This package is an experiment in using the Zygote automatic differentiation package and the lowrankupdate! function in the LinearAlgebra package to solve the linear least squares problem for a Gauss-Newton update.
The data are represented as a Tables.RowTable, which is a vector of NamedTuples. The model parameters are also a NamedTuple. The model function is given as a function of two arguments - the parameters and a data row.
In the Michaelis-Menten model for enzyme kinetics,
v = Vm * c / (K + c)the relationship between the velocity, v, of a reaction and the
concentration, c, of the substrate depends on two parameters; Vm,
the maximum velocity and K, the Michaelis parameter. The Vm
parameter occurs linearly in this expression whereas K is a
nonlinear parameter.
julia> using CSV, DataFrames, NLreg
julia> datadir = normpath(joinpath(dirname(pathof(NLreg)), "..", "data"));
julia> PurTrt = first(groupby(CSV.read(joinpath(datadir, "Puromycin.csv")), :state))
12×3 SubDataFrame
│ Row │ conc │ rate │ state │
│ │ Float64 │ Float64 │ String │
├─────┼─────────┼─────────┼─────────┤
│ 1 │ 0.02 │ 76.0 │ treated │
│ 2 │ 0.02 │ 47.0 │ treated │
│ 3 │ 0.06 │ 97.0 │ treated │
â‹®
│ 9 │ 0.56 │ 191.0 │ treated │
│ 10 │ 0.56 │ 201.0 │ treated │
│ 11 │ 1.1 │ 207.0 │ treated │
│ 12 │ 1.1 │ 200.0 │ treated │
julia> pm1 = fit(NLregModel, PurTrt, :rate, (p,d) -> p.Vm * d.conc/(p.K + d.conc),
(Vm = 200., K = 0.05))
Nonlinear regression model fit by maximum likelihood
Data schema (response variable is rate)
Tables.Schema:
:conc Float64
:rate Float64
:state String
Number of observations: 12
Parameter estimates
───────────────────────────────────────
Estimate Std.Error t-statistic
───────────────────────────────────────
Vm 212.684 6.94715 30.6145
K 0.064121 0.00828092 7.74322
───────────────────────────────────────
Sum of squared residuals at convergence: 1195.4488145417758
Achieved convergence criterion: 8.798637504793927e-6