Nonlinear regression with sampling weights (package survey) - r

Question

I would like to estimate the coefficients of a nonlinear model with a binary dependent variable. The nonlinearity arises because two regressors, A and B, depend on a subset of the dataset and on the two parameters lambda1 and lambda2 respectively:
y = alpha + beta1 * A(lambda1) + beta2 * B(lambda2) + delta * X + epsilon
where for each observation i, we have
Where a and Rs are variables in the data.frame. The regressor B(lambda2) is defined in a similar way.
Moreover, I need to include what in Stata are known as pweights, i.e. survey weights or sampling weights. For this reason, I'm working with the R package survey by Thomas Lumley.
First, I create a function for A (and B), i.e.:
A <- function(l1){
R <- as.matrix(data[,1:(80)])
a <- data[,169]
N = length(a)
var <- numeric(N)
for (i in 1:N) {
ai <- rep(a[i],a[i]-1) # vector of a(i)
k <- 1:(a[i]-1) # numbers from 1 to a(i)-1
num <- (ai-k)^l1
den <- sum((ai-k)^l1)
w <- num/den
w <- c(w,rep(0,dim(R)[2]-length(w)))
var[i] <- R[i,] %*% w
}
return(var)
}
B <- function(l2){
C <- as.matrix(data[,82:(161-1)])
a <- data[,169]
N = length(a)
var <- numeric(N)
for (i in 1:N) {
ai <- rep(a[i],a[i]-1) # vector of a(i)
k <- 1:(a[i]-1) # numbers from 1 to a(i)-1
num <- (ai-k)^l2
den <- sum((ai-k)^l2)
w <- num/den
w <- c(w,rep(0,dim(C)[2]-length(w)))
var[i] <- C[i,] %*% w
}
return(var)
}
But the problem is that I don't know how to include the nonlinear regressors in the model (or in the survey design, using the function svydesign):
d_test <- svydesign(id=~1, data = data, weights = ~data$hw0010)
Because, when I try to estimate the model:
# loglikelihood function:
LLsvy <- function(y, model, lambda1, lambda2){
aux1 <- y * log(pnorm(model))
aux2 <- (1-y) * log(1-pnorm(model))
LL <- (aux1) + (aux2)
return(LL)
}
fit <- svymle(loglike=LLsvy,
formulas=list(~y, model = ~ A(lambda1)+B(lambda2)+X,lambda1=~1,lambda2=~1),
design=d_test,
start=list(c(0,0,0,0),c(lambda1=11),c(lambda2=8)),
na.action="na.exclude")
I get the error message:
Error in eval(expr, envir, enclos) : object 'lambda1' not found
I think that the problem is in including the nonlinear part, because everything works fine if I fix A and B for some lambda1 and lambda2 (so that the model becomes linear):
lambda1=11
lambda2=8
data$A <- A(lambda1)
data$B <- B(lambda2)
d_test <- svydesign(id=~1, data = data, weights = ~data$hw0010)
LLsvylin <- function(y, model){
aux1 <- y * log(pnorm(model))
aux2 <- (1-y) * log(1-pnorm(model))
LL <- (aux1) + (aux2)
return(LL)
}
fitlin <- svymle(loglike=LLsvylin,
formulas=list(~y, model = ~A+B+X),
design=d_test,
start=list(0,0,0,0),
na.action="na.exclude")
On the contrary, if I don't use the sampling weights, I can easily estimate my nonlinear model using the function mle from package stats4 or the function mle2 from package bbmle.
To sum up,
how can I combine sampling weights (svymle) while estimating a nonlinear model (which I can do using mle or mle2)?
=========================================================================
A problem with the nonlinear part of the model arises also when using the function svyglm (with fixed lambda1 and lambda2, in order to get good starting values for svymle):
lambda1=11
lambda2=8
model0 = y ~ A(lambda1) + B(lambda2) + X
probit1 = svyglm(formula = model0,
data = data,
family = binomial(link=probit),
design = d_test)
Because I get the error message:
Error in svyglm.survey.design(formula = model0, data = data, family = binomial(link = probit), :
all variables must be in design= argument

Answer 1

This isn't what svymle does -- it's for generalised linear models, which have linear predictors and a potentially complicated likelihood or loss function. You want non-linear weighted least squares, with a simple loss function but complicated predictors.
There isn't an implementation of design-weighted nonlinear least squares in the survey package, probably because no-one has previously asked for one. You could try emailing the package author.

Answer 2

The upcoming version 4 of the survey package will have a function svynls, so if you know how to fit your model without sampling weights using nls you will be able to fit it with sampling weights.