# Log likelihood¶

Shortcuts for log likelihood functions

## biogeme.loglikelihood module¶

Functions to calculate the log likelihood

author

Michel Bierlaire

date

Fri Mar 29 17:11:44 2019

biogeme.loglikelihood.likelihoodregression(meas, model, sigma)[source]

Computes likelihood function of a regression model.

Parameters
Returns

The likelihood of the regression, assuming a normal distribution, that is

$\frac{1}{\sigma} \phi\left( \frac{y-m}{\sigma} \right)$

where $$\phi(\cdot)$$ is the pdf of the normal distribution.

Return type

biogeme.expressions.Expression

biogeme.loglikelihood.loglikelihood(prob)[source]

Simply computes the log of the probability

Parameters

prob (biogeme.expressions.Expression) – An expression providing the value of the probability.

Returns

the logarithm of the probability.

Return type

biogeme.expressions.Expression

biogeme.loglikelihood.loglikelihoodregression(meas, model, sigma)[source]

Computes log likelihood function of a regression model.

Parameters
Returns

the likelihood of the regression, assuming a normal distribution, that is

$-\left( \frac{(y-m)^2}{2\sigma^2} \right) - \log(\sigma) - \frac{1}{2}\log(2\pi)$
Return type

biogeme.expressions.Expression

biogeme.loglikelihood.mixedloglikelihood(prob)[source]

Compute a simulated loglikelihood function

Parameters

prob – An expression providing the value of the probability. Although it is not formally necessary, the expression should contain one or more random variables of a given distribution, and therefore is defined as

$P(i|\xi_1,\ldots,\xi_L)$
Returns

the simulated loglikelihood, given by

$\ln\left(\sum_{r=1}^R P(i|\xi^r_1,\ldots,\xi^r_L) \right)$

where $$R$$ is the number of draws, and $$\xi_j^r$$ is the rth draw of the random variable $$\xi_j$$.

Return type

biogeme.expressions.Expression