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@ -705,11 +705,11 @@ This chapter has focussed exclusively on the class of linear models, which assum
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* __Generalised additive models__, e.g. `mgcv::gam()`, extend generalised
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linear models to incorporate arbitrary smooth functions. That means you can
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write a formula like `y ~ s(x)` which becomes an equation like
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`y = f(x)` and the `gam()` estimate what that function is (subject to some
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`y = f(x)` and let `gam()` estimate what that function is (subject to some
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smoothness constraints to make the problem tractable).
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* __Penalised linear models__, e.g. `glmnet::glmnet()`, add a penalty term to
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the distance which penalises complex models (as defined by the distance
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the distance that penalises complex models (as defined by the distance
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between the parameter vector and the origin). This tends to make
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models that generalise better to new datasets from the same population.
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@ -718,8 +718,8 @@ This chapter has focussed exclusively on the class of linear models, which assum
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of outliers, at the cost of being not quite as good when there are no
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outliers.
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* __Trees__, e.g. `rpart::rpart()`, attack the problem in a complete different
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way to linear models. They fit a piece-wise constant model, splitting the
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* __Trees__, e.g. `rpart::rpart()`, attack the problem in a completely different
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way than linear models. They fit a piece-wise constant model, splitting the
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data into progressively smaller and smaller pieces. Trees aren't terribly
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effective by themselves, but they are very powerful when used in aggregate
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by models like __random forests__ (e.g. `randomForest::randomForest()`) or
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