevels - 1.) / nlevels
return contr
def code_with_intercept(self, levels):
c = np.column_stack(
(np.ones(len(levels)), self._simple_contrast(levels)))
return ContrastMatrix(c, _name_levels("Simp.", levels))
def code_without_intercept(self, levels):
c = self._simple_contrast(levels)
return ContrastMatrix(c, _name_levels("Simp.", levels[:-1]))
ctrst = Simple().code_without_intercept(levels)
mod = ols(dep_var + " ~ " + ind_vars_no_contrast_var + " + C(" +
contraststring + ", Simple)",
data=df_final)
res = mod.fit()
print(
"\n\nSimple Coding: Like Treatment Coding, Simple Coding compares each level to a fixed reference level. However, with simple coding, the intercept is the grand mean of all the levels of the factors."
)
print(res.summary())
if (o is not None):
# concatenate data frames
f = open(o, "a")
f.write(
"\n\n\nSimple Coding: Like Treatment Coding, Simple Coding compares each level to a fixed reference level. However, with simple coding, the intercept is the grand mean of all the levels of the factors."
)
f.write(res.summary().as_text())
f.close()
#With contrast (sum/deviation coding)
ctrst = Sum().code_without_intercept(levels)
mod = ols(dep_var + " ~ " + ind_vars_no_contrast_var + " + C(" +
contraststring + ", Sum)",
data=df_final)
res = mod.fit()
print(
"\n\nSum (Deviation) Coding: Sum coding compares the mean of the dependent variable for a given level to the overall mean of the dependent variable over all the levels."
)
print(res.summary())
if (o is not None):
# concatenate data frames
f = open(o, "a")
f.write(
"\n\n\nSum (Deviation) Coding: Sum coding compares the mean of the dependent variable for a given level to the overall mean of the dependent variable over all the levels."
)
f.write(res.summary().as_text())
f.close()
#With contrast (backward difference coding)
ctrst = Diff().code_without_intercept(levels)
mod = ols(dep_var + " ~ " + ind_vars_no_contrast_var + " + C(" +
contraststring + ", Diff)",
data=df_final)
res = mod.fit()
print(
"\n\nBackward Difference Coding: In backward difference coding, the mean of the dependent variable for a level is compared with the mean of the dependent variable for the prior level."
)
print(res.summary())
if (o is not None):
# concatenate data frames
f = open(o, "a")
f.write(
"\n\n\nBackward Difference Coding: In backward difference coding, the mean of the dependent variable for a level is compared with the mean of the dependent variable for the prior level."
)
f.write(res.summary().as_text())
f.close()
#With contrast (Helmert coding)
ctrst = Helmert().code_without_intercept(levels)
mod = ols(dep_var + " ~ " + ind_vars_no_contrast_var + " + C(" +
contraststring + ", Helmert)",
data=df_final)
res = mod.fit()
print(
"\n\nHelmert Coding: Our version of Helmert coding is sometimes referred to as Reverse Helmert Coding. The mean of the dependent variable for a level is compared to the mean of the dependent variable over all previous levels. Hence, the name ‘reverse’ being sometimes applied to differentiate from forward Helmert coding."
)
print(res.summary())
if (o is not None):
# concatenate data frames
f = open(o, "a")
f.write(
"\n\n\nHelmert Coding: Our version of Helmert coding is sometimes referred to as Reverse Helmert Coding. The mean of the dependent variable for a level is compared to the mean of the dependent variable over all previous levels. Hence, the name ‘reverse’ being sometimes applied to differentiate from forward Helmert coding."
)
f.write(res.summary().as_text())
f.close()
