r - ggtern + geom_interpolate_tern + expand.formula with unexpected output -

this followup my previous question,

so given following data,

> foo resp                 b         c 1  1.629 0.3333333 0.3333333 0.3333333 2  1.734 0.1666667 0.6666667 0.1666667 3   1.957 0.0000000 1.0000000 0.0000000 4  1.778 1.0000000 0.0000000 0.0000000 5  1.682 0.6666667 0.1666667 0.1666667 6  1.407 0.1666667 0.1666667 0.6666667 7  1.589 0.0000000 0.5000000 0.5000000 8  1.251 0.0000000 0.0000000 1.0000000 9  1.774 0.5000000 0.5000000 0.0000000 10 1.940 0.5000000 0.0000000 0.5000000 > 

i trying reproduce chart this article (private access). article claims use special cubic model

however, when try use notation value ~ (x + y + z)^3 -1, get

object 'z' not found 

which assume because z linearly dependent on x , y.

when try recreate special cubic model x , y, tried using cubics , quad functions expand.formula,

      > expand.formula(resp ~ cubics(a,b) + quad(a,b))        resp ~ (a + b)^3 + i(a * b * (a - b)) + (a + b)^2 + i(a^2) + i(b^2)       >  

however, geom_interpolate_tern using many predictors,

    foo <-       structure(         list(           resp = c(1.629, 1.734, 1.957, 1.778, 1.682, 1.407,                    1.589, 1.251, 1.774, 1.94),           = c(0.3333333, 0.1666667, 0, 1,                 0.6666667, 0.1666667, 0, 0, 0.5, 0.5),           b = c(0.3333333, 0.6666667,                 1, 0, 0.1666667, 0.1666667, 0.5, 0, 0.5, 0),           c = c(0.3333333,                 0.1666667, 0, 0, 0.1666667, 0.6666667, 0.5, 1, 0, 0.5)         ),         .names = c("resp",                    "a", "b", "c"),         class = "data.frame",         row.names = c("1", "2",                       "3", "4", "5", "6", "7", "8", "9", "10")       )      ggtern(data=foo,aes(y = a,x = b,z = c)) +       geom_interpolate_tern(         data = foo,         mapping = aes(           value = resp,color=..level..         ),         formula = expand.formula(value ~ cubics(x,y) + quad(x,y)),         base = "identity"       )  

output:

    warning messages:       1: in structure(c(), class = c(class(x), class(y))) :       calling 'structure(null, *)' deprecated, null cannot have attributes.     consider 'structure(list(), *)' instead.     2: computation failed in `stat_interpolate_tern()`:       1-4 predictors allowed  

by default, interpolation method 'loess', maintain consistent default smoothing method in ggplot2 things geom_smooth(...). error being thrown, due predictors limit loess regression.

no matter, fixed, specify method = lm instead. have added coloured points see how model fits respect data.

ggtern(data=foo,aes(y = a,x = b,z = c)) +   geom_point(aes(color=resp)) +    geom_interpolate_tern(     data = foo,     mapping = aes(       value = resp,color=..level..     ),     method=lm,   # <<<<<< specify method here <<<<<<<     formula = expand.formula(value ~ cubics(x,y) + quad(x,y)),     base = "identity" )