nls - Convergence failure: singular convergence (7)

问题

The following nls code throws the following error Convergence failure: singular convergence (7) for fm2(for Data2). But the same code for similar dataset works fine (fm1 for Data1). Any help to figure out this problem will be highly appreciate. Thanks

Works Fine for this Data Set

Data1 <-
structure(list(D = c(0L, 0L, 0L, 0L, 5L, 5L, 5L, 5L,
10L, 10L, 10L, 10L, 15L, 15L, 15L, 15L, 20L, 20L, 20L, 20L),
    Y = c(11.6, 9.3, 10.7, 9.2, 7.8, 8, 8.6, 7.9, 7.7,
    7.6, 7.5, 7.5, 7.2, 7.3, 7, 6.5, 6.3, 5.7, 5.6, 6)), .Names = c("D",
"Y"), class = "data.frame", row.names = c(NA, 20L))

fm1  <-
  nls(
      formula=Y~w*(1-(i*D/(100*(1+i*D/A))))
    , data=Data1
    , start=list(w=13, i=3, A=80)
    , algorithm="port"
    )

Does not Work for this Data Set

Data2 <-
structure(list(D = c(0L, 0L, 0L, 0L, 5L, 5L, 5L, 5L,
10L, 10L, 10L, 10L, 15L, 15L, 15L, 15L, 20L, 20L, 20L, 20L),
    Y = c(10.8, 10.7, 8.4, 8.5, 8, 8, 8, 7.9, 7.9, 7.2,
    7.8, 7.2, 6.6, 6.5, 6.5, 6.4, 2.2, 4.5, 4.2, 6.2)), .Names = c("D",
"Y"), class = "data.frame", row.names = 21:40)

fm2  <-
  nls(
      formula=Y~w*(1-(i*D/(100*(1+i*D/A))))
    , data=Data2
    , start=list(w=13, i=3, A=80)
    , algorithm="port"
    )

回答1:

I think its having problems with your parameterization. We can take advantage of linearlity by letting B be i/A, .lin1 = w and .lin2 = i*w in which case .lin1 and .lin2 enter linearly and using alg=plinear only the non-linear parameter needs a starting value:

> fo <- Y ~ cbind(1, -D/(100*(1+B*D)))
> nls(fo, Data, start = list(B = 3/80), alg = "plinear")
Nonlinear regression model
  model: Y ~ cbind(1, -D/(100 * (1 + B * D)))
   data: Data
       B    .lin1    .lin2 
-0.02217  9.26808 13.61471 
 residual sum-of-squares: 15.76

Number of iterations to convergence: 9 
Achieved convergence tolerance: 4.236e-06

From the result w = .lin1; i*w = .lin2 (so i = .lin2 / .lin1) and B = i/A (so A = i/B).

REVISED Improved the formulation.

来源：https://stackoverflow.com/questions/22229352/nls-convergence-failure-singular-convergence-7

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statistics

nls