6.2. Development of model and statistical technique

, (6.1)

and in the simplest case, r_i is determined by a multiple linear function of the covariates and 's:

. (6.2)

Alternatively, the covariates and 's may be incorporated in mechanistic functions motivated by salmon biology.

If t_i is the observed arrival time of the ith individual, the likelihood function is:

. (6.3)

The parameters can be determined by maximizing the log likelihood function,

, (6.4)

with respect to . This is performed numerically using the downhill simplex method (Nelder and Mead, 1965; Press, et al., 1988).

To analyze the importance of each covariate, I construct a sequence of nested models beginning with the simplest model that contains only the intercept term to the fullest model with all the covariates. The covariates are added one at a time. For each alternative model, parameters are estimated, and likelihoods are computed. The importance of each additional covariate (in the form that it is included in the model) is assessed by comparing the likelihoods and BIC values of alternative models.