Ejercicio_Multicolinealidad
JEIMMY YAMILETH SALAZAR CHAVEZ
2023-05-14
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 7.829630#Estimar modelo
Ecuacion_modelo<-lm(formula = price~ lotsize+sqrft+bdrms,data = hprice1)
library(stargazer)
stargazer(Ecuacion_modelo,"Estimar_Modelo",type = "text")##
## ===============================================
## 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<0.01
##
## ==============
## Estimar_Modelo
## --------------- Indice de Condición. #calculo manual
library(stargazer)
Mat_X<-model.matrix(Ecuacion_modelo)
stargazer(head(Mat_X,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
## ---------------------------------MAt_XX<-t(Mat_X)%*%Mat_X
stargazer(MAt_XX,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
## --------------------------------------------------------------#Calculo de Matriz de Normalizacion
library(stargazer)
options(scipen = 999)
Sn<-solve(diag(sqrt(diag(MAt_XX))))
stargazer(Sn,type = "text",
title = "Matriz Normalizada")##
## Matriz Normalizada
## ==========================
## 0.107 0 0 0
## 0 0.00001 0 0
## 0 0 0.0001 0
## 0 0 0 0.029
## --------------------------#X^tX normalizada
library(stargazer)
Norm_XX<-(Sn%*%MAt_XX)%*%Sn
stargazer(Norm_XX,type = "text",digits = 4,
title = "Norm XX")##
## Norm XX
## ===========================
## 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 Normalizada
library(stargazer)
#autovalores
lambdas<-eigen(Norm_XX,symmetric = TRUE)
stargazer(lambdas$values,type = "text",
title = "Autovalores")##
## Autovalores
## =======================
## 3.482 0.455 0.039 0.025
## -----------------------#Cálculo de κ(x)=√λmax/λmin
K<-sqrt(max(lambdas$values)/min(lambdas$values))
print(K)## [1] 11.86778R/ Como K(x) es < 20, la multicolinealidad es leve, no se considera un problema.
#Calculo del Indice de Condición usando librería “mctest”
library(mctest)
X_mat<-model.matrix(Ecuacion_modelo)
mctest(mod = Ecuacion_modelo)##
## 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 test#Cálculo del Indice de Condición usando librería “olsrr”
library(olsrr)
ols_eigen_cindex(model = Ecuacion_modelo)## 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#Prueba de FARRER GLAUBAR #Calculo de |R|
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))
#También se puede calcular R a través de cor(X_mat[,-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] 0.6917931#Aplicando la Prueba de FARRER GLAUBAR (BARTLETT) #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] 7.814728*Regla de desición: Como χ2FG≥V.C, se rechaza la Hipotesis Nula, por lo tanto hay evidencia de colinealidad en los regresores.
#Cálculo de FG usando “mctest”
library(mctest)
mctest::omcdiag(mod = Ecuacion_modelo)##
## Call:
## mctest::omcdiag(mod = Ecuacion_modelo)
##
##
## 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 test#Cálculo de FG usando la “psych”
library(psych)
FG_test<-cortest.bartlett(X_mat[,-1])
print(FG_test)## $chisq
## [1] 31.38122
##
## $p.value
## [1] 0.0000007065806
##
## $df
## [1] 3library(fastGraph)## Warning: package 'fastGraph' was built under R version 4.2.3shadeDist(chi_FG,ddist = "dnorm",lower.tail = TRUE)
#Factores Inflacionarios de la Varianza (FIV)
#Calculo Manual
#Matriz de Correlacion de los regresores
print(R)## lotsize sqrft bdrms
## lotsize 1.0000000 0.1838422 0.1363256
## sqrft 0.1838422 1.0000000 0.5314736
## bdrms 0.1363256 0.5314736 1.0000000#Inversa de la matriz de correlación 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 1.39666321#VIF’s para el modelo estimado
VIFs<-diag(Inversa_R)
print(VIFs)## lotsize sqrft bdrms
## 1.037211 1.418654 1.396663#Cálculo de los VIF’s usando “car”
library(car)
VIFs_car<-vif(Ecuacion_modelo)
print(VIFs_car)## lotsize sqrft bdrms
## 1.037211 1.418654 1.396663#Cálculo de los VIF’s usando “mctest”
library(mctest)
mc.plot(mod = Ecuacion_modelo,vif = 2)