Loglikelihood for negative binomial model
Parameters: | params : array-like
The parameters of the model. If loglike_method is nb1 or
nb2, then the ancillary parameter is expected to be the
last element.
|
Returns: | llf : float
The loglikelihood value at params
|
Notes
Following notation in Greene (2008), with negative binomial
heterogeneity parameter
System Message: WARNING/2 (\alpha)
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:
System Message: WARNING/2 (\lambda_i &= exp(X\beta) \\
\theta &= 1 / \alpha \\
g_i &= \theta \lambda_i^Q \\
w_i &= g_i/(g_i + \lambda_i) \\
r_i &= \theta / (\theta+\lambda_i) \\
ln \mathcal{L}_i &= ln \Gamma(y_i+g_i) - ln \Gamma(1+y_i) + g_iln (r_i) + y_i ln(1-r_i))
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where :math`Q=0` for NB2 and geometric and
System Message: WARNING/2 (Q=1)
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for NB1.
For the geometric,
System Message: WARNING/2 (\alpha=0)
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This is pdfTeX, Version 3.14159265-2.6-1.40.15 (TeX Live 2014) (preloaded format=latex)
restricted \write18 enabled.
entering extended mode
(./math.tex
LaTeX2e <2011/06/27>
Babel <3.9k> and hyphenation patterns for 2 languages loaded.
(/usr/share/texlive/texmf-dist/tex/latex/base/article.cls
Document Class: article 2007/10/19 v1.4h Standard LaTeX document class
(/usr/share/texlive/texmf-dist/tex/latex/base/size12.clo))
(/usr/share/texlive/texmf-dist/tex/latex/base/inputenc.sty
! LaTeX Error: File `utf8x.def’ not found.
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l.131 \endinput
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No pages of output.
Transcript written on math.log.
as well.