The two indices GC and E are characterized by a constant weighting function, which equals 1 for GC and (frac {4}{b_{h}-a_{h}}) for E. The other indices C and W have weighting functions that are functions of the mean health, and therefore also functions of the predictors of health.
An additional flexibility can be achieved if not only the mean μ i but also the dispersion parameter ϕ i is estimated as a function of the predictor variables by employing a second linear predictor (Eq. 2b).
We further investigated estimating α as a function of the predictor variables in the models (i.e., α0 + α1 x i ); however, no improvements in model fit or biologically meaningful values of α were noted.
To cope with that, a new root system biomass model form was obtained as a function of the predictor variables of the best taproot and lateral roots biomass model forms.
The logistic regression model defines a linear function of the predictor variables, and then estimates the probability of the target variable L̂ using the logit transformation: begin{aligned}& phi (c_{1}, c_{2}, ldots, c_{n}) = beta_{0}+beta_{1} c_{1}+beta_{2} c_{2}+cdots+beta_{n} c_{n}, & P hat{L}vert c_{1}, c_{2}, ldots, c_{n}) = frac{1}{1+e^{-phi }}.
We assumed that the probability of infant death in a given month was a logistic function
For both types of models the response variable was restricted to 0.0 1.0 (all possible RIC values) using the logit transformation of the mean [51], and modeled it as a linear function of the predictor for the GLM model and as cubic splines for the GAM model.
We used generalized semi-parametric Poisson regression to model the natural logarithm of the expected daily death counts as a function of the predictor variables.
We, therefore, used a special case of the linear mixed model to explore residual variance as a multiplicative linear function of the predictor variables (Harvey 1976; Guierrez 2008).
