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.

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.

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
#> Nonlinear regression model
#>   model: y ~ a * x/(b + x)
#>    data: parent.frame()
#>      a      b
#> 14.461  9.311
#>  residual sum-of-squares: 560.6
#>
#> Number of iterations to convergence: 4
#> Achieved convergence tolerance: 3.99e-06
(biased_sample<-nls(y~a*x/(b+x),data=sdf, start=c(a=15,b=5)))
#> Nonlinear regression model
#>   model: y ~ a * x/(b + x)
#>    data: sdf
#>     a     b
#> 16.35 13.74
#>  residual sum-of-squares: 105.7
#>
#> Number of iterations to convergence: 5
#> Achieved convergence tolerance: 5.098e-07
(corrected <- svynls(y~a*x/(b+x), design=des, start=c(a=15,b=5)))
#> Nonlinear survey regression model
#>   model: y ~ a * x/(b + x)
#>  design: Stratified Independent Sampling design (with replacement)
#> svydesign(id = ~1, strata = ~strata, prob = ~p, data = sdf)
#>      a      b
#> 14.453  9.569
#>  weighted residual sum-of-squares: 556.7