logLikStrat {StratSel}

Log-Likelihood Function of an Agent Error Model

Description

This function calculates the log-likelihood value for an agent error model (belongs to the general class of quantal response models). The underlying formal structure is

       1 
      /\  
     /  \  
    /    \ 2  
   u11   /\  
        /  \  
       /    \  
      0     u14  
      0     u24  

and shows a game where there are two players which move sequentially. Player 1 decides to move left or right and if she does move right player 2 gets to move. The final outcome in this case depends on the move of player 2.

Usage

logLikStrat(x11, x14, x24, y, beta)

Arguments

x11

A vector or a matrix containing the explanatory variables used to parametrize u11.

x14

A vector or a matrix containing the explanatory variables used to parametrize u14.

x24

A vector or a matrix containing the explanatory variables used to parametrize u24.

y

Vector. Outcome variable which can take values 1, 3, and 4 depending on which outcome occurred.

beta

Vector. Coefficients of the model.

Details

This function provides the likelihood of an agent error model (Signorino, 2003). Note, that to derive it one assumes that the two errors are independent. Further, as with probit and logit models, one needs to assume an error variance to achieve identification. Signorino uses \sqrt 2 while logLikStrat uses 1. Hence, the numeric results will differ, but all relevant statistics (predicted probabilities, z-values, ...) will be identical. Finally, u13 and u23 are set to 0 to achieve identification.

Value

Returns a numeric value for the log-likelihood function evaluated for \beta.

Note

The log-likelihood function:

\ell\ell = \sum_{i=1}^n \left(\log(p_{i1})\cdot I(Y_{i}=1) + \log((1-p_{i1})(1-p_{i4}))\cdot I(Y_{i}=3) + \log((1-p_{i1})(p_{i4}))\cdot I(Y_{i}=4) \right)

whereas

p_{i24} = \Phi(x_{24}\cdot\beta_{24})

and

p_{i1} = \Phi(x_{11}\cdot\beta_{11}-p_{24}(x_{14}\cdot\beta_{14}))

Author(s)

Lucas Leemann [e-mail]

References

Curtis S. Signorino. 2003. "Structure and Uncertainty in Discrete Choice Models." Political Analysis 11:316–344.

See Also

StratSel