library(wooldridge)
## Warning: package 'wooldridge' was built under R version 4.5.3
data(price1)
## Warning in data(price1): data set 'price1' not found
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
1. Estimar el modelo.
modelo_estimado <- lm(price ~ lotsize + sqrft + bdrms, data = hprice1)
summary(modelo_estimado)
##
## Call:
## lm(formula = price ~ lotsize + sqrft + bdrms, data = hprice1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -120.026 -38.530 -6.555 32.323 209.376
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.177e+01 2.948e+01 -0.739 0.46221
## lotsize 2.068e-03 6.421e-04 3.220 0.00182 **
## sqrft 1.228e-01 1.324e-02 9.275 1.66e-14 ***
## bdrms 1.385e+01 9.010e+00 1.537 0.12795
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 59.83 on 84 degrees of freedom
## Multiple R-squared: 0.6724, Adjusted R-squared: 0.6607
## F-statistic: 57.46 on 3 and 84 DF, p-value: < 2.2e-16
2. Verificación de independencia de los regresores.
a) Indice de condición
# Calculo Manual
library(stargazer)
##
## Please cite as:
## Hlavac, Marek (2022). stargazer: Well-Formatted Regression and Summary Statistics Tables.
## R package version 5.2.3. https://CRAN.R-project.org/package=stargazer
X_mat <- model.matrix(modelo_estimado)
stargazer(head(X_mat),n = 6, type = "text")
##
## ===============
## 1 6,126 2,438 4
## 1 9,903 2,076 3
## 1 5,200 1,374 3
## 1 4,600 1,448 3
## 1 6,095 2,514 4
## 1 8,566 2,754 5
## ---------------
##
## =
## 6
## -
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
## --------------------------------------------------------------
Normalización.
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
## --------------------------
X’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
## ---------------------------
Autovalores de X’X Normalizada
library(stargazer)
#autovalores
lambdas<-eigen(XX_norm,symmetric = TRUE)
stargazer(lambdas$values,type = "text")
##
## =======================
## 3.482 0.455 0.039 0.025
## -----------------------
K<-sqrt(max(lambdas$values)/min(lambdas$values))
print(K)
## [1] 11.86778
Como K(x) > 20 se considera multicolinealidad leve.
Cálculo del Indice de Condición usando librería “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 test
Cálculo del Indice de Condición usando librería “olsrr”
library(olsrr)
## Warning: package 'olsrr' was built under R version 4.5.3
##
## Adjuntando el paquete: 'olsrr'
## The following object is masked from 'package:wooldridge':
##
## cement
## The following object is masked from 'package:datasets':
##
## rivers
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
Prueba de Farrar-Glaubar
Cálculo de |R|
# Calculo Manual
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)
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 Crítico.
gl<-m*(m-1)/2
VC<-qchisq(p = 0.95,df = gl)
print(VC)
## [1] 7.814728
Regla de Decisión
chi_FG > VC
## [1] TRUE
Interpretación: Como el estadístico observado (31.38) cae
profundamente en la zona de rechazo (es mucho mayor el valor crítico),
se rechaza la Hipótesis Nula (H₀), por lo tanto existe colinealidad
entre los regresores.
Cálculo de FG usando “mctest”
library(mctest)
mctest::omcdiag(mod = modelo_estimado)
##
## Call:
## mctest::omcdiag(mod = modelo_estimado)
##
##
## 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)
## Warning: package 'psych' was built under R version 4.5.3
FG_test<-cortest.bartlett(X_mat[,-1])
## R was not square, finding R from data
print(FG_test)
## $chisq
## [1] 31.38122
##
## $p.value
## [1] 0.0000007065806
##
## $df
## [1] 3
3. Factores Inflacionarios de la Varianza (FIV)
Referencia entre Rj2
library(dplyr)
## Warning: package 'dplyr' was built under R version 4.5.3
##
## Adjuntando el paquete: 'dplyr'
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
R.cuadrado.regresores<-c(0,0.5,.8,.9)
as.data.frame(R.cuadrado.regresores) %>% mutate(VIF=1/(1-R.cuadrado.regresores))
## R.cuadrado.regresores VIF
## 1 0.0 1
## 2 0.5 2
## 3 0.8 5
## 4 0.9 10
Cálculo manual
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 VIFs usando “car”
library(car)
## Cargando paquete requerido: carData
##
## Adjuntando el paquete: 'car'
## The following object is masked from 'package:dplyr':
##
## recode
## The following object is masked from 'package:psych':
##
## logit
VIFs_car<-vif(modelo_estimado)
print(VIFs_car)
## lotsize sqrft bdrms
## 1.037211 1.418654 1.396663
Cálculo de los VIF’s usando “mctest”
library(mctest)
mc.plot(mod = modelo_estimado,vif = 2)
