Importacion de datos
library(haven)
hprice1 <- read_dta("C:/Users/USUARIO/Downloads/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
1. Estimacion del modelo
library(stargazer)
modelo_estimado<-lm(formula= price~assess+bdrms+lotsize+colonial+llotsize, data = hprice1)
stargazer(modelo_estimado, type="html", title="Modelo estimado")
Modelo estimado
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Dependent variable:
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price
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assess
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0.940***
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(0.072)
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bdrms
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8.620
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(6.791)
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lotsize
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0.001
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(0.001)
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colonial
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10.031
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(10.580)
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llotsize
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-13.357
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(17.813)
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Constant
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68.090
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(146.133)
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Observations
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88
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R2
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0.832
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Adjusted R2
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0.822
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Residual Std. Error
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43.364 (df = 82)
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F Statistic
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81.224*** (df = 5; 82)
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Note:
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p<0.1; p<0.05; p<0.01
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2.Verifique si hay evidencia: a)indice de condicion y prueba de FG
#calcular xmat
library(stargazer)
xmat<-model.matrix(modelo_estimado)
stargazer(head(xmat, n=6), type = "html")
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(Intercept)
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assess
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bdrms
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lotsize
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colonial
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llotsize
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1
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1
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349.100
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4
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6,126
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1
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8.720
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2
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1
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351.500
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3
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9,903
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1
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9.201
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3
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1
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217.700
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3
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5,200
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0
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8.556
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4
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1
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231.800
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3
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4,600
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1
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8.434
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5
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1
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319.100
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4
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6,095
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1
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8.715
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6
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1
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414.500
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5
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8,566
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1
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9.056
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continuando con la sigma matriz
xxmat<-t(xmat)%*%xmat
stargazer(xxmat, type = "html")
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(Intercept)
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assess
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bdrms
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lotsize
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colonial
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llotsize
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(Intercept)
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88
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27,784.800
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314
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793,748
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61
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783.649
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assess
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27,784.800
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9,563,053.000
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102,507.500
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278,300,049.000
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19,578.900
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250,005.600
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bdrms
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314
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102,507.500
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1,182
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2,933,767
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228
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2,802.953
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lotsize
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793,748
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278,300,049.000
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2,933,767
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16,165,159,010
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555,967
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7,457,452.000
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colonial
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61
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19,578.900
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228
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555,967
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61
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544.060
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llotsize
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783.649
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250,005.600
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2,802.953
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7,457,452.000
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544.060
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7,004.230
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sn matriz de normalizacion
library(stargazer)
options(scipen=999)
sn<-solve(diag(sqrt(diag(xxmat))))
stargazer(sn, type="html")
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0.107
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0
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0
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0
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0
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0
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0
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0.0003
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0
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0
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0
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0
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0
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0
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0.029
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0
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0
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0
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0
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0
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0
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0.00001
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0
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0
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0
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0
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0
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0
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0.128
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0
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0
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0
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0
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0
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0
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0.012
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xxmat normalizada
xx_norm<-(sn%*%xxmat)%*%sn
stargazer(xx_norm, type = "html", digits = 4)
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1
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0.9578
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0.9736
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0.6655
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0.8326
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0.9982
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0.9578
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1
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0.9642
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0.7078
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0.8106
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0.9660
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0.9736
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0.9642
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1
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0.6712
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0.8491
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0.9742
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0.6655
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0.7078
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0.6712
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1
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0.5599
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0.7008
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0.8326
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0.8106
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0.8491
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0.5599
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1
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0.8323
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0.9982
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0.9660
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0.9742
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0.7008
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0.8323
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1
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Autovalores
lambdas<-eigen(xx_norm, symmetric = TRUE)
stargazer(lambdas$values, type="html")
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5.193
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0.492
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0.237
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0.049
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0.028
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0.0005
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indice de condicion
k<-sqrt(max(lambdas$values)/min(lambdas$values))
print(k)
## [1] 106.4903
Indice de condicion usando mctest
library(mctest)
source(file ="C:/Users/USUARIO/Downloads/correccion_eigprop.R" )
eigprop(mod=modelo_estimado)
##
## Call:
## eigprop(mod = modelo_estimado)
##
## 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
Normalizar la matriz x calculo de R
library(stargazer)
zn<-scale(xmat[,-1])
stargazer(head(zn, n=6), type = "html")
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assess
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bdrms
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lotsize
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colonial
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llotsize
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1
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0.350
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0.513
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-0.284
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0.662
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-0.340
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2
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0.375
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-0.675
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0.087
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0.662
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0.543
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3
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-1.029
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-0.675
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-0.375
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-1.495
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-0.641
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4
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-0.881
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-0.675
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-0.434
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0.662
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-0.866
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5
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0.035
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0.513
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-0.287
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0.662
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-0.349
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6
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1.036
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1.702
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-0.045
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0.662
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0.277
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Calcular la matriz R
library(stargazer)
n<-nrow(zn)
R<-(t(zn)%*%zn)*(1/(n-1))
#tambien se puede calcular R atraves de cor(xmat[,-1])
stargazer(R, type= "html", digits=4)
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assess
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bdrms
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lotsize
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colonial
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llotsize
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assess
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1
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0.4825
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0.3281
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0.0829
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0.5717
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bdrms
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0.4825
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1
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0.1363
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0.3046
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0.1695
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lotsize
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0.3281
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0.1363
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1
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0.0140
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0.8079
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colonial
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0.0829
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0.3046
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0.0140
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1
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0.0386
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llotsize
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0.5717
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0.1695
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0.8079
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0.0386
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1
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usando cor
cor(xmat[,-1])
## assess bdrms lotsize colonial llotsize
## assess 1.00000000 0.4824739 0.32814633 0.08293582 0.5716654
## bdrms 0.48247394 1.0000000 0.13632563 0.30457549 0.1694902
## lotsize 0.32814633 0.1363256 1.00000000 0.01401865 0.8078552
## colonial 0.08293582 0.3045755 0.01401865 1.00000000 0.0386421
## llotsize 0.57166539 0.1694902 0.80785523 0.03864210 1.0000000
Determinante R
determinante_R<-det(R)
print(determinante_R)
## [1] 0.1419755
Aplicando la prueba FG
library(fastGraph)
## Warning: package 'fastGraph' was built under R version 4.0.5
m<-ncol(xmat[,-1])
# cantidad de variables explicativas k-1
n<-nrow(xmat[,-1])#numero de observaciones
det_R<-det(cor(xmat[,-1]))
chi_FG<--(n-1-(2*m+5)/6)*log(det_R)
print(chi_FG)
## [1] 164.9525
gl<-m*(m-1)/2
vc<-qchisq(p=0.95, df=gl)
print(vc)
## [1] 18.30704
Valor critico
gl<-m*(m-1)/2
vc<-qchisq(0.05,gl,lower.tail= FALSE)
print(vc)
## [1] 18.30704
gl<-m*(m-1)/2
vc<-qchisq(0.05,gl,lower.tail= FALSE)
print(vc)
## [1] 18.30704
shadeDist(xshade= chi_FG, ddist="dchisq", parm1= gl, lower.tail= FALSE, sub=paste("vc:", vc,"FG:", chi_FG))
FG con mctest
library(mctest)
mctest(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|: 0.1420 0
## Farrar Chi-Square: 164.9525 1
## Red Indicator: 0.3832 0
## Sum of Lambda Inverse: 12.3289 0
## Theil's Method: -0.8940 0
## Condition Number: 106.4903 1
##
## 1 --> COLLINEARITY is detected by the test
## 0 --> COLLINEARITY is not detected by the test
FG en psych
library(psych)
FG_test<-cortest.bartlett(xmat[,-1])
vc_1<-qchisq(0.05, FG_test$df, lower.tail = FALSE)
print(FG_test)
$chisq [1] 164.9525
$p.value [1] 0.000000000000000000000000000003072151
$df [1] 10
shadeDist(xshade=FG_test$chisq, ddist="dchisq", parm1=FG_test$df, lower.tail=FALSE, sub=paste("vc:", vc_1, "FG:", FG_test$chisq))
b) Factores inflacionarios de la Varianza
VIF<-diag(solve(cor(xmat[,-1])))
print(VIF)
## assess bdrms lotsize colonial llotsize
## 2.153558 1.510483 3.204965 1.114218 4.345674
Matriz de correlacion de los regresores
print(R)
## assess bdrms lotsize colonial llotsize
## assess 1.00000000 0.4824739 0.32814633 0.08293582 0.5716654
## bdrms 0.48247394 1.0000000 0.13632563 0.30457549 0.1694902
## lotsize 0.32814633 0.1363256 1.00000000 0.01401865 0.8078552
## colonial 0.08293582 0.3045755 0.01401865 1.00000000 0.0386421
## llotsize 0.57166539 0.1694902 0.80785523 0.03864210 1.0000000
Inversa de la matriz de correlacion
inversa_R<-solve(R)
print(inversa_R)
## assess bdrms lotsize colonial llotsize
## assess 2.1535576 -0.9010888 0.8347216 0.1520968 -1.7586001
## bdrms -0.9010888 1.5104833 -0.3640744 -0.4021983 0.5687703
## lotsize 0.8347216 -0.3640744 3.2049651 0.1130042 -3.0089889
## colonial 0.1520968 -0.4021983 0.1130042 1.1142184 -0.1531266
## llotsize -1.7586001 0.5687703 -3.0089889 -0.1531266 4.3456744
VIF para el modelo estimado
VIFs<-diag(inversa_R)
print(VIFs)
## assess bdrms lotsize colonial llotsize
## 2.153558 1.510483 3.204965 1.114218 4.345674
VIF con libreria car
library(car)
VIF_car<-vif(modelo_estimado)
print(VIF_car)
## assess bdrms lotsize colonial llotsize
## 2.153558 1.510483 3.204965 1.114218 4.345674
VIF con mctest
library(mctest)
mc.plot(modelo_estimado, vif=2)
cuatriplica la varianza es superior al 50% la variable que estan representando