Carga de Datos
library(wooldridge)## Warning: package 'wooldridge' was built under R version 4.5.3data(hprice1)
head(force(hprice1),n=5) #mostrar las primeras 5 observaciones## 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 7.829630Estimacion del Modelo
library(stargazer)
modelo_estimado<-lm(price~lotsize+sqrft+bdrms, data = hprice1)
stargazer(modelo_estimado, title = "Prueba de Multicolinealidad", type = "text")##
## Prueba de Multicolinealidad
## ===============================================
## 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<0.01Calculo Manual
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
## --------------------------------------------------------------library(stargazer)
options(scipen = 9999)
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
## --------------------------X^tX Normalizada: Calcular la Matriz 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
## ---------------------------Autovalores de X^tX
library(stargazer)
#autovalores
lamdas<-eigen(xx_norm, symmetric = TRUE)
stargazer(lamdas$values, type = "text")##
## =======================
## 3.482 0.455 0.039 0.025
## -----------------------CALCULO DE K(X)=√(λmax/λmin)
k<-sqrt(max(lamdas$values)/min(lamdas$values))
print(k)## [1] 11.86778Sí κ(x) es inferior o igual a 20, la multicolinealidad es leve, no se considera un problema. Para 20<κ(x)<30, la multicolinealidad se considera moderada. En el caso de que κ(x)≥30 la multicolinealidad es severa.
INTERPRETACION * Como k(x)<=20 con un valor de 11.86 la multicolinealidad no se considera un problema*
Calculo del indice de condicion utilizando la libreria mctest
library(mctest)
x_mat<-model.matrix(modelo_estimado)
mctest(mod = modelo_estimado)##
## Call:
## omcdiag(mod = mod, Inter = TRUE, detr = detr, red = red, conf = conf,
## theil = theil, cn = cn)
##
##
## Overall Multicollinearity Diagnostics
##
## MC Results detection
## Determinant |X'X|: 0.6918 0
## Farrar Chi-Square: 31.3812 1
## Red Indicator: 0.3341 0
## Sum of Lambda Inverse: 3.8525 0
## Theil's Method: -0.7297 0
## Condition Number: 11.8678 0
##
## 1 --> COLLINEARITY is detected by the test
## 0 --> COLLINEARITY is not detected by the testComo se puede observar donde dice “condition Number” es el indice y podemos concluir que: * Como k(x)<=20 con un valor de 11.86 la multicolinealidad no se considera un problema.
Calculo del Indice de Condicion usando la libreria “Otsrr”.
library(olsrr)
ols_eigen_cindex(model=modelo_estimado)## Eigenvalue Condition Index intercept lotsize sqrft bdrms
## 1 3.48158596 1.000000 0.003663034 0.0277802824 0.004156293 0.002939554
## 2 0.45518380 2.765637 0.006800735 0.9670803174 0.006067321 0.005096396
## 3 0.03851083 9.508174 0.472581427 0.0051085488 0.816079307 0.016938178
## 4 0.02471941 11.867781 0.516954804 0.0000308514 0.173697079 0.975025872