Cálculo “manual”

library(stargazer)
X_mat<-model.matrix(modelo_ejercicio)
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 = 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
## --------------------------

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   
## ---------------------------

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

Cálculo del Indice de Condición usando librería “mctest”

library(mctest)
X_mat<-model.matrix(modelo_ejercicio)
mctest(mod = modelo_ejercicio)

## 
## 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)

## 
## Attaching package: 'olsrr'

## The following object is masked from 'package:wooldridge':
## 
##     cement

## The following object is masked from 'package:datasets':
## 
##     rivers

ols_eigen_cindex(model = modelo_ejercicio)

##   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

Cálculo “manual”

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))
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

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

Grafica

library(fastGraph)
alphan_sig<-0.05
chi_FG<- -(n-1-(2*m+5)/6)*log(determinante_R)
gl<-m*(m-1)/2
VC<-qchisq(p = 0.95,df = gl)
shadeDist(chi_FG,ddist = "dchisq",
          parm1 = gl,
          lower.tail = FALSE, xmin = 0,
          sub=paste("VC:", round(VC,2)," ","chi_FG", round(chi_FG,2)))

- Cálculo de FG usando “mctest”

library(mctest)
mctest::omcdiag(mod = modelo_ejercicio)

## 
## Call:
## mctest::omcdiag(mod = modelo_ejercicio)
## 
## 
## 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])

## R was not square, finding R from data

print(FG_test)

## $chisq
## [1] 31.38122
## 
## $p.value
## [1] 0.0000007065806
## 
## $df
## [1] 3

Referencia entre R

library(dplyr)

## 
## Attaching package: '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_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

VIFs<-diag(inversa_R)
print(VIFs)

##  lotsize    sqrft    bdrms 
## 1.037211 1.418654 1.396663

Conclusión

Cálculo de los VIF’s usando “performance”

library(performance)
VIFs<-multicollinearity(x = modelo_ejercicio,verbose = FALSE)
VIFs

## # Check for Multicollinearity
## 
## Low Correlation
## 
##     Term  VIF    VIF 95% CI Increased SE Tolerance Tolerance 95% CI
##  lotsize 1.04 [1.00, 11.02]         1.02      0.96     [0.09, 1.00]
##    sqrft 1.42 [1.18,  1.98]         1.19      0.70     [0.51, 0.85]
##    bdrms 1.40 [1.17,  1.95]         1.18      0.72     [0.51, 0.86]

plot(VIFs)

## Variable `Component` is not in your data frame :/

Cálculo de los VIF’s usando “car”

library(car)

## Loading required package: carData

## 
## Attaching package: 'car'

## The following object is masked from 'package:dplyr':
## 
##     recode

## The following object is masked from 'package:psych':
## 
##     logit

VIFs_car<-vif(modelo_ejercicio)
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_ejercicio,vif = 2)