Probability-weighted nonlinear least squares

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.

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
#> 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