To illustrate applications of auditor to regression problems we will use an artificial dataset apartments available in the DALEX package. Our goal is to predict the price per square meter of an apartment based on selected features such as construction year, surface, floor, number of rooms, district. It should be noted that four of these variables are continuous while the fifth one is a categorical one. Prices are given in Euro.
library(DALEX)
data("apartments")
head(apartments)
## m2.price construction.year surface floor no.rooms district
## 1 5897 1953 25 3 1 Srodmiescie
## 2 1818 1992 143 9 5 Bielany
## 3 3643 1937 56 1 2 Praga
## 4 3517 1995 93 7 3 Ochota
## 5 3013 1992 144 6 5 Mokotow
## 6 5795 1926 61 6 2 Srodmiescie
lm_model <- lm(m2.price ~ construction.year + surface + floor + no.rooms + district, data = apartments)
library("randomForest")
set.seed(59)
rf_model <- randomForest(m2.price ~ construction.year + surface + floor + no.rooms + district, data = apartments)
The beginning of each analysis is creation of a modelAudit object. It’s an object that can be used to audit a model.
library("auditor")
lm_audit <- audit(lm_model, label = "lm", data = apartmentsTest, y = apartmentsTest$m2.price)
rf_audit <- audit(rf_model, label = "rf", data = apartmentsTest, y = apartmentsTest$m2.price)
In this section we give short overview of a visual validation of model errors and show the propositions for the validation scores. Auditor helps to find answers for questions that may be crucial for further analyses.
Does the model fit data? Is it not missing the information?
Which model has better performance?
How similar models are?
In further sections, we overview auditor functions for analysis of model residuals. They are discussed in alphabetical order.
The auditor provides 2 pipelines of observation influence audit.
model %>% audit() %>% observationInfluence() %>% plot(type=…)
This pipeline is recommended. Function observationInfluence() creates a observationInfluence object. Such object may be passed to a plot() function with defined type of plot. This approach requires one additional function within the pipeline. However, once created observationInfluence contains all nessesary calculations that all plots require. Therefore, generating multiple plots is fast. It is usefull as caluclating Coook's distances for models gifferent than liner may take a lot of time.
Alternative: model %>% audit() %>% observationInfluence() %>% plotType()
model %>% audit() %>% plot(type=…)
This pipeline is shorter than previous one. Calculations are carried out every time a function is called. However, it is faster to use.
Alternative model %>% audit() %>% plotType()
Help of functions plot[Type]() contains additional information about plots.
In this vignette we use first pipeline.
First, we need to create a modelResiduals objects.
lm_oi <- observationInfluence(lm_audit)
head(lm_oi)
## cooks.dist label index
## 320 0.003634294 lm 320
## 1320 0.003634294 lm 1320
## 2320 0.003634294 lm 2320
## 3320 0.003634294 lm 3320
## 4320 0.003634294 lm 4320
## 5320 0.003634294 lm 5320
Some plots may require specified variable or fitted values for modelResidual object.
Cook's distance is used to estimate of the influence of an single observation. It is a tool for identifying observations that may negatively affect the model.
Data points indicated by Cook's distances are worth checking for validity. Cook's distances may be also used for indicating regions of the design space where it would be good to obtain more observations.
Cook’s Distances are calculated by removing the i-th observation from the data and recalculating the model. It shows how much all the values in the model change when the i-th observation is removed.
In the case of models of classes other than lm and glm the distances are computed directly from the definition, so this may take a while.
In this example we will compute them for a linear model.
plot(lm_oi)
Other methods and plots are described in vignettes: