Ejemplos de Multicolinealidad

2023

Ejemplo 1: Salario

Ejemplo: Salario

El conjunto de datos salary.csv contiene información de un estudio para determinar el salario de una persona en una empresa en base a las siguientes características:

Sexo (0 - mujer, 1 - hombre)
Edad
Años de servicio (Años de trabajo en la empresa)
Nivel de educación (0 – sin educación formal, 1 – licenciatura, 2 – posgrado)

Ejemplo: Salario

salario <- read.csv("salary.csv")
salario$Education.level <- as.factor(salario$Education.level)
head(salario)

##   Gender Age Years.of.service Education.level Salary
## 1      0  27              1.7               0  39343
## 2      1  26              1.1               1  43205
## 3      1  26              1.2               0  47731
## 4      0  27              1.6               1  46525
## 5      0  26              1.5               1  40891
## 6      1  28              2.3               0  56642

Ejemplo: Salario

m1 <- lm (Salary ~ ., data = salario)
summary(m1)

## 
## Call:
## lm(formula = Salary ~ ., data = salario)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -9249.2 -2753.4   805.4  3127.8  9389.8 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)  
## (Intercept)        5422.2    16899.8   0.321   0.7520  
## Gender             4556.8     2358.3   1.932   0.0692 .
## Age                1575.3      747.9   2.106   0.0495 *
## Years.of.service   -378.2     2466.7  -0.153   0.8798  
## Education.level1   1933.7     2553.7   0.757   0.4587  
## Education.level2   2783.1     3161.0   0.880   0.3902  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5309 on 18 degrees of freedom
## Multiple R-squared:  0.5753, Adjusted R-squared:  0.4574 
## F-statistic: 4.877 on 5 and 18 DF,  p-value: 0.005388

Ejemplo: Salario

round(cor(salario[,-c(1,4)]), 3)

##                    Age Years.of.service Salary
## Age              1.000            0.888  0.670
## Years.of.service 0.888            1.000  0.584
## Salary           0.670            0.584  1.000

Ejemplo: Salario

library(rms)
vif(m1)

##           Gender              Age Years.of.service Education.level1 
##         1.175690         5.179300         5.305805         1.378581 
## Education.level2 
##         1.403231

Ejemplo: Salario

barplot(vif(m1), main = "VIF Values", horiz = TRUE, col = "steelblue")
abline(v = 4, lwd = 3, lty = 2)

Ejemplo: Salario

m2 <- lm (Salary ~ Gender + Years.of.service +Education.level, data = salario)
summary(m2)

## 
## Call:
## lm(formula = Salary ~ Gender + Years.of.service + Education.level, 
##     data = salario)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -9245.5 -2849.5   441.6  3166.0  9063.1 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         40221       3860  10.421  2.7e-09 ***
## Gender               5214       2540   2.052  0.05416 .  
## Years.of.service     4287       1180   3.634  0.00177 ** 
## Education.level1     2301       2769   0.831  0.41630    
## Education.level2     1165       3332   0.350  0.73048    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5769 on 19 degrees of freedom
## Multiple R-squared:  0.4707, Adjusted R-squared:  0.3592 
## F-statistic: 4.224 on 4 and 19 DF,  p-value: 0.01298

Ejemplo: Salario

vif(m2)

##           Gender Years.of.service Education.level1 Education.level2 
##         1.155135         1.027509         1.372164         1.320328

Ejemplo: Salario

m3 <- lm (Salary ~ Gender + Age +Education.level, data = salario)
summary(m3)

## 
## Call:
## lm(formula = Salary ~ Gender + Age + Education.level, data = salario)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -9181.4 -2692.8   714.6  3241.7  9314.1 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)        7518.8     9673.1   0.777 0.446557    
## Gender             4617.0     2264.9   2.038 0.055663 .  
## Age                1472.3      320.6   4.593 0.000199 ***
## Education.level1   1970.6     2476.2   0.796 0.435966    
## Education.level2   2658.7     2975.7   0.894 0.382767    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5171 on 19 degrees of freedom
## Multiple R-squared:  0.5748, Adjusted R-squared:  0.4853 
## F-statistic: 6.421 on 4 and 19 DF,  p-value: 0.001915

Ejemplo: Salario

vif(m3)

##           Gender              Age Education.level1 Education.level2 
##         1.143138         1.003011         1.366338         1.310838

Ejemplo: Salario

salario$age_at_joining <- salario$Age - salario$Years.of.service
m4 <- lm (Salary ~ Gender + age_at_joining +Education.level, data = salario)
summary(m4)

## 
## Call:
## lm(formula = Salary ~ Gender + age_at_joining + Education.level, 
##     data = salario)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -9641.1 -3047.6   843.4  2924.0  9785.7 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       -2258.8    12001.2  -0.188 0.852702    
## Gender             4292.8     2288.6   1.876 0.076147 .  
## age_at_joining     1969.7      438.2   4.495 0.000248 ***
## Education.level1   1767.2     2502.7   0.706 0.488691    
## Education.level2   3295.7     3016.7   1.093 0.288272    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5229 on 19 degrees of freedom
## Multiple R-squared:  0.5652, Adjusted R-squared:  0.4736 
## F-statistic: 6.174 on 4 and 19 DF,  p-value: 0.002333

Ejemplo: Salario

vif(m4)

##           Gender   age_at_joining Education.level1 Education.level2 
##         1.141427         1.006781         1.364957         1.317478