practica4_multicolinealidad

CINTHYA ABIGAIL LOPEZ UMANZOR

19/5/2019

Datos

library(haven) 
hprice1<- read_dta("F:/rPORTABLES/hprice1.dta") 
head(hprice1,n=6)
## # A tibble: 6 x 10
##   price assess bdrms lotsize sqrft colonial lprice lassess llotsize lsqrft
##   <dbl>  <dbl> <dbl>   <dbl> <dbl>    <dbl>  <dbl>   <dbl>    <dbl>  <dbl>
## 1  300    349.     4    6126  2438        1   5.70    5.86     8.72   7.80
## 2  370    352.     3    9903  2076        1   5.91    5.86     9.20   7.64
## 3  191    218.     3    5200  1374        0   5.25    5.38     8.56   7.23
## 4  195    232.     3    4600  1448        1   5.27    5.45     8.43   7.28
## 5  373    319.     4    6095  2514        1   5.92    5.77     8.72   7.83
## 6  466.   414.     5    8566  2754        1   6.14    6.03     9.06   7.92

Estimacion del modelo

library(stargazer)
modelo_estimado<-lm(price~assess+bdrms+lotsize+colonial+llotsize,data = hprice1) 
stargazer(modelo_estimado,type = "text",title = "modelo estimado")
## 
## modelo estimado
## ===============================================
##                         Dependent variable:    
##                     ---------------------------
##                                price           
## -----------------------------------------------
## assess                       0.940***          
##                               (0.072)          
##                                                
## bdrms                          8.620           
##                               (6.791)          
##                                                
## lotsize                        0.001           
##                               (0.001)          
##                                                
## colonial                      10.031           
##                              (10.580)          
##                                                
## llotsize                      -13.357          
##                              (17.813)          
##                                                
## Constant                      68.090           
##                              (146.133)         
##                                                
## -----------------------------------------------
## Observations                    88             
## R2                             0.832           
## Adjusted R2                    0.822           
## Residual Std. Error      43.364 (df = 82)      
## F Statistic           81.224*** (df = 5; 82)   
## ===============================================
## Note:               *p<0.1; **p<0.05; ***p<0.01

Calculo de matriz X´X

library(stargazer) 
X_mat<-model.matrix(modelo_estimado) 
stargazer(head(X_mat,n=6),type="text")
## 
## =====================================================
##   (Intercept) assess  bdrms lotsize colonial llotsize
## -----------------------------------------------------
## 1      1      349.100   4    6,126     1      8.720  
## 2      1      351.500   3    9,903     1      9.201  
## 3      1      217.700   3    5,200     0      8.556  
## 4      1      231.800   3    4,600     1      8.434  
## 5      1      319.100   4    6,095     1      8.715  
## 6      1      414.500   5    8,566     1      9.056  
## -----------------------------------------------------
sigma_m<-t(X_mat)%*%X_mat 
stargazer(sigma_m,type = "text")
## 
## ============================================================================================
##             (Intercept)     assess         bdrms        lotsize      colonial    llotsize   
## --------------------------------------------------------------------------------------------
## (Intercept)     88        27,784.800        314         793,748         61        783.649   
## assess      27,784.800   9,563,053.000  102,507.500 278,300,049.000 19,578.900  250,005.600 
## bdrms           314       102,507.500      1,182       2,933,767       228       2,802.953  
## lotsize       793,748   278,300,049.000  2,933,767  16,165,159,010   555,967   7,457,452.000
## colonial        61        19,578.900        228         555,967         61        544.060   
## llotsize      783.649     250,005.600    2,802.953   7,457,452.000   544.060     7,004.230  
## --------------------------------------------------------------------------------------------

Normalizacion de matriz X´X

Calculo de matriz de normalización

library(stargazer)
options(scipen = 999) 
Sn<-solve(diag(sqrt(diag(sigma_m)))) 
stargazer(Sn,type = "text")
## 
## ======================================
## 0.107   0      0      0      0     0  
## 0     0.0003   0      0      0     0  
## 0       0    0.029    0      0     0  
## 0       0      0   0.00001   0     0  
## 0       0      0      0    0.128   0  
## 0       0      0      0      0   0.012
## --------------------------------------

X´X Normalizada

library(stargazer)
sigma.m_norm<-(Sn%*%sigma_m)%*%Sn
stargazer(sigma.m_norm,type = "text",digits = 4)
## 
## =========================================
## 1      0.9578 0.9736 0.6655 0.8326 0.9982
## 0.9578   1    0.9642 0.7078 0.8106 0.9660
## 0.9736 0.9642   1    0.6712 0.8491 0.9742
## 0.6655 0.7078 0.6712   1    0.5599 0.7008
## 0.8326 0.8106 0.8491 0.5599   1    0.8323
## 0.9982 0.9660 0.9742 0.7008 0.8323   1   
## -----------------------------------------

Cálculo del indice de condición

Autovalores de X´X normalizada:

library(stargazer) 
lambdas<-eigen(sigma.m_norm,symmetric = TRUE) 
stargazer(lambdas$values,type = "text")
## 
## ====================================
## 5.193 0.492 0.237 0.049 0.028 0.0005
## ------------------------------------

Cálculo de K

K<-sqrt(max(lambdas$values)/min(lambdas$values)) 
print(K)
## [1] 106.4903

Uso de la libreria ?mctest”, para obtener el indice de condición

library(mctest) 
eigprop(x = X_mat[,-1])
## 
## Call:
## eigprop(x = X_mat[, -1])
## 
##   Eigenvalues       CI Intercept assess  bdrms lotsize colonial llotsize
## 1      5.1934   1.0000    0.0000 0.0014 0.0012  0.0037   0.0079   0.0000
## 2      0.4923   3.2479    0.0000 0.0001 0.0015  0.2963   0.0615   0.0000
## 3      0.2365   4.6860    0.0003 0.0113 0.0041  0.0322   0.8545   0.0002
## 4      0.0491  10.2888    0.0048 0.4576 0.0148  0.0101   0.0021   0.0027
## 5      0.0283  13.5505    0.0012 0.2138 0.9074  0.0093   0.0696   0.0017
## 6      0.0005 106.4903    0.9936 0.3158 0.0711  0.6484   0.0044   0.9954
## 
## ===============================
## Row 5==> bdrms, proportion 0.907364 >= 0.50 
## Row 6==> lotsize, proportion 0.648440 >= 0.50 
## Row 3==> colonial, proportion 0.854491 >= 0.50 
## Row 6==> llotsize, proportion 0.995427 >= 0.50

Calculo de R

■ Normalizar la matriz X

library(stargazer) 
Zn<-scale(X_mat[,-1])
stargazer(head(Zn,n=6),type = "text")
## 
## =========================================
##   assess bdrms  lotsize colonial llotsize
## -----------------------------------------
## 1 0.350  0.513  -0.284   0.662    -0.340 
## 2 0.375  -0.675  0.087   0.662    0.543  
## 3 -1.029 -0.675 -0.375   -1.495   -0.641 
## 4 -0.881 -0.675 -0.434   0.662    -0.866 
## 5 0.035  0.513  -0.287   0.662    -0.349 
## 6 1.036  1.702  -0.045   0.662    0.277  
## -----------------------------------------

■ Calcular la matriz R

library(stargazer)
n<-nrow(Zn)
R<-(t(Zn)%*%Zn)*(1/(n-1)) 
stargazer(R,type = "text",digits = 4)
## 
## ================================================
##          assess bdrms  lotsize colonial llotsize
## ------------------------------------------------
## assess     1    0.4825 0.3281   0.0829   0.5717 
## bdrms    0.4825   1    0.1363   0.3046   0.1695 
## lotsize  0.3281 0.1363    1     0.0140   0.8079 
## colonial 0.0829 0.3046 0.0140     1      0.0386 
## llotsize 0.5717 0.1695 0.8079   0.0386     1    
## ------------------------------------------------

■ Calcular R

determinante_R<-det(R) 
print(determinante_R)
## [1] 0.1419755

Aplicando la prueba de Farrer Glaubar (Bartlett)

Estadistico

p<-ncol(X_mat[,-1])
n<-nrow(X_mat[,-1]) 
chi_FG<--(n-1-(2*p+5)/6)*log(determinante_R) 
print(chi_FG)
## [1] 164.9525

Valor Critico

gl<-p*(p-1)/2 
VC<-qchisq(p = 0.95,df = gl)
print(VC)
## [1] 18.30704

Como se rechaza,χ2FG≥ V.C por lo tanto hay evidencia de colinealidad en los regresores

Uso de la libreria psych

library(psych) 
FG_test<-cortest.bartlett(X_mat[,-1])
print(FG_test)
## $chisq
## [1] 164.9525
## 
## $p.value
## [1] 0.000000000000000000000000000003072151
## 
## $df
## [1] 10