def add_interaction_formula(interaction1, interaction2):
return paste(
[
f"{i} * {j}"
for i, j in itertools.product(interaction1, interaction2)
],
collapse=" + ",
)
def add_poly(df, col, degree, inplace=False):
if not inplace:
df = df.copy(deep=True)
formula = [col]
for i in range(2, degree + 1):
col_name = f"{col}^{i}"
df[col_name] = df[col]**i
formula.append(col_name)
return df, paste(formula, collapse=" + ")
def add_poly_formula(col, degree):
return paste([col] + [f"I({col} ** {i})" for i in range(2, degree + 1)],
collapse=" + ")
def test_paste():
a = "beta"
b = ["a", "b", "c"]
c = range(5)
expect = ["beta.a.0", "beta.b.1", "beta.c.2", "beta.a.3", "beta.b.4"]
assert paste(a, b, c, sep=".") == expect
def statistics_coefficient(all_N, all_T, nsims, df_sim_result, **beta_true):
"""
Generate statistics of each N & T, take the mean of different simulations, and
store them in a data frame. We include mean, bias, the RMSE, standard error and
cofidence interval in our statistical results.
Parameters
----------
all_N : array-like
Different sample sizes of entity
all_T : array-like
Different sample sizes of time
nsims : int
Simulation times under the same N and T
df_sim_result : DataFrame
Simulation results from function `simulation_coefficient`
beta_true : float
Coefficients of variables used in dgp_func. Values in ("beta1", "beta2", "mu",
"gamma", "delta")
"""
# vectorize startswith() to apply it in a string list
startswith_vec = np.vectorize(str.startswith)
# guess number of variables from column names
p = sum(startswith_vec(df_sim_result.columns, "beta_interactive."))
assert len(beta_true) >= p, "short of beta_true"
beta_true_list = [
beta_true[k]
for k in ("beta1", "beta2", "mu", "gamma", "delta")
if k in beta_true
][:p]
df_statistic = pd.DataFrame(
index=range(len(all_N)),
columns=[
"T",
"N",
*paste("mean_interactive", range(1, p + 1), sep="."),
*paste("bias_interactive", range(1, p + 1), sep="."),
*paste("sde_interactive", range(1, p + 1), sep="."),
*paste("ci_l_interactive", range(1, p + 1), sep="."),
*paste("ci_u_interactive", range(1, p + 1), sep="."),
*paste("rmse_interactive", range(1, p + 1), sep="."),
*paste("mean_within", range(1, p + 1), sep="."),
*paste("bias_within", range(1, p + 1), sep="."),
*paste("sde_within", range(1, p + 1), sep="."),
*paste("ci_l_within", range(1, p + 1), sep="."),
*paste("ci_u_within", range(1, p + 1), sep="."),
*paste("rmse_within", range(1, p + 1), sep="."),
],
)
# three quick function to get and modify df_statistic and df_sim_result
def get_stat(col):
return df_statistic.iloc[i, startswith_vec(df_statistic.columns, col)]
def get_sim(col):
return df_sim_result.iloc[
row_range_df_sim, startswith_vec(df_sim_result.columns, col)
]
def set_stat(col, value):
df_statistic.iloc[i, startswith_vec(df_statistic.columns, col)] = value
for i in range(len(all_N)):
df_statistic.loc[i, "N"] = all_N[i]
df_statistic.loc[i, "T"] = all_T[i]
row_range_df_sim = range(i * nsims, (i + 1) * nsims)
set_stat("mean_interactive", get_sim("beta_interactive").mean())
set_stat("mean_within", get_sim("beta_within").mean())
set_stat(
"bias_interactive",
get_stat("mean_interactive").sub(beta_true_list).abs().div(beta_true_list),
)
set_stat(
"bias_within",
get_stat("mean_within").sub(beta_true_list).abs().div(beta_true_list),
)
if not np.isnan(get_sim("sde_interactive")).all(axis=None, skipna=False):
set_stat("sde_interactive", get_sim("sde_interactive").mean())
set_stat(
"ci_l_interactive",
get_stat("mean_interactive").sub(
get_stat("sde_interactive").mul(norm.ppf(0.975)).values
),
)
set_stat(
"ci_u_interactive",
get_stat("mean_interactive").add(
get_stat("sde_interactive").mul(norm.ppf(0.975)).values
),
)
set_stat("sde_within", get_sim("sde_within").mean())
set_stat(
"ci_l_within",
get_stat("mean_within").sub(
get_stat("sde_within").mul(norm.ppf(0.975)).values
),
)
set_stat(
"ci_u_within",
get_stat("mean_within").add(
get_stat("sde_within").mul(norm.ppf(0.975)).values
),
)
set_stat(
"rmse_interactive",
caculate_rmse(get_sim("beta_interactive"), beta_true_list),
)
set_stat("rmse_within", caculate_rmse(get_sim("beta_within"), beta_true_list))
return df_statistic
sde_interactive = np.sqrt(np.diag(sde_interactive))
else:
sde_interactive = np.full(shape=(p), fill_value=np.nan)
one_sim_result = pd.Series(
[
*T_N_sim.loc[case, ["T", "N", "sim"]],
*beta_hat_interactive,
*beta_hat_within,
*sde_interactive,
*sde_within,
],
index=[
"T",
"N",
"sim",
*paste("beta_interactive", range(1, p + 1), sep="."),
*paste("beta_within", range(1, p + 1), sep="."),
*paste("sde_interactive", range(1, p + 1), sep="."),
*paste("sde_within", range(1, p + 1), sep="."),
],
)
return one_sim_result
def statistics_coefficient(all_N, all_T, nsims, df_sim_result, **beta_true):
"""
Generate statistics of each N & T, take the mean of different simulations, and
store them in a data frame. We include mean, bias, the RMSE, standard error and
cofidence interval in our statistical results.
Parameters