Poisson of quasipoisson

Een van de aannames van Poisson-regressie om tellingen te voorspellen is dat de gebeurtenis die je telt Poisson-verdeeld is: het gemiddelde aantal per tijdseenheid is gelijk aan de variantie van de telling. In de praktijk betekent "gelijk" dat het gemiddelde en de variantie van een vergelijkbare orde van grootte moeten zijn.

Als de variantie veel groter is dan het gemiddelde, gaat de Poisson-aanname niet op. Een oplossing is dan quasipoisson-regressie, waarin niet wordt aangenomen dat \(variance = mean\).

Bepaal voor elk van de volgende situaties of Poisson-regressie geschikt is, of dat je beter quasipoisson-regressie kunt gebruiken.

Voor welke situaties kun je Poisson-regressie gebruiken?

Aantal dagen dat studenten afwezig zijn: gemiddelde 5,9, variantie 49
Aantal prijzen dat een student wint: gemiddelde 0,6, variantie 1,1
Aantal hits per webpagina: gemiddelde 108,2, variantie 108,5
Aantal fietsen verhuurd per dag: gemiddelde 273, variantie 45863,84

Deze oefening maakt deel uit van de cursus

Supervised Learning in R: Regressie

Cursus bekijken

Praktische interactieve oefening

Zet theorie om in actie met een van onze interactieve oefeningen.

Begin met trainen

Deze oefening maakt deel uit van de cursus

Supervised Learning in R: Regressie

SkillTag.level.intermediateSkillTag.label

4.6+

Begin de cursus gratis

In this chapter we introduce the concept of regression from a machine learning point of view. We will present the fundamental regression method: linear regression. We will show how to fit a linear regression model and to make predictions from the model.

Exercise 1: Welcome and Introduction Exercise 2: Identify the regression tasks Exercise 3: Linear regression - the fundamental method Exercise 4: Code a simple one-variable regression Exercise 5: Examining a model Exercise 6: Predicting once you fit a model Exercise 7: Predicting from the unemployment model Exercise 8: Multivariate linear regression (Part 1)Exercise 9: Multivariate linear regression (Part 2)Exercise 10: Wrapping up linear regression

Now that we have learned how to fit basic linear regression models, we will learn how to evaluate how well our models perform. We will review evaluating a model graphically, and look at two basic metrics for regression models. We will also learn how to train a model that will perform well in the wild, not just on training data. Although we will demonstrate these techniques using linear regression, all these concepts apply to models fit with any regression algorithm.

Exercise 1: Evaluating a model graphically Exercise 2: Graphically evaluate the unemployment model Exercise 3: The gain curve to evaluate the unemployment model Exercise 4: Root Mean Squared Error (RMSE)Exercise 5: Calculate RMSE Exercise 6: R-squared Exercise 7: Calculate R-squared Exercise 8: Correlation and R-squared Exercise 9: Properly Training a Model Exercise 10: Generating a random test/train split Exercise 11: Train a model using test/train split Exercise 12: Evaluate a model using test/train split Exercise 13: Create a cross validation plan Exercise 14: Evaluate a modeling procedure using n-fold cross-validation

Before moving on to more sophisticated regression techniques, we will look at some other modeling issues: modeling with categorical inputs, interactions between variables, and when you might consider transforming inputs and outputs before modeling. While more sophisticated regression techniques manage some of these issues automatically, it's important to be aware of them, in order to understand which methods best handle various issues -- and which issues you must still manage yourself.

Exercise 1: Categorical inputs Exercise 2: Examining the structure of categorical inputs Exercise 3: Modeling with categorical inputs Exercise 4: Interactions Exercise 5: Modeling an interaction Exercise 6: Modeling an interaction (2)Exercise 7: Transforming the response before modeling Exercise 8: Relative error Exercise 9: Modeling log-transformed monetary output Exercise 10: Comparing RMSE and root-mean-squared Relative Error Exercise 11: Transforming inputs before modeling Exercise 12: Input transforms: the "hockey stick"Exercise 13: Input transforms: the "hockey stick" (2)

Now that we have mastered linear models, we will begin to look at techniques for modeling situations that don't meet the assumptions of linearity. This includes predicting probabilities and frequencies (values bounded between 0 and 1); predicting counts (nonnegative integer values, and associated rates); and responses that have a non-linear but additive relationship to the inputs. These algorithms are variations on the standard linear model.

Exercise 1: Logistische regressie om kansen te voorspellen Exercise 2: Fit een model voor de overlevingskans van mussen Exercise 3: Voorspel de overleving van mussen Exercise 4: Poisson- en quasipoisson-regressie om aantallen te voorspellen Exercise 5: Poisson of quasipoisson

Huidige oefening

Exercise 6: Pas een model toe om aantallen fietsverhuur te voorspellen Exercise 7: Voorspel fietsverhuur op nieuwe data Exercise 8: Visualiseer de voorspellingen voor de fietsverhuur Exercise 9: GAM om niet-lineaire transformaties te leren Exercise 10: Formules schrijven voor GAM-modellen Exercise 11: Formules schrijven voor GAM-modellen (2)Exercise 12: Modelleer sojagroei met GAM Exercise 13: Voorspellen met het sojaboonmodel op testdata

In this chapter we will look at modeling algorithms that do not assume linearity or additivity, and that can learn limited types of interactions among input variables. These algorithms are *tree-based* methods that work by combining ensembles of *decision trees* that are learned from the training data.

Exercise 1: The intuition behind tree-based methods Exercise 2: Predicting with a decision tree Exercise 3: Random forests Exercise 4: Build a random forest model for bike rentals Exercise 5: Predict bike rentals with the random forest model Exercise 6: Visualize random forest bike model predictions Exercise 7: One-Hot-Encoding Categorical Variables Exercise 8: vtreat on a small example Exercise 9: Novel levels Exercise 10: vtreat the bike rental data Exercise 11: Gradient boosting machines Exercise 12: Find the right number of trees for a gradient boosting machine Exercise 13: Fit an xgboost bike rental model and predict Exercise 14: Evaluate the xgboost bike rental model Exercise 15: Visualize the xgboost bike rental model