def fit_logistic(X_hold,Y_hold,Firth=False,resBase=None,LRtest=True):
"""
Fits a logistic regression model using standard (when Firth = False) or Firth's method (when Firth = True).
resBase is the result of a previous call to a regression that is used to store data for Firth's method.
LRtest indicates if the likelihood ratio test should be reported.
"""
if not Firth:
res = GLM(Y_hold, X_hold, family=families.Binomial()).fit()#XXX Confirm this with logistic using older XXXX
# AICc adjustment
res.aicc = statsmodels.tools.eval_measures.aicc(res.llf, nobs=res.nobs, df_modelwc=res.df_model+1)
# Correct BIC
res.bic = statsmodels.tools.eval_measures.bic(res.llf, nobs=res.nobs, df_modelwc=res.df_model+1)
else:
if resBase is None:
sys.stderr.write('resBase must be provided to do Firth regression\n')
sys.exit(1)
elif type(resBase) is not statsmodels.genmod.generalized_linear_model.GLMResultsWrapper:
sys.stderr.write('resBase must be type statsmodels.genmod.generalized_linear_model.GLMResultsWrapper\n')
sys.exit(2)
else:
res = resBase
#Do Firth's logistic regression
(rint, rbeta, rbse, rfitll, pi) = fit_firth(Y_hold, X_hold, start_vec = None)
if LRtest:
# LRT
null_X = np.delete(arr=X_hold,obj=range(int(np.size(X_hold)/len(X_hold)))[1:int(np.size(X_hold)/len(X_hold))],axis=1)
(null_intercept, null_beta, null_bse, null_fitll, null_pi) = fit_firth(Y_hold, null_X, start_vec = None)
lrstat = -2.*(null_fitll - rfitll)
lrt_pvalue = 1.
if lrstat > 0.: # non-convergence
lrt_pvalue = stats.chi2.sf(lrstat, 1)
res.llnull = null_fitll
res.lrstat = lrstat
res.lrt_pval = lrt_pvalue
# AICc adjustment for Firth model
aicc = statsmodels.tools.eval_measures.aicc(rfitll, nobs=len(Y_hold), df_modelwc=np.shape(X_hold)[1])
# AIC
aic = statsmodels.tools.eval_measures.aic(rfitll, nobs=len(Y_hold), df_modelwc=np.shape(X_hold)[1])
# BIC
bic = statsmodels.tools.eval_measures.bic(rfitll, nobs=len(Y_hold), df_modelwc=np.shape(X_hold)[1])
#Store parameters, standard errors, likelihoods, and statistics
rint = np.array([rint])
rbeta = np.array(rbeta)
res.params = np.concatenate([rint,rbeta])
res.bse = rbse
res.llf = rfitll
res.aicc = aicc
res.aic = aic
res.bic = bic
#Get Wald p vals for parameters
res.pvalues = 1. - chi2.cdf(x=(res.params/res.bse)**2, df=1)
#Add predicted y
res.predict = pi
return res
def iterate_logistic(X_hold,Y_hold, fixed_columns = [0], Firth=False):
"""
Fits logistic regression to the provided data while using the fixed_columns in the regression.
Firth specifies if Firth regression should be used.
Returns matrices of fitted betas, pvalues, aic, aicc (second order aic), and bic
"""
l = np.size(fixed_columns)+1
k = np.shape(X_hold)[1]
betas = np.zeros([k,l])
pvalues = np.zeros([k,l])
aic = np.zeros([k,1])
aicc = np.zeros([k,1])
bic = np.zeros([k,1])
# Fit constant
if Firth:
null_X = np.delete(arr=X_hold,obj=range(int(np.size(X_hold)/len(X_hold)))[1:int(np.size(X_hold)/len(X_hold))],axis=1)
(null_intercept, null_beta, null_bse, null_fitll, null_pi) = fit_firth(Y_hold, null_X, start_vec = None)
#Using this as a way to return a model in the same class as GLM.
res = GLM(Y_hold, null_X, family=families.Binomial()).fit()
# AICc adjustment for Firth model
res.aicc = statsmodels.tools.eval_measures.aicc(null_fitll, nobs=res.nobs, df_modelwc=res.df_model+1)
# AIC
res.aic = statsmodels.tools.eval_measures.aic(null_fitll, nobs=res.nobs, df_modelwc=res.df_model+1)
# BIC
res.bic = statsmodels.tools.eval_measures.bic(null_fitll, nobs=res.nobs, df_modelwc=res.df_model+1)
#Store parameters, standard errors, likelihoods, and statistics
res.params = np.array([null_intercept])
#Get Wald p vals for parameters
res.pvalues = 1. - chi2.cdf(x=(res.params/null_bse)**2, df=1)
else:
res = fit_logistic(X_hold[:,0],Y_hold)
betas[0,:] = res.params
pvalues[0,:] = res.pvalues
aic[0] = res.aic
aicc[0] = res.aicc
bic[0] = res.bic
#Set variable for use later
resBase = copy.deepcopy(res)
NAN = ~np.isnan(X_hold).any(axis=0)
for i in range(1,k):
if NAN[i]:
if i not in fixed_columns:
columns = fixed_columns.copy()
columns.append(i)
res = fit_logistic(X_hold[:,columns],Y_hold, Firth=Firth, resBase=resBase,LRtest=False)
betas[i,:] = res.params
pvalues[i,:] = res.pvalues
aic[i] = res.aic
aicc[i] = res.aicc
bic[i] = res.bic
return betas, pvalues,aic,aicc,bic