Ejercicio multicolinealidad
Fabio Feliciano Abarca Espinoza AE17013 GT 03
27/5/2021
Importacion de datos
library(wooldridge)
data(hprice1)
head(force(hprice1),n=5)## price assess bdrms lotsize sqrft colonial lprice lassess llotsize lsqrft
## 1 300 349.1 4 6126 2438 1 5.703783 5.855359 8.720297 7.798934
## 2 370 351.5 3 9903 2076 1 5.913503 5.862210 9.200593 7.638198
## 3 191 217.7 3 5200 1374 0 5.252274 5.383118 8.556414 7.225482
## 4 195 231.8 3 4600 1448 1 5.273000 5.445875 8.433811 7.277938
## 5 373 319.1 4 6095 2514 1 5.921578 5.765504 8.715224 7.829630Estimando el modelo
library(stargazer)
modelo_estimado<-lm(formula = price~lotsize+sqrft+bdrms, data = hprice1)
stargazer(modelo_estimado, title = 'Modelo Estimado', type= 'text')##
## Modelo Estimado
## ===============================================
## Dependent variable:
## ---------------------------
## price
## -----------------------------------------------
## lotsize 0.002***
## (0.001)
##
## sqrft 0.123***
## (0.013)
##
## bdrms 13.853
## (9.010)
##
## Constant -21.770
## (29.475)
##
## -----------------------------------------------
## Observations 88
## R2 0.672
## Adjusted R2 0.661
## Residual Std. Error 59.833 (df = 84)
## F Statistic 57.460*** (df = 3; 84)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01Calcular la matrix |Xt X|
library(stargazer)
X_mat<-model.matrix(modelo_estimado)
stargazer(head(X_mat,n=6),type="text")##
## =================================
## (Intercept) lotsize sqrft bdrms
## ---------------------------------
## 1 1 6,126 2,438 4
## 2 1 9,903 2,076 3
## 3 1 5,200 1,374 3
## 4 1 4,600 1,448 3
## 5 1 6,095 2,514 4
## 6 1 8,566 2,754 5
## ---------------------------------XX_matrix<-t(X_mat)%*%X_mat
stargazer(XX_matrix,type = "text")##
## ==============================================================
## (Intercept) lotsize sqrft bdrms
## --------------------------------------------------------------
## (Intercept) 88 793,748 177,205 314
## lotsize 793,748 16,165,159,010 1,692,290,257 2,933,767
## sqrft 177,205 1,692,290,257 385,820,561 654,755
## bdrms 314 2,933,767 654,755 1,182
## --------------------------------------------------------------Indice de Condicion
Normalizacion |XtX|calculo de la matriz Sn
library(stargazer)
options(scipen = 999)
Sn<-solve(diag(sqrt(diag(XX_matrix))))
stargazer(Sn,type = "text")##
## ==========================
## 0.107 0 0 0
## 0 0.00001 0 0
## 0 0 0.0001 0
## 0 0 0 0.029
## --------------------------|Xt X|Normalizada:
library(stargazer)
XX_norm<-(Sn%*%XX_matrix)%*%Sn
stargazer(XX_norm,type = "text",digits = 4)##
## ===========================
## 1 0.6655 0.9617 0.9736
## 0.6655 1 0.6776 0.6712
## 0.9617 0.6776 1 0.9696
## 0.9736 0.6712 0.9696 1
## ---------------------------Calculo del indice de condición
Auto valores de |Xt X|Normalizada
library(stargazer)
#autovalores
lambdas<-eigen(XX_norm,symmetric = TRUE)
stargazer(lambdas$values,type = "text")##
## =======================
## 3.482 0.455 0.039 0.025
## -----------------------Calculo de k(x)
K<-sqrt(max(lambdas$values)/min(lambdas$values))
print(K)## [1] 11.86778Con un indice de k(x) = 11.86778 se puede decir que nuestro modelo tiene multicolinealidad leve.
Obtencion del indice de condición
library(mctest)
eigprop(mod = modelo_estimado)##
## Call:
## eigprop(mod = modelo_estimado)
##
## Eigenvalues CI (Intercept) lotsize sqrft bdrms
## 1 3.4816 1.0000 0.0037 0.0278 0.0042 0.0029
## 2 0.4552 2.7656 0.0068 0.9671 0.0061 0.0051
## 3 0.0385 9.5082 0.4726 0.0051 0.8161 0.0169
## 4 0.0247 11.8678 0.5170 0.0000 0.1737 0.9750
##
## ===============================
## Row 2==> lotsize, proportion 0.967080 >= 0.50
## Row 3==> sqrft, proportion 0.816079 >= 0.50
## Row 4==> bdrms, proportion 0.975026 >= 0.50Prueba de Farrar-Glaubar
NORMALIZAR LA MATRIZ X
library(stargazer)
Zn<-scale(X_mat[,-1])
stargazer(head(Zn,n=6),type = "text")##
## =======================
## lotsize sqrft bdrms
## -----------------------
## 1 -0.284 0.735 0.513
## 2 0.087 0.108 -0.675
## 3 -0.375 -1.108 -0.675
## 4 -0.434 -0.980 -0.675
## 5 -0.287 0.867 0.513
## 6 -0.045 1.283 1.702
## -----------------------CALCULAR LA MATRIZ R
library(stargazer)
n<-nrow(Zn)
R<-(t(Zn)%*%Zn)*(1/(n-1))
stargazer(R,type = "text",digits = 4)##
## =============================
## lotsize sqrft bdrms
## -----------------------------
## lotsize 1 0.1838 0.1363
## sqrft 0.1838 1 0.5315
## bdrms 0.1363 0.5315 1
## -----------------------------CALCULAR |R|
determinante_R<-det(R)
print(determinante_R)## [1] 0.6917931Aplicando la prueba de FG
Estadistico χ2FG
m<-ncol(X_mat[,-1])
n<-nrow(X_mat[,-1])
chi_FG<--(n-1-(2*m+5)/6)*log(determinante_R)
print(chi_FG)## [1] 31.38122# Valor Critico
gl<-m*(m-1)/2
VC<-qchisq(p=0.95, df= gl)
print(VC)## [1] 7.814728library(fastGraph)
shadeDist(chi_FG, ddist = 'dchisq',parm1 = VC,lower.tail = FALSE, sub=paste("VC:",VC,"FG:",chi_FG))
Como χ2FG > VC se rechaza la hipotesis nula y se dice que existe evidencia de multicolinealidad.
Calculando los VIF
Matriz de correlación de los regresores del modelo
print(R)## lotsize sqrft bdrms
## lotsize 1.0000000 0.1838422 0.1363256
## sqrft 0.1838422 1.0000000 0.5314736
## bdrms 0.1363256 0.5314736 1.0000000Inversa de la matriz de correlacion R−1
inversa_R<-solve(R)
print(inversa_R)## lotsize sqrft bdrms
## lotsize 1.03721145 -0.1610145 -0.05582352
## sqrft -0.16101454 1.4186543 -0.73202696
## bdrms -0.05582352 -0.7320270 1.39666321VIF’s para el modelo estimado
VIFs<-diag(inversa_R)
print(VIFs)## lotsize sqrft bdrms
## 1.037211 1.418654 1.396663Obtención de los VIF’s
library(mctest)
mc.plot(modelo_estimado,vif = 2)