Find the Cinelli and Hazlett (2020) robustness value for a generalised linear model.

robustness_value.jl

"""
	robustness_value(;fit::StatsModels.TableRegressionModel, treatment::String = "D", q::Int64 = 1)

Find the Cinelli and Hazlett (2020) robustness value for a generalised linear model. 
The response will be a in the range 0 and 1. Values closer to 0 indicate that 
the conclusions from the original model are highly subject to omitted variable 
bias. Values closer to 1 indicate that the original model is less likely to be 
caused by omitted variable bias.
"""
function robustness_value(;fit::StatsModels.TableRegressionModel,
						  treatment::String = "D", q::Int64 = 1)	
	# Extract coefficient table from fitted model	
	m = coeftable(fit)
	
	# find treatment parameter row in coefficient table
	treat_position = findfirst(x -> x == treatment, m.rownms)
	t_value_position = findfirst(x -> x == "t", m.colnms)
	
	
	t_value = m.cols[t_value_position][treat_position][1]
	df = dof_residual(fit)
	fq = abs(t_value / sqrt(df)) * q
	1/2 * (sqrt(fq^4 + 4 * fq^2) - fq^2)
end