AnovaGLM.jl

anova(<glmmodels>...; test::Type{<: GoodnessOfFit},  <keyword arguments>)
anova(<anovamodel>; test::Type{<: GoodnessOfFit},  <keyword arguments>)
anova(test::Type{<: GoodnessOfFit}, <glmmodels>...;  <keyword arguments>)
anova(test::Type{<: GoodnessOfFit}, <anovamodel>;  <keyword arguments>)

Analysis of variance.

Return AnovaResult{M, test, N}. See AnovaResult for details.

Arguments

• glmmodels: model objects
  1. TableRegressionModel{<: LinearModel} fitted by GLM.lm
  2. TableRegressionModel{<: GeneralizedLinearModel} fitted by GLM.glm
  If mutiple models are provided, they should be nested and the last one is the most complex.
• anovamodel: wrapped model objects; FullModel and NestedModels.
• test: test statistics for goodness of fit. Available tests are LikelihoodRatioTest (LRT) and FTest. The default is based on the model type.
  1. TableRegressionModel{<: LinearModel}: FTest.
  2. TableRegressionModel{<: GeneralizedLinearModel}: based on distribution function, see canonicalgoodnessoffit.

Other keyword arguments

• When one model is provided:
  1. type specifies type of anova (1, 2 or 3). Default value is 1.
• When multiple models are provided:
  1. check: allows to check if models are nested. Defalut value is true. Some checkers are not implemented now.

anova_lm(X, y; test::Type{<: GoodnessOfFit} = FTest, <keyword arguments>) 

anova_lm(test::Type{<: GoodnessOfFit}, X, y; <keyword arguments>)

anova(test::Type{<: GoodnessOfFit}, ::Type{LinearModel}, X, y; 
    type::Int = 1, 
    <keyword arguments>)

ANOVA for simple linear regression.

Arguments

• X and y can be a Matrix and a Vector or a Formula and a Tables.jl compatible data.
• test: test statistics for goodness of fit.

Keyword arguments

• test: test statistics for goodness of fit.
• type specifies type of anova (1, 2 or 3). Default value is 1.
• dropcollinear controls whether or not lm accepts a model matrix which is less-than-full rank. If true (the default), only the first of each set of linearly-dependent columns is used. The coefficient for redundant linearly dependent columns is 0.0 and all associated statistics are set to NaN.

anova_lm generate a TableRegressionModel object, which is fitted by lm.

anova_glm(X, y, d::UnivariateDistribution, l::Link = canonicallink(d); 
        test::Type{<: GoodnessOfFit} = canonicalgoodnessoffit(d), <keyword arguments>)

anova_glm(test::Type{<: GoodnessOfFit}, X, y, d::UnivariateDistribution, l::Link = canonicallink(d); <keyword arguments>)

anova(test::Type{<: GoodnessOfFit}, X, y, d::UnivariateDistribution, l::Link = canonicallink(d); <keyword arguments>)

ANOVA for genaralized linear models.

Arguments

• X and y can be a Matrix and a Vector or a Formula and a Tables.jl compatible data.
• d: a GLM.UnivariateDistribution.
• l: a GLM.Link
• test: test statistics for goodness of fit based on distribution function. See canonicalgoodnessoffit.

For other keyword arguments, see fit.

nestedmodels(trm::TableRegressionModel{<: LinearModel}; null::Bool = true, <keyword arguments>)
nestedmodels(trm::TableRegressionModel{<: GeneralizedLinearModel}; null::Bool = true, <keyword arguments>)

nestedmodels(::Type{LinearModel}, formula, data; null::Bool = true, <keyword arguments>)
nestedmodels(::Type{GeneralizedLinearModel}, formula, data, distr::UnivariateDistribution, link::Link = canonicallink(d); null::Bool = true, <keyword arguments>)

Generate nested nested models NestedModels from a model or formula and data.

The null model will be a model with at least one factor (including intercept) if the link function does not allow factors to be 0 (factors in denominators) or the keyword argument null is false (default value is true).

• InverseLink for Gamma
• InverseSquareLink for InverseGaussian
• LinearModel fitted with CholeskyPivoted when dropcollinear = true

Otherwise, it will be an empty model.