Adding missing MLE file

Author: gvegayon

src/pydefm/defm_mle.py

@@ -0,0 +1,57 @@
+from scipy.optimize import minimize
+import numpy as np
+
+# Function to print an array using two digits
+def print_array(arr):
+  return "[" + ", ".join([f"{'' if x < 0 else ' '}{x:.2f}" for x in arr]) + "]"
+
+class defm_mle_fit:
+  """
+  Represents the result of a Maximum Likelihood Estimation (MLE) fit in the DEFM model.
+
+  Attributes:
+    par (list): The estimated parameter values.
+    or_ (list): The odds ratios corresponding to the estimated parameter values.
+    se (list): The standard errors of the estimated parameter values.
+    ll (float): The log-likelihood value of the fit.
+    optimres (object): The optimization result object containing additional information.
+  """
+
+  def __init__(self, par, or_, se, ll, optimres):
+    self.par = par
+    self.or_ = or_
+    self.se = se
+    self.ll = ll
+    self.optimres = optimres
+
+  def __str__(self):
+    return f"defm_mle_fit\n\tpar =" + \
+      print_array(self.par) + \
+      ",\n\tor  =" + \
+      print_array(self.or_) + \
+      ",\n\tse  ="+ \
+      print_array(self.se) + \
+      f"\n\tll  ={self.ll: .2f}"
+
+def defm_mle(obj, par):
+  """
+  Maximum Likelihood Estimation using the defm method.
+
+  Parameters:
+  obj (object): The object containing the likelihood function.
+  par (array-like): The initial parameter values.
+
+  Returns:
+  defm_mle_fit: An instance of the defm_mle_fit class containing the estimated parameters, odds ratios, standard errors, log-likelihood value, and optimization results.
+  """
+  def ll(par):
+    return -obj.likelihood(par, as_log=True)
+
+  res = minimize(ll, par)
+  return defm_mle_fit(
+    par=res.x,
+    or_=np.exp(res.x),
+    se=np.sqrt(np.diag(res.hess_inv)),
+    ll=-res.fun,
+    optimres=res
+  )