Methods and xspliner environment

Krystian Igras

2018-12-12

Predict

As xspliner final model is GLM, predict method is just wrapper of stats::predict.glm function. Let’s see it on the below example:

library(xspliner)
library(randomForest)
library(magrittr)

rf_iris <- randomForest(Petal.Width ~  Sepal.Length + Petal.Length + Species, data = iris)
model_xs <- xspline(Petal.Width ~ 
  Sepal.Length + 
  xs(Petal.Length, effect = list(grid.resolution = 100), transition = list(bs = "cr")) + 
  xf(Species, transition = list(stat = "loglikelihood", value = -300)),
  model = rf_iris)
newdata <- data.frame(
  Sepal.Length = 10, 
  Petal.Length = 2, 
  Species = factor("virginica", levels = levels(iris$Species)))
predict(model_xs, newdata = newdata)
##          1 
## -0.4880222

Summary

Summary method allows you to check the basic model details. See below what possibilities the method to xspliner model offers.

GLM summary

Standard summary method is just wrapper for summary::glm. In order to use this just type:

## 
## Call:
## glm(formula = Petal.Width ~ Sepal.Length + xs(Petal.Length) + 
##     xf(Species), family = family, data = data)
## 
## Deviance Residuals: 
##      Min        1Q    Median        3Q       Max  
## -0.68325  -0.07925  -0.02485   0.10265   0.50723  
## 
## Coefficients:
##                                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                    -1.99718    0.14136 -14.128  < 2e-16 ***
## Sepal.Length                   -0.01340    0.03652  -0.367    0.714    
## xs(Petal.Length)                3.21878    0.22377  14.384  < 2e-16 ***
## xf(Species)versicolorvirginica -0.73479    0.12926  -5.685  6.9e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for gaussian family taken to be 0.03553466)
## 
##     Null deviance: 86.5699  on 149  degrees of freedom
## Residual deviance:  5.1881  on 146  degrees of freedom
## AIC: -68.96
## 
## Number of Fisher Scoring iterations: 2

Predictor based summary

Summary method allows you to check details about transformation of specific variable.

Standard usage summary(xspliner_object, variable_name)

Quantitative variable When predictor is quantitative variable its transition is based on GAM model. For this case summary displays summary of that model.

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## yhat ~ s(Petal.Length, bs = "cr")
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.20307    0.00397     303   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                   edf Ref.df     F p-value    
## s(Petal.Length) 8.816   8.99 637.1  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.983   Deviance explained = 98.5%
## GCV = 0.0017478  Scale est. = 0.0015762  n = 100

Qualitative variable

In case of qualitative predictor, the method displays data.frame storing information how factors were merged during the transition.

##         orig                pred
## 1     setosa              setosa
## 2 versicolor versicolorvirginica
## 3  virginica versicolorvirginica

Print

Print method works similarly to the summary. In case of passing just the model, standard print.glm is used.

print(model_xs)
## 
## Call:  glm(formula = Petal.Width ~ Sepal.Length + xs(Petal.Length) + 
##     xf(Species), family = family, data = data)
## 
## Coefficients:
##                    (Intercept)                    Sepal.Length  
##                        -1.9972                         -0.0134  
##               xs(Petal.Length)  xf(Species)versicolorvirginica  
##                         3.2188                         -0.7348  
## 
## Degrees of Freedom: 149 Total (i.e. Null);  146 Residual
## Null Deviance:       86.57 
## Residual Deviance: 5.188     AIC: -68.96

Predictor based print

Summary method allows you to check details about transformation of specific variable.

Standard usage print(xspliner_object, variable_name)

Quantitative variable When predictor is the quantitative variable its transition is based on GAM model. For this case print uses standard print.gam method.

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## yhat ~ s(Petal.Length, bs = "cr")
## 
## Estimated degrees of freedom:
## 8.82  total = 9.82 
## 
## GCV score: 0.001747755

Qualitative variable

In case of qualitative predictor, standard print.factorMerger method is used.

## Family: gaussian Factor Merger.
## 
## Factor levels were merged in the following order:
## 
##      groupA       groupB                     model   pvalVsFull   pvalVsPrevious
## ---  -----------  --------------------  ----------  -----------  ---------------
## 0                                        -262.1572            1                1
## 1    versicolor   virginica              -278.4864            0                0
## 2    setosa       versicolorvirginica    -354.2443            0                0

Plot

You can see all details in graphics

Transition

Transition method allows you to extract objects used during building transition of variables. There are three possible object types that can be extracted.

Extracting effect

Each transition is built on top of the black box response data. For example the default response for quantitative variables is PDP - for qualitative ones ICE.

In order to extract the effect use transition method with type parameter equals to data

##   Petal.Length      yhat
## 1     1.000000 0.7103410
## 2     1.059596 0.7102940
## 3     1.119192 0.7102940
## 4     1.178788 0.7139648
## 5     1.238384 0.7152855
## 6     1.297980 0.7179491
##      Species      yhat yhat.id
## 1     setosa 0.2433265       1
## 2 versicolor 0.6857316       1
## 3  virginica 0.8473016       1
## 4     setosa 0.2157995       2
## 5 versicolor 0.6870610       2
## 6  virginica 0.8488110       2

Extracting transition model

After we built transition basing on continuity of variable specific model is created. In case of quantitative predictor we build GAM model in order to get spline approximation of effect. In case of qualitative predictor we build factorMerger object and get optimal factor division on that.

To extract the model, use transition method with type = "base":

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## yhat ~ s(Petal.Length, bs = "cr")
## 
## Estimated degrees of freedom:
## 8.82  total = 9.82 
## 
## GCV score: 0.001747755
## Family: gaussian Factor Merger.
## 
## Factor levels were merged in the following order:
## 
##      groupA       groupB                     model   pvalVsFull   pvalVsPrevious
## ---  -----------  --------------------  ----------  -----------  ---------------
## 0                                        -262.1572            1                1
## 1    versicolor   virginica              -278.4864            0                0
## 2    setosa       versicolorvirginica    -354.2443            0                0

Extracting transition function

The final result of building transition is transformation function, that is used in the final GLM model estimation.

To extract the function just use transition method with type = "function".

## [1] setosa              versicolorvirginica versicolorvirginica
## Levels: setosa versicolorvirginica