Table 1.

Definitions of the Model Parameters Used in an Application of the CDDmlr Method to Test the Wilcox-Russell Hypothesis With Respect to Maternal Age, New York State, 1985–1988

Symbol	Definition
Birth weight density submodel parameters for the i subpopulation ($i=s$ and p)a
${\text{π}}_s(t)$	Mixing proportion (% secondary subpopulation)
${\text{α}}_0$	Constant in $\text{logit}[{\text{π}}_s(t)]$
${\text{α}}_1$	Linear term in $\text{logit}[{\text{π}}_s(t)]$
${\text{α}}_2$	Square term in $\text{logit}[{\text{π}}_s(t)]$
${\text{μ}}_i(t)$	Mean birth weight
${\text{γ}}_{i,0}$	Constant in ${\text{μ}}_i(t)$
${\text{γ}}_{i,1}$	Linear term in ${\text{μ}}_i(t)$
${\text{γ}}_{i,2}$	Square term in ${\text{μ}}_i(t)$
${\text{σ}}_i(t)$	Standard deviation of birth weight
${\text{λ}}_{i,0}$	Constant in ${\text{σ}}_i(t)$
${\text{λ}}_{i,1}$	Linear term in ${\text{σ}}_i(t)$
${\text{λ}}_{i,2}$	Square term in ${\text{σ}}_i(t)$
Conditional mortality submodel parameters for the i subpopulation ($i=s$ and p)b
$a_{i,z}$	Constant
$b_{i,z}$	Linear term for standardized birth weight (z)
$c_{i,z}$	Square term for z
$b_{i,t}$	Linear term for maternal age (t)
$c_{i,t}$	Square term for t
$d_i$	Interaction term for z and t

Abbreviation: CDDmlr, covariate density defined mixture of logistic regressions.

^aCoefficients of a nonlinear function of a continuous exogenous covariate t.

^bCoefficients of a second-degree bivariate polynomial function.