svynls {survey}

Probability-weighted nonlinear least squares

Description

Fits a nonlinear model by probability-weighted least squares. Uses nls to do the fitting, but estimates design-based standard errors with either linearisation or replicate weights. See nls for documentation of model specification and fitting.

Usage

svynls(formula, design, start, weights=NULL, ...)

Arguments

formula

Nonlinear model specified as a formula; see nls

design

Survey design object

start

starting values, passed to nls

weights

Non-sampling weights, eg precision weights to give more efficient estimation in the presence of heteroscedasticity.

...

Other arguments to nls (especially, start). Also supports return.replicates for replicate-weight designs and influence for other designs.

Value

Object of class svynls. The fitted nls object is included as the fit element.

See Also

svymle for maximum likelihood with linear predictors on one or more parameters

Examples

set.seed(2020-4-3)
x<-rep(seq(0,50,1),10)
y<-((runif(1,10,20)*x)/(runif(1,0,10)+x))+rnorm(510,0,1)

pop_model<-nls(y~a*x/(b+x), start=c(a=15,b=5))

df<-data.frame(x=x,y=y)
df$p<-ifelse((y-fitted(pop_model))*(x-mean(x))>0, .4,.1)

df$strata<-ifelse(df$p==.4,"a","b")

in_sample<-stratsample(df$strata, round(table(df$strat)*c(0.4,0.1)))

sdf<-df[in_sample,]
des<-svydesign(id=~1, strata=~strata, prob=~p, data=sdf)
pop_model
(biased_sample<-nls(y~a*x/(b+x),data=sdf, start=c(a=15,b=5)))
(corrected <- svynls(y~a*x/(b+x), design=des, start=c(a=15,b=5)))