10 Regresión Spline adaptativa multivariante (MARS)

Paquetes de esta sección

if(!require(ISLR)){install.packages("earth")}
if(!require(ISLR)){install.packages("caret")}
if(!require(ISLR)){install.packages("AmesHousing")}

  • En las clases pasadas hemos revisado extensiones de la regresión linear (nls, regresión polinómica, entre otras).

  • Existen otras variaciones como la regresión Ridge, LASSO y Elastic NET (algunas se verán en el módulo de Aprendizaje Automático).

10.1 Introducción

  • En estadística, MARS es una forma de regresión lineal introducida por Jorome Friedan en 1991.

  • MARS es una técnica de regresión no paramétrica y puede ser vista como una extensión de los modelos lineales que automáticamente no linealidades e interacciones entre variables.

  • El término MARS está protegido por derechos de autor y pertenece a Salford Systems.

  • Para evitar violentar esos derechos, las implementaciones abiertas de MARS se suelen llamar Earth (El paquete earth en R, por ejemplo).

  • La Regresión Spline adaptativa multivariante (Multivariate adaptive regression spline - MARS)

10.1.1 ¿Por qué usar modelos MARS?

  • MARS es ideal para usuarios que prefieren obtener resultados similares a la regresión tradicional mientras capturan no linealidades e interacciones necesarias.

  • MARS revela patrones importantes en los datos que otras técnicas suelen fallar en revelar.

  • MARS construye su modelo uniendo pedazos de líneas rectas que mantienen su propia pendiente.

  • Esto permite que se detecte cualquier patrón en los datos.

  • Se puede utilizar para cuando se tiene variables de respuesta cuantitativa y cualitativa.

  • MARS realiza (todo automático y con gran velocidad):

    • selección de variables.
    • transformación de variables.
    • detección de interacciones.
    • testeo

Áreas donde ha mostrado ser una técnica exitosa

  • Predicción de demanda de electricidad de companías generadoras.
  • Relacionar puntajes de satisfacción del cliente con las especificaciones técnicas del producto.
  • Modelización en sistemas de información geográfica.
Fuente: ESLII
Fuente: ESLII
  • MARS es una técnica de regresión muy versátil y es una herramienta necesaria en nuestra caja de herramientas en Analítica de Datos.

10.1.2 La estrucura de MARS

Fuente: Yaseena2018
Fuente: Yaseena2018

10.2 Ejemplo 1

Cargamos los datos:

library(earth)
## Loading required package: Formula
## Loading required package: plotmo
## Loading required package: plotrix
load("~/Documents/Consultorias&Cursos/DataLectures/banckfull.RData")

Construimos el modelo basado en los datos:

mars <- earth(y~age+job+marital+education+default+balance+housing+
loan+contact+day+month+duration+campaign+pdays+previous+poutcome,
data=bankfull,pmethod="backward",nprune=20, nfold=10)

Notemos los argumentos usando en la función:

  • pmethod: Es el método para podar las variables regresoras. Las opciones son backward, forward, cv (se necesita especificar nfold), y exhaustive.
  • nprune: Numero máximo de funciones base que se usan.

En resumen, para plantear el modelo, necesitamos 3 elementos:

  1. Definir el modelo (como en cualquier regresión)
  2. Definir el método de testeo (pmethod)
  3. Número de funciones base (nprune) y de interacciones (degree)

Veamos el resumen:

summary(mars,digit=3)
## Call: earth(formula=y~age+job+marital+education+default+balance+housin...), data=bankfull,
##             pmethod="backward", nprune=20, nfold=10)
## 
##                  coefficients
## (Intercept)            0.7775
## housingyes            -0.0408
## loanyes               -0.0294
## contactunknown        -0.0713
## monthdec               0.1876
## monthjun               0.0519
## monthmar               0.3301
## monthoct               0.1916
## monthsep               0.1789
## poutcomesuccess        0.3809
## h(age-27)              0.0072
## h(54-age)              0.0087
## h(duration-375)        0.0003
## h(1080-duration)      -0.0004
## h(duration-1080)      -0.0004
## h(2-campaign)          0.0268
## h(pdays-53)           -0.0020
## h(349-pdays)          -0.0016
## h(pdays-349)           0.0061
## h(pdays-425)          -0.0044
## 
## Selected 20 of 22 terms, and 13 of 42 predictors (nprune=20)
## Termination condition: RSq changed by less than 0.001 at 22 terms
## Importance: duration, poutcomesuccess, monthmar, housingyes, monthoct, contactunknown, ...
## Number of terms at each degree of interaction: 1 19 (additive model)
## GCV 0.0707  RSS 3192  GRSq 0.315  RSq 0.316  CVRSq 0.316
## 
## Note: the cross-validation sd's below are standard deviations across folds
## 
## Cross validation:   nterms 22.40 sd 1.65    nvars 14.10 sd 1.52
## 
##      CVRSq    sd     ClassRate    sd     MaxErr   sd
##      0.316 0.013         0.901 0.002      -1.26 1.06

El gráfico de resultado:

plotd(mars)

El GCV (generalized cross validation) es

\[ GCV = \frac{RSS}{N\times (1-Num.Par.Efectivos/N)^2} \]

donde RSS es la suma de cuadrados de los residuos medidos en los datos de entrenamiento y N es el número de observaciones.

\[ Num.Par.Efectivos = NumeroTerminosMARS + Penalidad\times (NumeroTerminosMARS-1)/2 \]

La penalidad es alrededor de 2 o 3, pero se puede elegir la penalidad.

10.2.1 Output

El objeto de resultado es un earth.object que contiene mucha información (ver help(earth.object).

str(mars)
## List of 39
##  $ rss                      : num 3192
##  $ rsq                      : num 0.316
##  $ gcv                      : num 0.0707
##  $ grsq                     : num 0.315
##  $ bx                       : num [1:45211, 1:20] 1 1 1 1 1 1 1 1 1 1 ...
##   ..- attr(*, "dimnames")=List of 2
##   .. ..$ : NULL
##   .. ..$ : chr [1:20] "(Intercept)" "h(duration-1080)" "h(1080-duration)" "poutcomesuccess" ...
##  $ dirs                     : num [1:22, 1:42] 0 0 0 0 0 0 0 0 0 1 ...
##   ..- attr(*, "dimnames")=List of 2
##   .. ..$ : chr [1:22] "(Intercept)" "h(duration-1080)" "h(1080-duration)" "poutcomesuccess" ...
##   .. ..$ : chr [1:42] "age" "jobblue-collar" "jobentrepreneur" "jobhousemaid" ...
##  $ cuts                     : num [1:22, 1:42] 0 0 0 0 0 0 0 0 0 54 ...
##   ..- attr(*, "dimnames")=List of 2
##   .. ..$ : chr [1:22] "(Intercept)" "h(duration-1080)" "h(1080-duration)" "poutcomesuccess" ...
##   .. ..$ : chr [1:42] "age" "jobblue-collar" "jobentrepreneur" "jobhousemaid" ...
##  $ selected.terms           : num [1:20] 1 2 3 4 5 6 7 8 9 11 ...
##  $ prune.terms              : num [1:22, 1:22] 1 1 1 1 1 1 1 1 1 1 ...
##  $ fitted.values            : num [1:45211, 1] 0.0261 -0.0314 -0.074 -0.0597 0.0452 ...
##   ..- attr(*, "dimnames")=List of 2
##   .. ..$ : NULL
##   .. ..$ : chr "yes"
##  $ residuals                : num [1:45211, 1] -0.0261 0.0314 0.074 0.0597 -0.0452 ...
##   ..- attr(*, "dimnames")=List of 2
##   .. ..$ : NULL
##   .. ..$ : chr "yes"
##  $ coefficients             : num [1:20, 1] 0.777457 -0.000382 -0.000402 0.380944 0.330111 ...
##   ..- attr(*, "dimnames")=List of 2
##   .. ..$ : chr [1:20] "(Intercept)" "h(duration-1080)" "h(1080-duration)" "poutcomesuccess" ...
##   .. ..$ : chr "yes"
##  $ rss.per.response         : num 3192
##  $ rsq.per.response         : num 0.316
##  $ gcv.per.response         : num 0.0707
##  $ grsq.per.response        : num 0.315
##  $ rss.per.subset           : num [1:22] 4670 3880 3497 3433 3378 ...
##  $ gcv.per.subset           : num [1:22] 0.1033 0.0858 0.0774 0.076 0.0747 ...
##  $ leverages                : num [1:45211] 0.000243 0.000165 0.000299 0.000194 0.00025 ...
##  $ pmethod                  : chr "backward"
##  $ nprune                   : num 20
##  $ penalty                  : num 2
##  $ nk                       : num 85
##  $ thresh                   : num 0.001
##  $ termcond                 : int 4
##  $ weights                  : NULL
##  $ call                     : language earth(formula = y ~ age + job + marital + education + default + balance + housing + loan +      contact + day + m| __truncated__ ...
##  $ namesx                   : chr [1:16] "age" "job" "marital" "education" ...
##  $ modvars                  : num [1:16, 1:42] 1 0 0 0 0 0 0 0 0 0 ...
##   ..- attr(*, "dimnames")=List of 2
##   .. ..$ : chr [1:16] "age" "job" "marital" "education" ...
##   .. ..$ : chr [1:42] "age" "jobblue-collar" "jobentrepreneur" "jobhousemaid" ...
##  $ terms                    :Classes 'terms', 'formula'  language y ~ age + job + marital + education + default + balance + housing + loan + contact + day +      month + duration | __truncated__
##   .. ..- attr(*, "variables")= language list(y, age, job, marital, education, default, balance, housing, loan, contact, day, month,      duration, campai| __truncated__
##   .. ..- attr(*, "factors")= int [1:17, 1:16] 0 1 0 0 0 0 0 0 0 0 ...
##   .. .. ..- attr(*, "dimnames")=List of 2
##   .. .. .. ..$ : chr [1:17] "y" "age" "job" "marital" ...
##   .. .. .. ..$ : chr [1:16] "age" "job" "marital" "education" ...
##   .. ..- attr(*, "term.labels")= chr [1:16] "age" "job" "marital" "education" ...
##   .. ..- attr(*, "order")= int [1:16] 1 1 1 1 1 1 1 1 1 1 ...
##   .. ..- attr(*, "intercept")= int 1
##   .. ..- attr(*, "response")= int 1
##   .. ..- attr(*, ".Environment")=<environment: R_GlobalEnv> 
##   .. ..- attr(*, "predvars")= language list(y, age, job, marital, education, default, balance, housing, loan, contact, day, month,      duration, campai| __truncated__
##   .. ..- attr(*, "dataClasses")= Named chr [1:17] "factor" "numeric" "factor" "factor" ...
##   .. .. ..- attr(*, "names")= chr [1:17] "y" "age" "job" "marital" ...
##  $ xlevels                  :List of 9
##   ..$ job      : chr [1:12] "admin." "blue-collar" "entrepreneur" "housemaid" ...
##   ..$ marital  : chr [1:3] "divorced" "married" "single"
##   ..$ education: chr [1:4] "primary" "secondary" "tertiary" "unknown"
##   ..$ default  : chr [1:2] "no" "yes"
##   ..$ housing  : chr [1:2] "no" "yes"
##   ..$ loan     : chr [1:2] "no" "yes"
##   ..$ contact  : chr [1:3] "cellular" "telephone" "unknown"
##   ..$ month    : chr [1:12] "apr" "aug" "dec" "feb" ...
##   ..$ poutcome : chr [1:4] "failure" "other" "success" "unknown"
##  $ levels                   : chr [1:2] "no" "yes"
##  $ cv.list                  :List of 10
##   ..$ fold1 :List of 29
##   .. ..$ rss              : num 2854
##   .. ..$ rsq              : num 0.321
##   .. ..$ gcv              : num 0.0703
##   .. ..$ grsq             : num 0.319
##   .. ..$ dirs             : num [1:25, 1:42] 0 0 0 0 0 0 0 0 0 1 ...
##   .. .. ..- attr(*, "dimnames")=List of 2
##   .. .. .. ..$ : chr [1:25] "(Intercept)" "h(duration-1125)" "h(1125-duration)" "poutcomesuccess" ...
##   .. .. .. ..$ : chr [1:42] "age" "jobblue-collar" "jobentrepreneur" "jobhousemaid" ...
##   .. ..$ cuts             : num [1:25, 1:42] 0 0 0 0 0 0 0 0 0 53 ...
##   .. .. ..- attr(*, "dimnames")=List of 2
##   .. .. .. ..$ : chr [1:25] "(Intercept)" "h(duration-1125)" "h(1125-duration)" "poutcomesuccess" ...
##   .. .. .. ..$ : chr [1:42] "age" "jobblue-collar" "jobentrepreneur" "jobhousemaid" ...
##   .. ..$ selected.terms   : num [1:24] 1 2 3 4 5 6 7 8 9 10 ...
##   .. ..$ fitted.values    : num [1:40681, 1] 0.0448 -0.0398 -0.0564 -0.0508 0.0309 ...
##   .. .. ..- attr(*, "dimnames")=List of 2
##   .. .. .. ..$ : NULL
##   .. .. .. ..$ : chr "yes"
##   .. ..$ coefficients     : num [1:24, 1] 0.575313 -0.000394 -0.000398 0.376758 0.330166 ...
##   .. .. ..- attr(*, "dimnames")=List of 2
##   .. .. .. ..$ : chr [1:24] "(Intercept)" "h(duration-1125)" "h(1125-duration)" "poutcomesuccess" ...
##   .. .. .. ..$ : chr "yes"
##   .. ..$ rss.per.response : num 2854
##   .. ..$ rsq.per.response : num 0.321
##   .. ..$ gcv.per.response : num 0.0703
##   .. ..$ grsq.per.response: num 0.319
##   .. ..$ rss.per.subset   : num [1:25] 4203 3485 3141 3080 3031 ...
##   .. ..$ gcv.per.subset   : num [1:25] 0.1033 0.0857 0.0772 0.0757 0.0745 ...
##   .. ..$ leverages        : num [1:40681] 0.000325 0.000191 0.000224 0.000238 0.000293 ...
##   .. ..$ pmethod          : chr "backward"
##   .. ..$ nprune           : NULL
##   .. ..$ penalty          : num 2
##   .. ..$ nk               : num 85
##   .. ..$ thresh           : num 0.001
##   .. ..$ termcond         : int 4
##   .. ..$ weights          : NULL
##   .. ..$ call             : language earth(x = infold.x, y = infold.y, weights = infold.weights, wp = wp, subset = subset, pmethod = if (pmethod ==   | __truncated__ ...
##   .. ..$ namesx           : chr [1:42] "age" "jobblue-collar" "jobentrepreneur" "jobhousemaid" ...
##   .. ..$ modvars          : num [1:42, 1:42] 1 0 0 0 0 0 0 0 0 0 ...
##   .. .. ..- attr(*, "dimnames")=List of 2
##   .. .. .. ..$ : chr [1:42] "age" "jobblue-collar" "jobentrepreneur" "jobhousemaid" ...
##   .. .. .. ..$ : chr [1:42] "age" "jobblue-collar" "jobentrepreneur" "jobhousemaid" ...
##   .. ..$ levels           : num [1:2] 0 1
##   .. ..$ icross           : int 1
##   .. ..$ ifold            : int 1
##   .. ..- attr(*, "class")= chr "earth"
##   ..$ fold2 :List of 29
##   .. ..$ rss              : num 2863
##   .. ..$ rsq              : num 0.319
##   .. ..$ gcv              : num 0.0705
##   .. ..$ grsq             : num 0.317
##   .. ..$ dirs             : num [1:24, 1:42] 0 0 0 0 0 0 0 0 0 1 ...
##   .. .. ..- attr(*, "dimnames")=List of 2
##   .. .. .. ..$ : chr [1:24] "(Intercept)" "h(duration-1080)" "h(1080-duration)" "poutcomesuccess" ...
##   .. .. .. ..$ : chr [1:42] "age" "jobblue-collar" "jobentrepreneur" "jobhousemaid" ...
##   .. ..$ cuts             : num [1:24, 1:42] 0 0 0 0 0 0 0 0 0 53 ...
##   .. .. ..- attr(*, "dimnames")=List of 2
##   .. .. .. ..$ : chr [1:24] "(Intercept)" "h(duration-1080)" "h(1080-duration)" "poutcomesuccess" ...
##   .. .. .. ..$ : chr [1:42] "age" "jobblue-collar" "jobentrepreneur" "jobhousemaid" ...
##   .. ..$ selected.terms   : num [1:23] 1 2 3 4 5 6 7 8 9 10 ...
##   .. ..$ fitted.values    : num [1:40709, 1] 0.0433 -0.0429 -0.0567 -0.0536 0.0122 ...
##   .. .. ..- attr(*, "dimnames")=List of 2
##   .. .. .. ..$ : NULL
##   .. .. .. ..$ : chr "yes"
##   .. ..$ coefficients     : num [1:23, 1] 1.059987 -0.000351 -0.000399 0.371647 0.332723 ...
##   .. .. ..- attr(*, "dimnames")=List of 2
##   .. .. .. ..$ : chr [1:23] "(Intercept)" "h(duration-1080)" "h(1080-duration)" "poutcomesuccess" ...
##   .. .. .. ..$ : chr "yes"
##   .. ..$ rss.per.response : num 2863
##   .. ..$ rsq.per.response : num 0.319
##   .. ..$ gcv.per.response : num 0.0705
##   .. ..$ grsq.per.response: num 0.317
##   .. ..$ rss.per.subset   : num [1:24] 4203 3495 3151 3091 3041 ...
##   .. ..$ gcv.per.subset   : num [1:24] 0.1033 0.0859 0.0774 0.076 0.0747 ...
##   .. ..$ leverages        : num [1:40709] 0.000326 0.00019 0.000219 0.000236 0.00021 ...
##   .. ..$ pmethod          : chr "backward"
##   .. ..$ nprune           : NULL
##   .. ..$ penalty          : num 2
##   .. ..$ nk               : num 85
##   .. ..$ thresh           : num 0.001
##   .. ..$ termcond         : int 4
##   .. ..$ weights          : NULL
##   .. ..$ call             : language earth(x = infold.x, y = infold.y, weights = infold.weights, wp = wp, subset = subset, pmethod = if (pmethod ==   | __truncated__ ...
##   .. ..$ namesx           : chr [1:42] "age" "jobblue-collar" "jobentrepreneur" "jobhousemaid" ...
##   .. ..$ modvars          : num [1:42, 1:42] 1 0 0 0 0 0 0 0 0 0 ...
##   .. .. ..- attr(*, "dimnames")=List of 2
##   .. .. .. ..$ : chr [1:42] "age" "jobblue-collar" "jobentrepreneur" "jobhousemaid" ...
##   .. .. .. ..$ : chr [1:42] "age" "jobblue-collar" "jobentrepreneur" "jobhousemaid" ...
##   .. ..$ levels           : num [1:2] 0 1
##   .. ..$ icross           : int 1
##   .. ..$ ifold            : int 2
##   .. ..- attr(*, "class")= chr "earth"
##   ..$ fold3 :List of 29
##   .. ..$ rss              : num 2867
##   .. ..$ rsq              : num 0.318
##   .. ..$ gcv              : num 0.0706
##   .. ..$ grsq             : num 0.317
##   .. ..$ dirs             : num [1:22, 1:42] 0 0 0 0 0 0 0 0 0 1 ...
##   .. .. ..- attr(*, "dimnames")=List of 2
##   .. .. .. ..$ : chr [1:22] "(Intercept)" "h(duration-1077)" "h(1077-duration)" "poutcomesuccess" ...
##   .. .. .. ..$ : chr [1:42] "age" "jobblue-collar" "jobentrepreneur" "jobhousemaid" ...
##   .. ..$ cuts             : num [1:22, 1:42] 0 0 0 0 0 0 0 0 0 54 ...
##   .. .. ..- attr(*, "dimnames")=List of 2
##   .. .. .. ..$ : chr [1:22] "(Intercept)" "h(duration-1077)" "h(1077-duration)" "poutcomesuccess" ...
##   .. .. .. ..$ : chr [1:42] "age" "jobblue-collar" "jobentrepreneur" "jobhousemaid" ...
##   .. ..$ selected.terms   : num [1:21] 1 2 3 4 5 6 7 8 9 10 ...
##   .. ..$ fitted.values    : num [1:40693, 1] 0.0274 -0.0336 -0.0557 -0.0595 0.034 ...
##   .. .. ..- attr(*, "dimnames")=List of 2
##   .. .. .. ..$ : NULL
##   .. .. .. ..$ : chr "yes"
##   .. ..$ coefficients     : num [1:21, 1] 0.680276 -0.000397 -0.000402 0.384156 0.325384 ...
##   .. .. ..- attr(*, "dimnames")=List of 2
##   .. .. .. ..$ : chr [1:21] "(Intercept)" "h(duration-1077)" "h(1077-duration)" "poutcomesuccess" ...
##   .. .. .. ..$ : chr "yes"
##   .. ..$ rss.per.response : num 2867
##   .. ..$ rsq.per.response : num 0.318
##   .. ..$ gcv.per.response : num 0.0706
##   .. ..$ grsq.per.response: num 0.317
##   .. ..$ rss.per.subset   : num [1:22] 4203 3488 3140 3083 3034 ...
##   .. ..$ gcv.per.subset   : num [1:22] 0.1033 0.0857 0.0772 0.0758 0.0746 ...
##   .. ..$ leverages        : num [1:40693] 0.000269 0.000178 0.000224 0.000212 0.000296 ...
##   .. ..$ pmethod          : chr "backward"
##   .. ..$ nprune           : NULL
##   .. ..$ penalty          : num 2
##   .. ..$ nk               : num 85
##   .. ..$ thresh           : num 0.001
##   .. ..$ termcond         : int 4
##   .. ..$ weights          : NULL
##   .. ..$ call             : language earth(x = infold.x, y = infold.y, weights = infold.weights, wp = wp, subset = subset, pmethod = if (pmethod ==   | __truncated__ ...
##   .. ..$ namesx           : chr [1:42] "age" "jobblue-collar" "jobentrepreneur" "jobhousemaid" ...
##   .. ..$ modvars          : num [1:42, 1:42] 1 0 0 0 0 0 0 0 0 0 ...
##   .. .. ..- attr(*, "dimnames")=List of 2
##   .. .. .. ..$ : chr [1:42] "age" "jobblue-collar" "jobentrepreneur" "jobhousemaid" ...
##   .. .. .. ..$ : chr [1:42] "age" "jobblue-collar" "jobentrepreneur" "jobhousemaid" ...
##   .. ..$ levels           : num [1:2] 0 1
##   .. ..$ icross           : int 1
##   .. ..$ ifold            : int 3
##   .. ..- attr(*, "class")= chr "earth"
##   ..$ fold4 :List of 29
##   .. ..$ rss              : num 2856
##   .. ..$ rsq              : num 0.321
##   .. ..$ gcv              : num 0.0704
##   .. ..$ grsq             : num 0.319
##   .. ..$ dirs             : num [1:24, 1:42] 0 0 0 0 0 0 0 0 0 1 ...
##   .. .. ..- attr(*, "dimnames")=List of 2
##   .. .. .. ..$ : chr [1:24] "(Intercept)" "h(duration-1130)" "h(1130-duration)" "poutcomesuccess" ...
##   .. .. .. ..$ : chr [1:42] "age" "jobblue-collar" "jobentrepreneur" "jobhousemaid" ...
##   .. ..$ cuts             : num [1:24, 1:42] 0 0 0 0 0 0 0 0 0 53 ...
##   .. .. ..- attr(*, "dimnames")=List of 2
##   .. .. .. ..$ : chr [1:24] "(Intercept)" "h(duration-1130)" "h(1130-duration)" "poutcomesuccess" ...
##   .. .. .. ..$ : chr [1:42] "age" "jobblue-collar" "jobentrepreneur" "jobhousemaid" ...
##   .. ..$ selected.terms   : num [1:23] 1 2 3 4 5 6 7 8 9 10 ...
##   .. ..$ fitted.values    : num [1:40674, 1] 0.0431 -0.0431 -0.0571 -0.0525 0.031 ...
##   .. .. ..- attr(*, "dimnames")=List of 2
##   .. .. .. ..$ : NULL
##   .. .. .. ..$ : chr "yes"
##   .. ..$ coefficients     : num [1:23, 1] 1.031902 -0.000392 -0.000398 0.375766 0.339415 ...
##   .. .. ..- attr(*, "dimnames")=List of 2
##   .. .. .. ..$ : chr [1:23] "(Intercept)" "h(duration-1130)" "h(1130-duration)" "poutcomesuccess" ...
##   .. .. .. ..$ : chr "yes"
##   .. ..$ rss.per.response : num 2856
##   .. ..$ rsq.per.response : num 0.321
##   .. ..$ gcv.per.response : num 0.0704
##   .. ..$ grsq.per.response: num 0.319
##   .. ..$ rss.per.subset   : num [1:24] 4203 3485 3141 3081 3031 ...
##   .. ..$ gcv.per.subset   : num [1:24] 0.1033 0.0857 0.0773 0.0758 0.0745 ...
##   .. ..$ leverages        : num [1:40674] 0.000332 0.000191 0.00022 0.000239 0.00029 ...
##   .. ..$ pmethod          : chr "backward"
##   .. ..$ nprune           : NULL
##   .. ..$ penalty          : num 2
##   .. ..$ nk               : num 85
##   .. ..$ thresh           : num 0.001
##   .. ..$ termcond         : int 4
##   .. ..$ weights          : NULL
##   .. ..$ call             : language earth(x = infold.x, y = infold.y, weights = infold.weights, wp = wp, subset = subset, pmethod = if (pmethod ==   | __truncated__ ...
##   .. ..$ namesx           : chr [1:42] "age" "jobblue-collar" "jobentrepreneur" "jobhousemaid" ...
##   .. ..$ modvars          : num [1:42, 1:42] 1 0 0 0 0 0 0 0 0 0 ...
##   .. .. ..- attr(*, "dimnames")=List of 2
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##   .. .. ..- attr(*, "dimnames")=List of 2
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##   .. .. ..- attr(*, "dimnames")=List of 2
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##   .. ..$ leverages        : num [1:40718] 0.000328 0.000186 0.00022 0.00029 0.00018 ...
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##   .. ..$ penalty          : num 2
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##   .. .. ..- attr(*, "dimnames")=List of 2
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##   .. .. ..- attr(*, "dimnames")=List of 2
##   .. .. .. ..$ : chr [1:21] "(Intercept)" "h(duration-1073)" "h(1073-duration)" "poutcomesuccess" ...
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##   .. ..$ pmethod          : chr "backward"
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##   .. .. .. ..$ : chr [1:42] "age" "jobblue-collar" "jobentrepreneur" "jobhousemaid" ...
##   .. ..$ selected.terms   : num [1:21] 1 2 3 4 5 6 7 8 9 10 ...
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##   .. .. ..- attr(*, "dimnames")=List of 2
##   .. .. .. ..$ : NULL
##   .. .. .. ..$ : chr "yes"
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##   .. .. ..- attr(*, "dimnames")=List of 2
##   .. .. .. ..$ : chr [1:21] "(Intercept)" "h(duration-1084)" "h(1084-duration)" "poutcomesuccess" ...
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##   .. ..$ rss.per.subset   : num [1:23] 4203 3499 3152 3095 3046 ...
##   .. ..$ gcv.per.subset   : num [1:23] 0.1033 0.086 0.0775 0.0761 0.0749 ...
##   .. ..$ leverages        : num [1:40689] 0.000314 0.000188 0.000219 0.000229 0.000289 ...
##   .. ..$ pmethod          : chr "backward"
##   .. ..$ nprune           : NULL
##   .. ..$ penalty          : num 2
##   .. ..$ nk               : num 85
##   .. ..$ thresh           : num 0.001
##   .. ..$ termcond         : int 4
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##   .. .. ..- attr(*, "dimnames")=List of 2
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##   .. .. ..- attr(*, "dimnames")=List of 2
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##   .. ..$ leverages        : num [1:40680] 0.000333 0.00019 0.000224 0.000239 0.000294 ...
##   .. ..$ pmethod          : chr "backward"
##   .. ..$ nprune           : NULL
##   .. ..$ penalty          : num 2
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##   .. .. ..- attr(*, "dimnames")=List of 2
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##   .. .. ..- attr(*, "dimnames")=List of 2
##   .. .. .. ..$ : chr [1:26] "(Intercept)" "h(duration-1076)" "h(1076-duration)" "poutcomesuccess" ...
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##   .. ..$ rss.per.subset   : num [1:29] 4203 3490 3153 3094 3045 ...
##   .. ..$ gcv.per.subset   : num [1:29] 0.1033 0.0858 0.0775 0.0761 0.0749 ...
##   .. ..$ leverages        : num [1:40692] 0.000323 0.000201 0.000241 0.000244 0.000322 ...
##   .. ..$ pmethod          : chr "backward"
##   .. ..$ nprune           : NULL
##   .. ..$ penalty          : num 2
##   .. ..$ nk               : num 85
##   .. ..$ thresh           : num 0.001
##   .. ..$ termcond         : int 4
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##   .. ..$ call             : language earth(x = infold.x, y = infold.y, weights = infold.weights, wp = wp, subset = subset, pmethod = if (pmethod ==   | __truncated__ ...
##   .. ..$ namesx           : chr [1:42] "age" "jobblue-collar" "jobentrepreneur" "jobhousemaid" ...
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##   .. ..$ levels           : num [1:2] 0 1
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##   .. ..$ rsq              : num 0.318
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##   .. ..$ grsq             : num 0.317
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##   .. .. .. ..$ : chr [1:42] "age" "jobblue-collar" "jobentrepreneur" "jobhousemaid" ...
##   .. ..$ cuts             : num [1:22, 1:42] 0 0 0 0 0 0 0 0 0 55 ...
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##   .. .. .. ..$ : chr [1:42] "age" "jobblue-collar" "jobentrepreneur" "jobhousemaid" ...
##   .. ..$ selected.terms   : num [1:21] 1 2 3 4 5 6 7 8 9 10 ...
##   .. ..$ fitted.values    : num [1:40689, 1] 0.0176 -0.062 0.0391 -0.0274 0.0615 ...
##   .. .. ..- attr(*, "dimnames")=List of 2
##   .. .. .. ..$ : NULL
##   .. .. .. ..$ : chr "yes"
##   .. ..$ coefficients     : num [1:21, 1] 0.962214 -0.000393 -0.000407 0.383956 0.322482 ...
##   .. .. ..- attr(*, "dimnames")=List of 2
##   .. .. .. ..$ : chr [1:21] "(Intercept)" "h(duration-1073)" "h(1073-duration)" "poutcomesuccess" ...
##   .. .. .. ..$ : chr "yes"
##   .. ..$ rss.per.response : num 2867
##   .. ..$ rsq.per.response : num 0.318
##   .. ..$ gcv.per.response : num 0.0706
##   .. ..$ grsq.per.response: num 0.317
##   .. ..$ rss.per.subset   : num [1:22] 4204 3492 3147 3089 3038 ...
##   .. ..$ gcv.per.subset   : num [1:22] 0.1033 0.0858 0.0774 0.0759 0.0747 ...
##   .. ..$ leverages        : num [1:40689] 0.000262 0.000208 0.000278 0.000176 0.000251 ...
##   .. ..$ pmethod          : chr "backward"
##   .. ..$ nprune           : NULL
##   .. ..$ penalty          : num 2
##   .. ..$ nk               : num 85
##   .. ..$ thresh           : num 0.001
##   .. ..$ termcond         : int 4
##   .. ..$ weights          : NULL
##   .. ..$ call             : language earth(x = infold.x, y = infold.y, weights = infold.weights, wp = wp, subset = subset, pmethod = if (pmethod ==   | __truncated__ ...
##   .. ..$ namesx           : chr [1:42] "age" "jobblue-collar" "jobentrepreneur" "jobhousemaid" ...
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##   .. .. ..- attr(*, "dimnames")=List of 2
##   .. .. .. ..$ : chr [1:42] "age" "jobblue-collar" "jobentrepreneur" "jobhousemaid" ...
##   .. .. .. ..$ : chr [1:42] "age" "jobblue-collar" "jobentrepreneur" "jobhousemaid" ...
##   .. ..$ levels           : num [1:2] 0 1
##   .. ..$ icross           : int 1
##   .. ..$ ifold            : int 10
##   .. ..- attr(*, "class")= chr "earth"
##  $ cv.nterms.selected.by.gcv: Named num [1:11] 24 23 21 23 22 21 21 22 26 21 ...
##   ..- attr(*, "names")= chr [1:11] "fold1" "fold2" "fold3" "fold4" ...
##  $ cv.nvars.selected.by.gcv : Named num [1:11] 15 14 13 14 13 13 14 13 18 14 ...
##   ..- attr(*, "names")= chr [1:11] "fold1" "fold2" "fold3" "fold4" ...
##  $ cv.groups                : int [1:45211, 1:2] 1 1 1 1 1 1 1 1 1 1 ...
##   ..- attr(*, "dimnames")=List of 2
##   .. ..$ : NULL
##   .. ..$ : chr [1:2] "cross" "fold"
##  $ cv.rsq.tab               : num [1:11, 1:2] 0.3 0.31 0.311 0.294 0.334 ...
##   ..- attr(*, "dimnames")=List of 2
##   .. ..$ : chr [1:11] "fold1" "fold2" "fold3" "fold4" ...
##   .. ..$ : chr [1:2] "yes" "mean"
##  $ cv.maxerr.tab            : num [1:11, 1:2] -1.09 -1.26 -1.14 -1.14 -1.04 ...
##   ..- attr(*, "dimnames")=List of 2
##   .. ..$ : chr [1:11] "fold1" "fold2" "fold3" "fold4" ...
##   .. ..$ : chr [1:2] "yes" "max"
##  $ cv.class.rate.tab        : num [1:11, 1:2] 0.899 0.9 0.904 0.898 0.903 ...
##   ..- attr(*, "dimnames")=List of 2
##   .. ..$ : NULL
##   .. ..$ : chr [1:2] "yes" "mean"
##  - attr(*, "class")= chr "earth"

De todos este conjunto, vamos a destacar 3 elementos

  1. Importancia de las variables
  2. Funciones base (modelo resultado)
  3. Curvas y superficie (contribución)

Importancia de las variables

library(caret)
varImp( mars  ) 
##                    Overall
## duration        100.000000
## poutcomesuccess  68.109084
## monthmar         45.171762
## housingyes       40.087272
## monthoct         35.114270
## contactunknown   31.401977
## monthsep         27.823303
## age              24.185852
## monthjun         21.090675
## pdays            16.010587
## monthdec         14.461722
## campaign         12.631608
## loanyes           5.779968

Funciones Base

mars$coefficients
##                            yes
## (Intercept)       0.7774569240
## h(duration-1080) -0.0003818948
## h(1080-duration) -0.0004020631
## poutcomesuccess   0.3809444003
## monthmar          0.3301108826
## housingyes       -0.0407997273
## monthoct          0.1916481210
## contactunknown   -0.0712999709
## monthsep          0.1788583816
## h(54-age)         0.0087017318
## h(duration-375)   0.0003026388
## monthjun          0.0518693660
## h(2-campaign)     0.0268377535
## monthdec          0.1876019796
## h(pdays-349)      0.0061454449
## h(349-pdays)     -0.0015968138
## h(age-27)         0.0071639964
## h(pdays-53)      -0.0020353430
## h(pdays-425)     -0.0043865936
## loanyes          -0.0293712807

Curvas y superficie

plotmo( mars,  all1 = T   ) 
##  plotmo grid:    age         job marital education default balance housing loan  contact day month
##                   39 blue-collar married secondary      no     448     yes   no cellular  16   may
##  duration campaign pdays previous poutcome
##       180        2    -1        0  unknown

plot(mars$fitted.values~bankfull$duration)

10.2.2 Tu turno

Sobre los datos ames_train ajusta un modelo MARS que tenga como variable dependiente al precio de venta Sale_Price.

library(rsample)
## 
## Attaching package: 'rsample'
## The following object is masked from 'package:e1071':
## 
##     permutations
# Create training (70%) and test (30%) sets for the AmesHousing::make_ames() data.
# Use set.seed for reproducibility

set.seed(123)
ames_split <- initial_split(AmesHousing::make_ames(), prop = .7, strata = "Sale_Price")
ames_train <- training(ames_split)
ames_test  <- testing(ames_split)