Using mob() trees (partykit package) with nls() model

I'm trying to use model-based recursive partitioning (MOB) with the mob() function (from the partykit package) to separate several curves that were derived using the nls() function. I had to define my model and determine the starting values. I've been trying to see if this could be used with the mob() function to no avail.

I tried following this example on page 7: https://cran.r-project.org/web/packages/partykit/vignettes/mob.pdf I created a fit function that estimates the starting values and would return the estimates etc. of the nls(). But I can't seem to get anything going after that. I'd like to know if it is at all possible to use a custom model, with coefficients and both dependent and independent variables and to include them in mob() and get it to work. I tried the lmtree() function but of course this will only give a straight line.

My code is below. Basically I use a segmented linear regression to get the starting values of a double exponential curve that I am using. This is the furthest I got basically. The parameter estimates give an error etc, if you even get past that it just won't run. I just need to know if it is at possible for the mob() function to run nls().

I loaded sample data, but if it is possible to use the nls()

    photo.try <- function(y, x,start = NULL, weights = NULL, offset = NULL, estfun = FALSE, object = TRUE) 
        {
            lin.mod1 <- lm(y ~ x)
            segmented.mod.2 <- segmented(lin.mod1, seg.Z = ~x, psi=1)
            segmented.mod1 <- segmented(lin.mod1, seg.Z = ~x, psi =  segmented.mod.2$psi[1,2])
            nls(y ~ (a*exp(-b * x) - c* exp(-d* x)), start = list(a = -1*(intercept(segmented.mod1)[[1]][1,1]) , b = slope(segmented.mod1)[[1]][1,1], 
            c = -1*(intercept(segmented.mod1)[[1]][2,1]), 
            d = -1*slope(segmented.mod1)[[1]][2,1]))

        }

photo_form <- Pn ~ (a*exp(-b * PAR) - c* exp(-d* PAR))| Species


photo_tree <- mob(photo_form, data = eco, fit = (photo.try))

Here is my sample data:

eco <- structure(list(Species = structure(c(1L, 1L, 1L, 1L, 1L, 1L, 
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 
4L, 4L, 4L, 4L, 4L, 4L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 
5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 
5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 
5L, 5L, 5L, 5L, 5L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 
6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 
6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 
6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 
6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 
6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 
6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 
6L, 6L, 6L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 
7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 
7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 
7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 
7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 
7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 
7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L), .Label = c("Bogum", 
"Clethra", "Eugene", "Guarria", "Melo", "Santa", "Sapium"), class = "factor"), 
    PAR = c(0, 58.6, 101.4, 228.6, 462.4, 904.7, 1565.8, 1992.1, 
    2395.9, 0, 72.8, 125.9, 232.8, 411, 841.1, 1669.6, 2394.5, 
    2394.9, 0, 53.5, 122.1, 231.6, 451, 808.5, 1575, 2394.6, 
    2395.1, 0, 70.9, 104.8, 251.1, 474.6, 858.3, 1612.3, 2393.3, 
    2395.1, 0, 63.1, 124.6, 277.1, 417.7, 824.4, 1649.6, 2377.7, 
    2381.9, 0, 31, 46.5, 115.7, 228.1, 424.3, 822.5, 1644.2, 
    2380.7, 2381.2, 0, 50.1, 118.1, 203.3, 413.2, 804.5, 1587.3, 
    2385.3, 0, 28.8, 36.9, 101.2, 211.7, 423.1, 793, 0, 43.6, 
    106.7, 200.8, 468.6, 808.4, 1567, 2367.1, 2376.5, 0.1, 40.4, 
    104.1, 202.2, 447.3, 794.7, 1546, 2391.8, 2393.3, 0.1, 44.1, 
    107.5, 227.4, 429.6, 802.5, 1668.4, 2391, 0, 42.2, 125.3, 
    126.2, 127.3, 240.3, 433.4, 791, 1600, 2396.8, 2397, 2399.3, 
    0, 72.7, 118.1, 236.9, 425, 828.4, 1613.3, 1615.4, 2396.1, 
    2396.5, 2397.2, 2397.5, 0, 62, 116.2, 235.5, 401.7, 879, 
    879.8, 1552.2, 1553.9, 2394.3, 2394.4, 2394.7, 2396.6, 0, 
    84.8, 135, 209.8, 425.3, 859.1, 1597.6, 2377.3, 2379.5, 2385.1, 
    0.1, 62, 106.3, 226.2, 442.9, 822.5, 1462.3, 2389.8, 2392.1, 
    0.1, 0.1, 73.9, 126, 249.8, 428.5, 846.5, 1555.3, 2390.1, 
    2390.7, 2390.8, 0, 68.7, 121.5, 209.7, 426.2, 803, 1525.9, 
    2389.8, 0, 52.8, 96.9, 211.1, 441.3, 787.9, 1566.5, 2415.2, 
    2415.3, 2415.5, 2417.5, 2417.7, 2418.5, 0.1, 46.5, 108.4, 
    233.5, 461.7, 792.3, 1635.7, 2415.1, 2415.6, 2415.6, 2416.5, 
    2416.6, 2417.8, 0.1, 68.3, 110, 239.5, 531.7, 847.2, 1591.4, 
    2387.3, 2387.6, 2389.7, 0, 49.7, 114.6, 230.6, 397.7, 398.2, 
    817.7, 1596.4, 2376.2, 2376.4, 2380.9, 0, 62.9, 65.5, 117, 
    209, 431.2, 854.5, 1611.3, 2387.3, 2388.5, 2390.3, 0, 49.1, 
    108.9, 200.3, 408.8, 842.2, 1630.2, 2386.5, 2386.8, 2388.2, 
    0, 64.8, 122.9, 226, 422.9, 801.6, 1635.7, 2383.6, 2383.6, 
    2384.3, 2386.1, 0, 36.7, 143.2, 213.7, 444.9, 814.9, 816.2, 
    1496.5, 2384.7, 2386.5, 2388.6, 0.1, 45.6, 105.2, 206.7, 
    494.8, 901.2, 1610.9, 2388, 2388.1, 2388.3, 2388.6, 0, 0.1, 
    45.9, 48.5, 100.2, 209.4, 432.4, 778, 1600.3, 2408.8, 2408.8, 
    0, 71.8, 121.6, 216.4, 404.3, 815.2, 1622, 2414.9, 2415.1, 
    2416.1, 2416.1, 0, 36.2, 97.5, 186.7, 417.9, 840.4, 1597.5, 
    2390.7, 2390.9, 2391.2, 2391.2, 2391.5, 2392.1, 2392.5, 0, 
    53.8, 138.2, 227, 403.6, 800.8, 1642.3, 2396.9, 2397.1, 0, 
    57.9, 95.1, 246.6, 466.8, 796.2, 1574.2, 2395.5, 2397.3, 
    0, 54.9, 94.9, 201.7, 408.1, 822.6, 1596, 2384.1, 0, 55.6, 
    131, 202.5, 419.8, 798.5, 1614, 2387.4, 2387.8, 0, 39.1, 
    109.6, 197.1, 403.3, 835.4, 836.9, 1725.9, 1727.4, 1729.3, 
    1730.6, 54.5, 58.6, 125.4, 226.9, 409, 806.8, 1578.8, 2377.2, 
    2380.1, 2388.3, 0, 68, 127.4, 206.9, 510.5, 814.9, 1561, 
    2404.1, 2404.8, 0, 58.4, 95.3, 229.6, 457.2, 781.5, 1634.4, 
    2399.8, 2401, 2403, 0.1, 56.5, 101.9, 221.8, 394.3, 815.1, 
    1655.4, 2411.8, 2411.9, 0, 50.2, 107.3, 220.5, 434.4, 819.8, 
    1630.6, 2412.4, 2412.6, 0, 48.4, 117.7, 195.3, 403.2, 801, 
    1632.7, 2388.9, 2389.3, 2390.7, 0, 50.4, 120.3, 234.7, 460.3, 
    829.1, 1581.7, 2398.5, 2402.3, 0, 60.8, 105.8, 215.8, 466.6, 
    826, 828.3, 1570.8, 2405.6, 2406.1, 2408.8, 0, 52.6, 106.9, 
    206.5, 414.3, 868.4, 1629.9, 1655.1, 2409.1, 2413, 0, 49.5, 
    100.6, 232.9, 389.4, 808.2, 1588.2, 2412.4, 2413.3, 2415.9, 
    0.1, 70.9, 110.5, 208.4, 409, 807.5, 1579.9, 2382.2, 2382.5, 
    2383.6, 2383.8, 0, 61.5, 106.5, 213.9, 473.8, 814.2, 1561.9, 
    2390.7, 2391.9, 2393.1, 0, 59.9, 64, 112, 216, 397.6, 807.4, 
    1625, 2392.3, 2395.1, 0, 74, 108.8, 109.7, 236.1, 433.6, 
    794.7, 1590.3, 2381.9, 2382.5, 0.1, 56.3, 114.5, 254.1, 487.7, 
    864.3, 1593.5, 2369.3, 2369.3, 2372.3, 2373.9, 0.2, 57.1, 
    110, 201.4, 402.7, 807.2, 1572.9, 2392.8, 2393.5, 0.1, 56.4, 
    122.5, 224.5, 420.2, 853.7, 1502.1, 2390.3, 2392.9, 0, 50.5, 
    53.7, 118.2, 230, 462.8, 794.3, 1513.4, 2391.4, 2392.3, 2393.4, 
    2393.4, 2394.1, 0.1, 49.7, 98.3, 208.3, 383.2, 850.7, 1653.5, 
    2395.3, 2396, 2397.1, 0, 48.4, 121.2, 228.8, 423.9, 817, 
    1708.5, 2389.9, 2389.9, 0, 66.4, 129.7, 209.4, 431.5, 794.1, 
    1673.7, 2383.7, 2384.2, 0, 57, 122.6, 215, 434.1, 838.5, 
    1657.5, 2386.4, 0.1, 22.6, 127.8, 220.4, 404.3, 810.9, 1592.3, 
    2386.7, 2388.7, 0, 49.8, 119.7, 200.5, 463.8, 828.7, 1560.7, 
    2384.5, 2385.7, 2391.2, 0, 73.1, 138.2, 226.6, 408.5, 815.3, 
    1627.3, 2390.2, 2395.4, 0, 61.2, 108.8, 233.8, 417.7, 824.5, 
    1502.7, 2395, 2396.2, 0, 56, 101.4, 226.3, 282.1, 412.9, 
    873.8, 1672.6, 2380.4, 2380.9, 2381.5, 0.1, 70.7, 138, 246, 
    444.4, 817.1, 1643.2, 2391.5, 2391.8, 2392), Pn = c(-0.95, 
    0.75, 0.94, 1.27, 1.5, 1.9, 2.14, 2.35, 2.38, 1.48, 3.51, 
    3.7, 3.99, 4.4, 4.32, 4.52, 4.73, 4.72, 1.97, 3.24, 4.23, 
    4.35, 4.41, 4.66, 4.57, 4.68, 4.88, 1.16, 3.64, 4.05, 4.75, 
    5.42, 5.57, 5.55, 5.89, 5.8, 1.48, 3.89, 4.7, 5.34, 5.47, 
    5.62, 5.71, 5.7, 6.08, 1.26, 0.59, 2.96, 4.34, 5, 4.82, 5.22, 
    5.2, 5.33, 5.51, 1.2, 2.95, 3.67, 3.9, 4.06, 4.59, 4.6, 4.62, 
    2.01, 1.92, 2.41, 2.19, 2.22, 2.41, 2.21, 1.6, 3.29, 3.97, 
    4.39, 4.89, 5.12, 4.93, 5.12, 5.1, 2.39, 3.84, 4.45, 4.63, 
    4.43, 4.93, 4.78, 4.73, 5.04, 3.09, 3.74, 4.03, 3.89, 4.52, 
    4.43, 4.24, 4.26, 1.5, 2.73, 2.83, 3.14, 2.89, 3.39, 2.89, 
    2.84, 3.34, 3.11, 3.16, 3.31, 0.1, 1.17, 1.72, 1.61, 1.64, 
    2.06, 2.17, 1.99, 2.31, 2.14, 2.27, 2.08, 0.17, 1.17, 1.32, 
    1.33, 1.4, 1.8, 1.48, 2, 1.81, 1.95, 2.09, 1.73, 1.85, 2.95, 
    4.33, 4.82, 4.98, 4.97, 5.03, 5.08, 5.22, 5.32, 4.88, 2.17, 
    3.08, 3.32, 3.42, 3.45, 3.67, 3.64, 3.71, 3.71, 2.85, 2.33, 
    3.15, 2.81, 3.22, 2.99, 3.16, 3.33, 3.56, 3.61, 3.63, 2.52, 
    3.55, 4.07, 4.1, 4.17, 4.41, 4.53, 4.56, 2.06, 2.57, 2.91, 
    2.61, 3.08, 3.29, 3.99, 6.49, 5.23, 6.08, 5.74, 4.41, 6.5, 
    1.59, 3.22, 3.59, 3.75, 3.84, 4.5, 4.93, 6.87, 6.75, 6.97, 
    6.53, 6.04, 6.82, 1.28, 3.56, 4.39, 5.27, 5.51, 6.38, 7.05, 
    7.46, 7.16, 7.24, 0.87, 2.45, 3.86, 4.32, 4.57, 4.43, 4.68, 
    4.71, 4.86, 4.36, 4.68, 1.06, 2.79, 4.05, 4.86, 5.48, 5.9, 
    6.38, 6.79, 7.46, 7.12, 7.03, 2.76, 3.92, 3.96, 4.07, 4.2, 
    4.5, 4.91, 5.52, 5.49, 5.33, 2.84, 4.78, 4.83, 4.76, 4.74, 
    4.84, 5.19, 5.59, 5.74, 5.7, 5.65, 3.02, 3.61, 4.14, 4.23, 
    4.45, 4.37, 4.5, 4.6, 4.78, 4.79, 4.85, 2.71, 4.26, 5.42, 
    6.24, 6.58, 6.63, 6.55, 7.29, 7.43, 7.24, 7, 3.36, 2.19, 
    2.86, 2.87, 2.37, 3.16, 2.68, 3, 3.4, 3.6, 4.35, 1.28, 2.62, 
    2.92, 3.3, 3.35, 3.58, 3.73, 4.02, 4, 3.7, 3.75, 1.61, 2.26, 
    2.5, 2.52, 2.71, 2.61, 2.75, 3.19, 2.92, 3.99, 4.36, 3.67, 
    4.14, 4.37, -0.28, 1.91, 2.78, 2.84, 2.96, 3.04, 3.24, 3.44, 
    3.58, 1.78, 4.12, 4.58, 4.33, 4.8, 4.7, 5.02, 5.09, 5.22, 
    2.79, 4.71, 4.89, 4.93, 4.87, 4.92, 4.83, 4.81, 1.66, 3, 
    4.04, 4.35, 4.56, 4.75, 4.75, 4.66, 4.89, 1.56, 2.77, 3.86, 
    3.58, 3.7, 3.76, 3.58, 4.55, 4.63, 4.05, 3.73, 1.76, 2.71, 
    2.98, 3.01, 3.06, 3.22, 2.99, 3.15, 3.32, 3.34, 1.58, 3.76, 
    4.97, 5.21, 5.29, 5.5, 5.59, 5.71, 5.74, 1.89, 2.67, 3.01, 
    3.14, 3.39, 3.57, 3.45, 3.91, 4.11, 3.94, 1.15, 2.88, 3.63, 
    4.32, 4.09, 4.43, 4.58, 4.61, 4.63, 1.23, 2.26, 3.15, 3.33, 
    3.3, 3.61, 3.46, 3.65, 3.67, 0.19, 2.23, 3.43, 4.1, 4.85, 
    5.21, 5.8, 6.27, 6.34, 6.08, 1.94, 3.72, 4.88, 5.51, 6.71, 
    6.51, 6.96, 7.01, 7.4, 0.48, 2.29, 2.5, 2.87, 3.18, 3.51, 
    3.13, 3.86, 4.13, 4.34, 4.03, 1.63, 3.64, 5.15, 5.95, 6.43, 
    6.57, 6.61, 6.51, 6.65, 6.56, 1.93, 3.95, 4.63, 5.66, 6.03, 
    6.28, 6.67, 6.69, 6.95, 6.75, 0.93, 3.14, 3.46, 3.9, 4.19, 
    4.27, 4.77, 5.39, 5.36, 5.24, 5.02, 1.71, 3.31, 3.86, 4.02, 
    4.02, 4.29, 4.36, 4.73, 4.88, 4.59, 1.63, 2.65, 2.63, 2.48, 
    2.93, 3.45, 4.01, 4.67, 5.02, 5.08, 1.93, 3.54, 3.8, 3.81, 
    4.04, 4.17, 4.38, 4.55, 4.99, 4.99, 1.29, 2.73, 3.32, 3.66, 
    3.77, 3.79, 4.14, 4.37, 4.22, 4.1, 4.14, 1.06, 2.89, 3.65, 
    4.01, 4.11, 4.19, 4.66, 5.03, 5.12, 0.97, 2.45, 2.99, 3.32, 
    3.34, 3.35, 3.47, 3.12, 3.38, 2.29, 1.72, 4.33, 5.49, 6.44, 
    6.96, 7.91, 7.49, 8.45, 8.21, 8.17, 8.71, 8.35, 0.29, 2.99, 
    3.93, 4.52, 5.69, 6.23, 6.23, 6.81, 6.96, 6.68, 0.99, 3.67, 
    4.62, 5.52, 5.86, 6.23, 5.91, 6.64, 6.29, -0.08, 3.34, 4.89, 
    6.02, 6.37, 6.59, 6.99, 6.95, 7.2, 0.99, 2.28, 2.72, 2.67, 
    2.99, 3.18, 3.55, 3.58, 1.31, 2.18, 5.55, 7.37, 8.42, 9.14, 
    9.44, 9.26, 9.5, 1.23, 3.11, 5.01, 6.21, 7.14, 7.44, 7.79, 
    7.73, 8.1, 7.96, 1.35, 3.33, 5.67, 6.58, 7.05, 7.36, 7.73, 
    7.75, 7.99, 0.4, 2.25, 2.83, 3.31, 3.55, 3.66, 3.96, 3.54, 
    3.77, 1.46, 2.91, 3.51, 3.64, 4.5, 3.83, 3.96, 4.17, 4.66, 
    4.09, 4.44, 2.41, 4.77, 5.49, 6.05, 6.15, 6.28, 6.6, 6.76, 
    6.75, 6.78)), .Names = c("Species", "PAR", "Pn"), class = "data.frame", row.names = c(NA, 
-628L))

Solution

Yes, we can! ;-)

In principle, you were attempting to do the right thing but a few aspects were not quite correct. The main issue is how you pass around the data and the formula: As mob() does not know anything about the way nls() specifies its formulas, a plain formula Pn ~ PAR | Species needs to be used and then the fit function needs to know what to do with the data. The pre-processing offered by mob() can either set up a model matrix (with intercept, dummy/contrast codings, etc.) or a model frame (where factors are still factors etc.). In this case it is easiest to use the default model matrix and then to omit the intercept in the fitting function.

The second problem with your code was that you used the extended specification of the fit function (with estfun and object arguments) but only supplied the fitted model object. With that specification mob() expects that the fit function sets up a suitable list with coefficients and objfun etc.

In combination, this means that your fit function should look like this:

photofit <- function(y, x = NULL, start = NULL, weights = NULL, offset = NULL, ...,
  estfun = FALSE, object = FALSE)
{
  ## only use first real regressor (without intercept)
  x <- x[, 2]

  ## obtain starting values if necessary
  if(is.null(start)) {
    aux_lm <- lm(y ~ x)
    aux_seg_2 <- segmented::segmented(aux_lm, seg.Z = ~ x, psi = 1)
    aux_seg_1 <- segmented::segmented(aux_lm, seg.Z = ~ x, psi = aux_seg_2$psi[1, 2])
    start <- list(
      a = -1 * (segmented::intercept(aux_seg_1)[[1]][1, 1]),
      b =           segmented::slope(aux_seg_1)[[1]][1, 1], 
      c = -1 * (segmented::intercept(aux_seg_1)[[1]][2, 1]), 
      d = -1 *      segmented::slope(aux_seg_1)[[1]][2, 1]
    )
  } else {
    start <- as.list(start)
  }

  ## estimate NLS model
  rval <- nls(y ~ (a * exp(-b * x) - c * exp(-d * x)), start = start)

  ## return processed information for mob()
  list(
    coefficients = coef(rval),
    objfun = deviance(rval),
    estfun = if(estfun) sandwich::estfun(rval) else NULL,
    object = if(object) rval else NULL    
  )
}

And then you can grow the MOB tree. Specifying the verbose = TRUE control option will give you a little bit of progress information while you wait:

photomob <- mob(Pn ~ PAR | Species, data = eco, fit = photofit,
  control = mob_control(verbose = TRUE))
coef(photomob)
##           a             b         c             d
## 4  2.967680 -3.216708e-05  1.519680  1.076879e+01
## 5 -1.811596  1.967366e-02 -3.573079 -4.877852e-05
## 6 -2.772783  1.438087e-02 -4.177953 -7.821814e-05
## 8 -2.427253  1.757744e-02 -4.449105 -1.328930e-04
## 9 -4.579248  1.020021e-02 -5.714575 -7.502393e-05

You can then also visualize the tree. By default a numeric summary is shown in each node but you can also easily display the fitted curves:

plot(photomob)
plot(photomob, terminal_panel = node_bivplot, tnex = 2)

As you see the tree selected five terminal nodes with different parameters. I would recommend that you do some more diagnostics on the model fits in the different nodes because I'm not sure how well all parameters are identified. I'm not very familiar with NLS and might be completely wrong but it seems that not always all parameters can be reliably determined.

As one illustration I do the following: I extract all nine fitted nls objects from the tree. For the model from the root node (node 1) I compute the gradient by summing over all observation-wise gradient contributions (as computed by the estfun() method):

photonls <- refit.modelparty(photomob)
library("sandwich")
colSums(estfun(photonls[[1]]))
##             a             b             c             d 
##  2.010552e-05  5.753230e-02 -1.166331e-04  6.771585e+00

The gradients of parameters a-c are reasonably close to zero but for d it isn't. This may also affect the inference in mob() which is based on the observation-wise gradient contributions (aka model scores or estimating functions).

In short: What you want to do, can be done! But I would recommend considering a simpler model. If you do, you just need to modify the photofit() function accordingly and run it through mob() again.