Untitled
Luz Virginia Pérez Ramírez
2024-05-13
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##Modelo a estimar
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=stargazermodelo_hrpice <- lm(formula = price ~ lotsize + sqrft + bdrms, data = hprice1)
stargazer(modelo_hrpice, title = "Modelo estimado" , type = "text" , digits = 5)##
## Modelo estimado
## ===============================================
## Dependent variable:
## ---------------------------
## price
## -----------------------------------------------
## lotsize 0.00207***
## (0.00064)
##
## sqrft 0.12278***
## (0.01324)
##
## bdrms 13.85252
## (9.01015)
##
## Constant -21.77031
## (29.47504)
##
## -----------------------------------------------
## Observations 88
## R2 0.67236
## Adjusted R2 0.66066
## Residual Std. Error 59.83348 (df = 84)
## F Statistic 57.46023*** (df = 3; 84)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01Indice de condicion
matriz_x <- model.matrix(modelo_hrpice)
matriz_xx <- t(matriz_x)%*%matriz_x
print(matriz_xx)## (Intercept) lotsize sqrft bdrms
## (Intercept) 88 793748 177205 314
## lotsize 793748 16165159010 1692290257 2933767
## sqrft 177205 1692290257 385820561 654755
## bdrms 314 2933767 654755 1182normalizada
options(scipen = 999)
matriz_normalizacion <- solve(diag(sqrt(diag(matriz_xx))))
print(matriz_normalizacion)## [,1] [,2] [,3] [,4]
## [1,] 0.1066004 0.000000000000 0.00000000000 0.00000000
## [2,] 0.0000000 0.000007865204 0.00000000000 0.00000000
## [3,] 0.0000000 0.000000000000 0.00005091049 0.00000000
## [4,] 0.0000000 0.000000000000 0.00000000000 0.02908649Matriz transpuesta normalizada
matriz_normalizacion_t <- (matriz_normalizacion%*%matriz_xx)%*%matriz_normalizacion
print(matriz_normalizacion_t)## [,1] [,2] [,3] [,4]
## [1,] 1.0000000 0.6655050 0.9617052 0.9735978
## [2,] 0.6655050 1.0000000 0.6776293 0.6711613
## [3,] 0.9617052 0.6776293 1.0000000 0.9695661
## [4,] 0.9735978 0.6711613 0.9695661 1.0000000Autovalores normalizada
autovalor <- eigen(matriz_xx, symmetric = TRUE)
print (autovalor)## eigen() decomposition
## $values
## [1] 16344612181.206480 206368582.800828 73.018955 3.973713
##
## $vectors
## [,1] [,2] [,3] [,4]
## [1,] -0.00004943579 -0.0004483067 0.194276588766 0.9809466874580
## [2,] -0.99442458432 0.1054502064 -0.000007308921 -0.0000004752379
## [3,] -0.10545003681 -0.9944231045 -0.001721880551 -0.0001187612469
## [4,] -0.00018271796 -0.0016559655 0.980945279886 -0.1942770760042K
K <- sqrt(max(autovalor$values)/min(autovalor$values))
print(K)## [1] 64134.11#Cálculo del Indice de Condición usando librería “mctest”
library(mctest)
X_mat<-model.matrix(modelo_hrpice)
mctest(mod = modelo_hrpice)##
## 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':
##
## riversols_eigen_cindex(model = modelo_hrpice)## 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 0.975025872prueba de Farrar-Glaubar
fg <- scale(matriz_x[,-1])
print(fg)## lotsize sqrft bdrms
## 1 -0.284432952 0.73512302 0.5132184
## 2 0.086801976 0.10794824 -0.6752874
## 3 -0.375447923 -1.10828571 -0.6752874
## 4 -0.434420906 -0.98007871 -0.6752874
## 5 -0.287479889 0.86679507 0.5132184
## 6 -0.044609488 1.28260155 1.7017243
## 7 -0.001952363 0.09235550 -0.6752874
## 8 -0.276176734 -0.48977357 -0.6752874
## 9 -0.296817278 -0.42740260 -0.6752874
## 10 -0.602297331 -0.21430178 -0.6752874
## 11 -0.296817278 0.55840526 0.5132184
## 12 -0.193909423 1.07469831 1.7017243
## 13 0.316206880 2.35850081 -0.6752874
## 14 -0.251604658 -0.19870903 -0.6752874
## 15 -0.245805648 0.51682462 -0.6752874
## 16 -0.533004076 -0.43953029 0.5132184
## 17 -0.304483766 -0.02372381 0.5132184
## 18 -0.186439512 -0.41527491 -0.6752874
## 19 -0.332004492 -1.10482065 -0.6752874
## 20 -0.041071109 -0.30959076 0.5132184
## 21 -0.346551161 0.05943749 -0.6752874
## 22 -0.119898329 0.19110954 -0.6752874
## 23 -0.296522414 -0.42567007 -0.6752874
## 24 -0.373678733 -0.48804104 0.5132184
## 25 0.039820167 -0.99393893 -0.6752874
## 26 -0.285612412 -0.14153564 -0.6752874
## 27 -0.227032582 -0.14153564 -0.6752874
## 28 -0.043528316 0.15992405 -0.6752874
## 29 -0.060925346 2.62530997 4.0787359
## 30 0.074024497 0.06463507 0.5132184
## 31 -0.414173515 -0.76351284 0.5132184
## 32 0.596230262 1.41254107 0.5132184
## 33 -0.320111607 -0.66475880 -0.6752874
## 34 -0.259172858 -0.30092813 0.5132184
## 35 -0.001952363 0.09062297 0.5132184
## 36 -0.542538041 -0.54001685 0.5132184
## 37 0.184009110 1.27567144 0.5132184
## 38 0.650092253 3.23342695 1.7017243
## 39 -0.257501956 -0.27667275 0.5132184
## 40 -0.013746960 -1.02685694 -1.8637932
## 41 -0.265954751 -0.60931793 -0.6752874
## 42 1.888230032 2.28226963 1.7017243
## 43 -0.193614558 -0.61971309 0.5132184
## 44 -0.365127650 -1.45998869 -0.6752874
## 45 -0.234207628 0.48390660 1.7017243
## 46 -0.116556527 -0.43260018 -0.6752874
## 47 -0.788258804 1.30685693 -0.6752874
## 48 -0.089232378 2.97874548 0.5132184
## 49 -0.311560524 -0.82761633 -0.6752874
## 50 -0.231946997 -0.65089858 0.5132184
## 51 -0.234207628 -0.07223456 -0.6752874
## 52 0.614020445 -0.92810290 -1.8637932
## 53 -0.380755491 -1.04937979 -0.6752874
## 54 -0.295146377 -0.34943888 -0.6752874
## 55 -0.059942463 -0.50536631 -0.6752874
## 56 -0.333675393 -0.40487975 0.5132184
## 57 -0.336132600 -0.58852761 0.5132184
## 58 -0.245215918 -0.28360286 0.5132184
## 59 -0.290919980 -0.15366333 -0.6752874
## 60 -0.342128187 0.57053295 0.5132184
## 61 -0.142897793 -0.77390800 -0.6752874
## 62 -0.347534044 -0.60585288 0.5132184
## 63 -0.360901253 -1.08749538 2.8902301
## 64 0.669749914 1.04524535 1.7017243
## 65 -0.098078326 0.53241736 0.5132184
## 66 0.289570750 1.08162842 0.5132184
## 67 -0.055028048 -0.17098860 0.5132184
## 68 0.598097739 0.99673459 0.5132184
## 69 0.180765596 1.20463783 0.5132184
## 70 -0.267330787 -0.73925746 -0.6752874
## 71 0.249075968 -0.55387707 -0.6752874
## 72 -0.296817278 -0.82761633 -0.6752874
## 73 2.160390349 2.85573606 1.7017243
## 74 -0.488086320 -0.48111093 -0.6752874
## 75 1.148020806 0.33144423 -1.8637932
## 76 -0.343504223 -0.88652225 -0.6752874
## 77 8.222911296 -0.55041201 0.5132184
## 78 -0.082745350 0.29852621 -0.6752874
## 79 -0.302321424 -0.14846575 0.5132184
## 80 0.965007982 -1.24688787 -0.6752874
## 81 -0.462433073 -0.82934886 0.5132184
## 82 -0.378691437 -0.05837435 -0.6752874
## 83 -0.110757517 0.13220362 0.5132184
## 84 -0.291313133 -0.30612571 -0.6752874
## 85 -0.313722867 -0.51749400 -0.6752874
## 86 -0.263300966 -0.76178031 -0.6752874
## 87 -0.261236912 -1.43573331 -1.8637932
## 88 -0.400019999 -0.41527491 0.5132184
## attr(,"scaled:center")
## lotsize sqrft bdrms
## 9019.863636 2013.693182 3.568182
## attr(,"scaled:scale")
## lotsize sqrft bdrms
## 10174.1504141 577.1915827 0.8413926Matriz R
nR <- nrow(fg)
matrizR <- (t(fg)%*%fg)*(1/(nR-1))
print(matrizR)## lotsize sqrft bdrms
## lotsize 1.0000000 0.1838422 0.1363256
## sqrft 0.1838422 1.0000000 0.5314736
## bdrms 0.1363256 0.5314736 1.0000000Determinante R
D_R <- det(matrizR)
print(D_R)## [1] 0.6917931FG
P_FG <- ncol(matriz_x[,-1])
n_R <- nrow(matriz_x[,-1])
chi_FG <- -(n_R-1-(2*P_FG+5)/6)*log(D_R)
print(chi_FG)## [1] 31.38122VC
gl_FG <- P_FG*(P_FG-1)/2
vc_FG <- qchisq(p=0.95,df= gl_FG)
print(vc_FG)## [1] 7.814728FG
library(ggplot2)
df <- data.frame(
Test = c("Chi_FG", "VC_FG"),
Resultado = c(chi_FG, vc_FG)
)
ggplot(df, aes(x=Test, y=Resultado)) +
geom_bar(stat="identity", fill="steelblue") +
theme_minimal() +
labs(title="Resultados de la prueba Farrar-Glaubar", x="Test", y="Resultado") +
geom_text(aes(label=Resultado), vjust=-0.3, size=3.5)
FIV
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, unionR.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 10print(matrizR)## lotsize sqrft bdrms
## lotsize 1.0000000 0.1838422 0.1363256
## sqrft 0.1838422 1.0000000 0.5314736
## bdrms 0.1363256 0.5314736 1.0000000Inversa
inversa_R <- solve(matrizR)
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 1.39666321VIF’s
VIFs <-diag(inversa_R)
print(VIFs)## lotsize sqrft bdrms
## 1.037211 1.418654 1.396663##Gráfico
library(ggplot2)
library(dplyr)
R.cuadrado.regresores <- c(0, 0.5, .8, .9)
datos <- as.data.frame(R.cuadrado.regresores) %>% mutate(VIF = 1 / (1 - R.cuadrado.regresores))
ggplot(datos, aes(x = R.cuadrado.regresores, y = VIF)) +
geom_line() +
labs(title = "Factores Inflacionarios de la Varianza (FIV)",
x = "R cuadrado de los regresores",
y = "VIF") +
theme_minimal()
## Cálculo de los VIF’s usando “performance”
library(performance)
VIFs<-multicollinearity(x = modelo_hrpice,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]Cálculo de los VIF’s “car”
library(car)## Loading required package: carData##
## Attaching package: 'car'## The following object is masked from 'package:dplyr':
##
## recodeVIFs_car<-vif(modelo_hrpice)
print(VIFs_car)## lotsize sqrft bdrms
## 1.037211 1.418654 1.396663Cálculo de los VIF’s usando “mctest
library(mctest)
mc.plot(mod = modelo_hrpice,vif = 2)