/
LM.jl
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/
LM.jl
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import Distributions, DataFrames, GLM, StatsModels
function standardize(model::StatsModels.DataFrameRegressionModel{<:GLM.LinearModel})
std_data = standardize(model_data(model))
std_model = lm(StatsModels.Formula(model.mf.terms), std_data)
return std_model
end
function model_data(model::StatsModels.DataFrameRegressionModel{<:GLM.LinearModel})
return model.mf.df
end
function model_description(model::StatsModels.DataFrameRegressionModel{<:GLM.LinearModel})
modelname = "linear model"
outcome = model.mf.terms.eterms[1]
predictors = model.mf.terms.eterms[2:end]
formula = StatsModels.Formula(model.mf.terms)
output = Dict(
"Model" => modelname,
"Outcome" => outcome,
"Predictors" => predictors,
"Formula" => formula,
"text_description" => "We fitted a linear regression to predict $outcome with $(join(predictors, ", ", " and ")) ($formula)."
)
return Report(text=output["text_description"], values=output)
end
function model_effects_existence(model::StatsModels.DataFrameRegressionModel{<:GLM.LinearModel})
# p value formula
# TODO: Damn it's complicated for now!
coef_table = GLM.coeftable(model)
p = [x.v for x in coef_table.cols[4]]
output = Dict(
"p" => p,
"p_interpretation" => interpret_p.(p),
"p_formatted" => format_p.(p))
return output
end
function model_performance(model::StatsModels.DataFrameRegressionModel{<:GLM.LinearModel})
R2 = GLM.r2(model)
R2_adj = GLM.adjr2(model)
output = Dict(
"R2" => R2,
"R2_adj" => R2_adj,
"text_performance" => "The model's explanatory power (R²) is of $(round(R2, digits=2)) (adj. R² = $(round(R2_adj, digits=2))).")
return Report(text=output["text_performance"], values=output)
end
function model_std_parameters(model::StatsModels.DataFrameRegressionModel{<:GLM.LinearModel}; CI=95)
std_model = standardize(model)
# Gather values
coefs = GLM.coef(std_model)
std_errors = GLM.stderror(std_model)
ci = GLM.confint(std_model, CI/100)
ci_lower = ci[:, 1]
ci_higher = ci[:, 2]
parameters = Dict{Any, Any}(
"Std_Coef" => coefs,
"Std_SE" => std_errors,
"Std_CI" => ci,
"Std_CI_lower" => ci_lower,
"Std_CI_higher" => ci_higher)
return parameters
end
function model_effect_size(model::StatsModels.DataFrameRegressionModel{<:GLM.LinearModel}, coefs::Vector{<:Number}; rules="cohen1988", add_std::Bool=true)
effect_size = interpret_d.(coefs, rules=rules)
output = Dict{Any, Any}("Effect_Size" => effect_size)
# Effects
# --------
# Generate empty vector
output["text_effect_size"] = string.(zeros(length(output["Effect_Size"])))
for i in 1:length(output["text_effect_size"])
effect = " and can be considered as $(output["Effect_Size"][i])"
if add_std == true
effect = effect * " (Std. Coef = $(round(coefs[i], digits=2)))."
else
effect = effect * "."
end
output["text_effect_size"][i] = effect
end
return output
end
function model_initial_parameters(model::StatsModels.DataFrameRegressionModel{<:GLM.LinearModel})
intercept = GLM.coef(model)[1]
output = Dict(
"Intercept" => intercept,
"text_initial" => "The model's intercept is at $(round(intercept, digits=2)).")
return Report(text=output["text_initial"], values=output)
end
function model_parameters(model::StatsModels.DataFrameRegressionModel{<:GLM.LinearModel};
CI::Number=95,
std_coefs::Bool=true,
effect_size="cohen1988")
# Gather everything
# ------------------
parameters = GLM.coefnames(model)
coefs = GLM.coef(model)
std_errors = GLM.stderror(model)
t = GLM.coeftable(model).cols[3]
DoF = repeat([GLM.dof_residual(model)], length(parameters))
ci = GLM.confint(model, CI/100)
ci_bounds = [(100-CI)/2, 100-(100-CI)/2]
ci_lower = ci[:, 1]
ci_higher = ci[:, 2]
LogLikelihood = GLM.loglikelihood(model)
deviance = GLM.deviance(model)
sigma = sqrt(deviance/GLM.dof_residual(model))
parameters = Dict{Any, Any}(
"Parameter" => parameters,
"Coef" => coefs,
"SE" => std_errors,
"t" => t,
"DoF" => DoF,
"CI_level" => CI,
"CI" => ci,
"CI_bounds" => ci_bounds,
"CI_lower" => ci_lower,
"CI_higher" => ci_higher,
"CI_lower_formatted" => "CI_$(ci_bounds[1])",
"CI_higher_formatted" => "CI_$(ci_bounds[2])",
"LogLikelihood" => LogLikelihood,
"Deviance" => deviance)
parameters = merge(parameters, model_description(model).values)
parameters = merge(parameters, model_performance(model).values)
parameters = merge(parameters, model_initial_parameters(model).values)
parameters = merge(parameters, model_effects_existence(model))
parameters = merge(parameters, model_std_parameters(model, CI=CI))
if effect_size != nothing
if std_coefs == true
parameters = merge(parameters, model_effect_size(model, parameters["Std_Coef"], rules=effect_size, add_std=true))
else
parameters = merge(parameters, model_effect_size(model, coefs, rules=effect_size, add_std=false))
end
end
# Effects
# --------
# Generate empty vector
parameters["text_parameters"] = string.(zeros(length(parameters["Parameter"])))
for (i, var) in enumerate(parameters["Parameter"])
effect =
"$var is $(parameters["p_interpretation"][i]) " *
"(Coef = $(round(parameters["Coef"][i], digits=2)), " *
"t($(Int(parameters["DoF"][i]))) = $(round(parameters["t"][i], digits=2)), " *
"$(parameters["CI_level"])% CI "*
"[$(round(parameters["CI_lower"][i], digits=2)); " *
"$(round(parameters["CI_higher"][i], digits=2))]" *
", $(parameters["p_formatted"][i]))"
if effect_size != nothing
effect = effect * parameters["text_effect_size"][i]
else
effect = effect * "."
end
parameters["text_parameters"][i] = effect
end
return parameters
end
"""
report(model::StatsModels.DataFrameRegressionModel{<:GLM.LinearModel};
CI::Number=95,
std_coefs::Bool=true,
effect_size="cohen1988")
Describe a linear model.
# Arguments
- `model`: A `LinearModel`.
- `CI`: Confidence interval level.
- `std_coefs`: Interpret effect sizes of standardized, rather than raw, coefs.
- `effect_size`: Can be 'cohen1988', 'sawilowsky2009', or custom set of [Rules](@ref) (See [cohen_d](@ref)). Set to `nothing` to omit interpretation.
# Examples
```julia
using GLM, DataFrames
model = lm(@formula(y ~ Var1), DataFrame(y=[0, 1, 2, 3], Var1=[2, 3, 3.5, 4]))
report(model)
```
"""
function report(model::StatsModels.DataFrameRegressionModel{<:GLM.LinearModel};
CI::Number=95,
std_coefs::Bool=true,
effect_size="cohen1988")
# Parameters
parameters = model_parameters(model,
CI=CI,
std_coefs=std_coefs,
effect_size=effect_size)
# Text
description = parameters["text_description"]
performance = parameters["text_performance"]
initial = parameters["text_initial"]
text = "$description $performance $initial Within this model:"
text = text * join("\n - " .* parameters["text_parameters"][2:end])
text = format_text(text)
# Table
table = hcat(parameters["Parameter"],
parameters["Coef"],
parameters["SE"],
parameters["t"],
parameters["DoF"],
parameters["CI_lower"],
parameters["CI_higher"],
parameters["p"])
table = DataFrames.DataFrame(table,
[:Parameter,
:Coef,
:SE,
:t,
:DoF,
Symbol(parameters["CI_lower_formatted"]),
Symbol(parameters["CI_higher_formatted"]),
:p])
return Report(text=text, values=parameters, table=table)
end