library(serosv)
Refer to Chapter 7.1
Proposed model
Within the local polynomial framework, the linear predictor η(a) is approximated locally at one particular value a0 for age by a line (local linear) or a parabola (local quadratic).
The estimator for the k-th derivative of η(a0), for k=0,1,…,p (degree of local polynomial) is as followed:
ˆη(k)(a0)=k!ˆβk(a0)
The estimator for the prevalence at age a0 is then given by
ˆπ(a0)=g−1{ˆβ0(a0)}
The estimator for the force of infection at age a0 by assuming p≥1 is as followed
ˆλ(a0)=ˆβ1(a0)δ{ˆβ0(a0)}
Fitting data
<- mumps_uk_1986_1987
mump <- mump$age
age <- mump$pos
pos <- mump$tot
tot <- pos/tot y
Use plot_gcv()
to show GCV curves for the nearest
neighbor method (left) and constant bandwidth (right).
plot_gcv(
age, pos, tot,nn_seq = seq(0.2, 0.8, by=0.1),
h_seq = seq(5, 25, by=1)
)
Use lp_model()
to fit a local estimation by
polynomials.
<- lp_model(age, pos = pos, tot = tot, kern="tcub", nn=0.7, deg=2)
lp plot(lp)