def fit(self, framework='GLM', Quasi=False):
"""
Method that fits a particular count model usign the appropriate
estimation technique. Models include Poisson GLM, Negative Binomial GLM,
Quasi-Poisson - at the moment Poisson GLM is the only option.
TODO: add zero inflated variants and hurdle variants.
Parameters
----------
framework : string
estimation framework; default is GLM
"GLM" | "QUASI" |
"""
if (framework.lower() == 'glm'):
if not Quasi:
results = GLM(self.y,
self.X,
family=Poisson(),
constant=self.constant).fit()
else:
results = GLM(self.y,
self.X,
family=QuasiPoisson(),
constant=self.constant).fit()
return CountModelResults(results)
else:
raise NotImplemented(
'Poisson GLM is the only count model currently implemented')
def __init__(self,
coords,
y,
X,
bw,
family=Gaussian(),
offset=None,
sigma2_v1=False,
kernel='bisquare',
fixed=False,
constant=True):
"""
Initialize class
"""
GLM.__init__(self, y, X, family, constant=constant)
self.constant = constant
self.sigma2_v1 = sigma2_v1
self.coords = coords
self.bw = bw
self.kernel = kernel
self.fixed = fixed
if offset is None:
self.offset = np.ones((self.n, 1))
else:
self.offset = offset * 1.0
self.fit_params = {}
self.W = self._build_W(fixed, kernel, coords, bw)
self.points = None
self.exog_scale = None
self.exog_resid = None
self.P = None
def summaryGLM(self):
XNames = ["X"+str(i) for i in range(self.k)]
glm_rslt = GLM(self.model.y,self.model.X,constant=False,family=self.family).fit()
summary = "%s\n" %('Global Regression Results')
summary += '-' * 75 + '\n'
if isinstance(self.family, Gaussian):
summary += "%-62s %12.3f\n" % ('Residual sum of squares:', glm_rslt.deviance)
summary += "%-62s %12.3f\n" % ('Log-likelihood:', glm_rslt.llf)
summary += "%-62s %12.3f\n" % ('AIC:', glm_rslt.aic)
summary += "%-62s %12.3f\n" % ('AICc:', get_AICc(glm_rslt))
summary += "%-62s %12.3f\n" % ('BIC:', glm_rslt.bic)
summary += "%-62s %12.3f\n" % ('R2:', glm_rslt.D2)
summary += "%-62s %12.3f\n\n" % ('Adj. R2:', glm_rslt.adj_D2)
else:
summary += "%-62s %12.3f\n" % ('Deviance:', glm_rslt.deviance)
summary += "%-62s %12.3f\n" % ('Log-likelihood:', glm_rslt.llf)
summary += "%-62s %12.3f\n" % ('AIC:', glm_rslt.aic)
summary += "%-62s %12.3f\n" % ('AICc:', get_AICc(glm_rslt))
summary += "%-62s %12.3f\n" % ('BIC:', glm_rslt.bic)
summary += "%-62s %12.3f\n" % ('Percent deviance explained:', glm_rslt.D2)
summary += "%-62s %12.3f\n\n" % ('Adj. percent deviance explained:', glm_rslt.adj_D2)
summary += "%-31s %10s %10s %10s %10s\n" % ('Variable', 'Est.', 'SE' ,'t(Est/SE)', 'p-value')
summary += "%-31s %10s %10s %10s %10s\n" % ('-'*31, '-'*10 ,'-'*10, '-'*10,'-'*10)
for i in range(self.k):
summary += "%-31s %10.3f %10.3f %10.3f %10.3f\n" % (XNames[i], glm_rslt.params[i], glm_rslt.bse[i], glm_rslt.tvalues[i], glm_rslt.pvalues[i])
summary += "\n"
return summary
def alpha_disp(model, alt_var=lambda x: x):
"""
Test the hypothesis that var[y] = mu (equidispersion) against the
alternative hypothesis that var[y] = mu + alpha * alt_var(mu) where mu
is the expected value of y, alpha is an estimated coefficient, and
alt_var() specifies an alternative variance as a function of mu.
alt_var=lambda x:x corresponds to an alternative hypothesis of a negative
binomimal model with a linear variance function and alt_var=lambda
x:x**2 correspinds to an alternative hypothesis of a negative binomial
model with a quadratic varaince function.
alpha > 0: overdispersion
alpha = 1: equidispersion
alpha < 0: underdispersion
Parameters
----------
model : Model results class
function can only be called on a sucessfully fitted model
which has a valid response variable, y, and a valid
predicted response variable, yhat.
alt_var : function
specifies an alternative varaince as a function of mu.
Function must take a single scalar as input and return a
single scalar as output
Returns
-------
array : [alpha coefficient, tvalue of alpha, pvalue of alpha]
"""
try:
y = model.y.reshape((-1, 1))
yhat = model.yhat.reshape((-1, 1))
ytest = (((y - yhat)**2 - y) / yhat).reshape((-1, 1))
except:
raise AttributeError(
"Make sure model passed has been estimated and has a valid 'y' and 'yhat' attribute"
)
if isinstance(alt_var, FunctionType):
X = (alt_var(yhat) / yhat).reshape((-1, 1))
test_results = GLM(ytest, X, constant=False).fit()
alpha = test_results.params[0]
zval = test_results.tvalues[0]
pval = stats.norm.sf(zval)
else:
raise TypeError(
"The alternative variance function, 'alt_var', must be a valid function'"
)
return np.array([alpha, zval, pval])