Error in nls(formula.gompertz, d, starting.values) : singular gradient

General
1

hi, I have a dataset that wants to fit nonlinear model fit to all data but I get this error and when slice data to small rows don't give this error!!!

library(tidyverse)
data <- read_csv("~/data.csv")
data <- data %>% mutate(day = c(1:nrow(data))

fit.gompertz <- function(data, time){
    d <- data.frame(y=data, t=time)
    if (length(unique(d$t)) < 3) stop("too few data points to fit curve")
    i <- which.max(diff(d$y))
    starting.values <- c(a=max(d$y),
                         mu=max(diff(d$y))/(d[i+1,"t"]-d[i, "t"]),
                         lambda=i)
    print("Starting Values for Optimization: ")
    print(starting.values)
    formula.gompertz <- "y~a*exp(-exp(mu*exp(1)/a*(lambda-t)+1))"
    nls(formula.gompertz, d, starting.values)
}
model <- fit.gompertz(data$confirmed, data$day)

error:

Error in nls(formula.gompertz, d, starting.values) : singular gradient

dataset link: https://github.com/Mgavahi/Covid-19/blob/master/data/Iran(2020-03-29).csv

2

It looks like

mu=max(diff(d$y))/(d[i+1,"t"]-d[i, "t"]), lambda=i)

is returning NA, which would explain the result. No \mu

suppressPackageStartupMessages(library(dplyr))

dat <- structure(list(
  confirmed =
    c(2, 5, 18, 28, 43, 61, 95, 139, 245, 388, 593, 978, 1501, 2336, 2922, 3513, 4747, 5823, 6566, 7161, 8042, 9000, 10075, 11364, 12729, 13938, 14991, 16169, 17361, 18407, 19644, 20610, 21638, 23049, 24811, 27017, 29406, 32332, 35408, 38309),
  deaths =
    c(2, 2, 4, 5, 8, 12, 16, 19, 26, 34, 43, 54, 66, 77, 92, 107, 124, 145, 194, 237, 291, 354, 429, 514, 611, 724, 853, 988, 1135, 1284, 1433, 1556, 1685, 1812, 1934, 2077, 2234, 2378, 2517, 2640),
  recovered =
    c(0, 0, 0, 0, 0, 0, 0, 49, 49, 73, 123, 175, 291, 291, 552, 739, 913, 1669, 2134, 2394, 2731, 2959, 2959, 2959, 2959, 4590, 4590, 5389, 5389, 5710, 6745, 7635, 7931, 7931, 8913, 9625, 10457, 11133, 11679, 12391)),
  class =c("spec_tbl_df", "tbl_df", "tbl", "data.frame"),
  row.names =c(NA, -40L), spec = structure(list(cols = list(confirmed = structure(list(),
  class =c("collector_double", "collector")), deaths = structure(list(),
  class =c("collector_double", "collector")), recovered = structure(list(),class =c("collector_double", "collector"))), default = structure(list(),class =c("collector_guess", "collector")), skip = 1), class = "col_spec"))

tibble::rownames_to_column(dat) %>% rename(day = rowname) -> dat
dat
#> # A tibble: 40 x 4
#>    day   confirmed deaths recovered
#>    <chr>     <dbl>  <dbl>     <dbl>
#>  1 1             2      2         0
#>  2 2             5      2         0
#>  3 3            18      4         0
#>  4 4            28      5         0
#>  5 5            43      8         0
#>  6 6            61     12         0
#>  7 7            95     16         0
#>  8 8           139     19        49
#>  9 9           245     26        49
#> 10 10          388     34        73
#> # … with 30 more rows
fit.gompertz <- function(data, time){
  d <- data.frame(y=data, t=time)
  if (length(unique(d$t)) < 3) stop("too few data points to fit curve")
  i <- which.max(diff(d$y))
  starting.values <- c(a=max(d$y),
                       mu=max(diff(d$y))/(d[i+1,"t"]-d[i, "t"]),
                       lambda=i)
  print("Starting Values for Optimization: ")
  print(starting.values)
  formula.gompertz <- "y~a*exp(-exp(mu*exp(1)/a*(lambda-t)+1))"
  nls(formula.gompertz, d, starting.values)
}
model <- fit.gompertz(dat$confirmed, dat$day)
#> Warning in Ops.factor(d[i + 1, "t"], d[i, "t"]): '-' not meaningful for factors
#> [1] "Starting Values for Optimization: "
#>      a     mu lambda 
#>  38309     NA     38
#> Warning in Ops.factor(lambda, t): '-' not meaningful for factors
#> Warning in Ops.factor(lambda, t): '-' not meaningful for factors
#> Error in numericDeriv(form[[3L]], names(ind), env): Missing value or an infinity produced when evaluating the model

Created on 2020-03-30 by the reprex package (v0.3.0)

3

@technocrat but how can to resolve it. if we slice data for example to 1:25 , then code ran without any error!!!

4

I wish I could say, but without a reprex, I have to go all Wittgenstein:

Whereof we cannot speak we must perforce remain silent.

Enough tongue-in-check: really, all that I can do is speculate: Beyond [1:25] are there any NA, NaN, Inf, -Inf or 0 occurrences?

5

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