def pooled(df,
yvar,
xvar,
groupvar,
model='probit',
cov_type='sandwich',
theta0=0,
deriv=2):
print('Pooled', model)
Nobs, k, n, T, y, x = panel_setup(df, yvar, xvar, groupvar)
Qfun = lambda beta, out: Q_pooled(y, x, T, beta, model, out)
if np.isscalar(theta0):
theta0 = np.zeros((k + 1, 1))
res = M.estimation(Qfun,
theta0=np.zeros((k, 1)),
deriv=deriv,
cov_type=cov_type,
parnames=xvar)
xb, Gx, gx = Qfun(res.theta_hat, out='predict')
APE = np.mean(gx) * res.theta_hat
res.update(
dict(
zip(['yvar', 'xvar', 'Nobs', 'k', 'n', 'T', 'APE'],
[yvar, xvar, Nobs, k, n, T, APE])))
print_output(res)
return res
def rand_effect(df,
yvar,
xvar,
groupvar,
model='probit',
cov_type='Ainv',
theta0=0,
deriv=1):
print('Random effects', model)
Nobs, k, n, T, y, x = panel_setup(df, yvar, xvar, groupvar)
Qfun = lambda beta, out: Q_RE(y, x, T, beta, model, out)
if np.isscalar(theta0):
theta0 = np.zeros((k + 1, 1))
theta0[-1] = 1
res = M.estimation(Qfun,
theta0,
deriv=deriv,
cov_type=cov_type,
parnames=xvar + ['sigma_a'])
res.sigma_a = res.theta_hat[-1]
xb, Gx, gx = Qfun(res.theta_hat / np.sqrt(1 + res.sigma_a**2),
out='predict')
APE = np.mean(gx) * res.theta_hat / np.sqrt(1 + res.sigma_a**2)
res.update(
dict(
zip(['yvar', 'xvar', 'Nobs', 'k', 'n', 'T', 'APE'],
[yvar, xvar, Nobs, k, n, T, APE])))
print_output(res,
['parnames', 'theta_hat', 'se', 't-values', 'jac', 'APE'])
return res
def clogit(y, x, cov_type='Ainv', theta0=None, deriv=0, quiet=False):
# Objective function and derivatives for
N, J, K, palt, xalt, xvars = labels(x)
Qfun = lambda theta, out: Q_clogit(theta, y, x, out)
if theta0 is None:
theta0 = np.zeros((K, 1))
res = M.estimation(Qfun, theta0, deriv, cov_type, parnames=xvars)
# v, p, dv = Qfun(res.theta_hat, out='predict')
res.update(
dict(zip(['yvar', 'xvars', 'N', 'K', 'n'], ['y', xvars, N, K, N])))
if quiet == False:
print('Conditional logit')
print('Initial log-likelihood', -Qfun(theta0, 'Q'))
print('Initial gradient\n', -Qfun(theta0, 'dQ'))
print_output(res)
return res
def tobit(y, x, cov_type='Ainv', theta0=None, deriv=1, quiet=False):
# Objective function and derivatives for
Qfun = lambda theta, out: Q_tobit(theta, y, x, out)
N, K, xvars = labels(x)
if theta0 is None:
theta0 = np.zeros((K + 1, 1))
b = la.inv(x.T @ x) @ x.T @ y
theta0[0:-1, :] = b
theta0[-1, :] = np.sqrt(np.mean((y - x @ b)**2))
res = M.estimation(Qfun, theta0, deriv, cov_type, parnames=xvars)
res.update(
dict(zip(['yvar', 'xvars', 'N', 'K', 'n'], ['y', xvars, N, K, N])))
if quiet == False:
print('Tobit model')
print('Fractions of observations that are censored: ',
np.mean(1 * (y == 0)))
print('Initial log-likelihood', -Qfun(theta0, 'Q'))
print('Initial gradient\n', -Qfun(theta0, 'dQ'))
print_output(res)
return res