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--- multicollinearity [2016/04/27 06:47] – hkimscil
+++ multicollinearity [2023/05/22 07:57] (current) – [Testing with correlation matrix] hkimscil
@@ Line 6: / Line 6: @@
 see [[:Singularity]] \\
-[[:Multicollinearity]]
+====== Testing multicollinearity with correlation matrix ======
+<code>
+options(digits = 4)
+HSGPA <- c(3.0, 3.2, 2.8, 2.5, 3.2, 3.8, 3.9, 3.8, 3.5, 3.1)
+FGPA <-  c(2.8, 3.0, 2.8, 2.2, 3.3, 3.3, 3.5, 3.7, 3.4, 2.9)
+SATV <-  c(500, 550, 450, 400, 600, 650, 700, 550, 650, 550)
+scholar <- data.frame(FGPA, HSGPA, SATV) # collect into a data frame
+# install.packages("psych")
+# library(psych)
+describe(scholar) # provides descrptive information about each variable
+corrs <- cor(scholar) # find the correlations and set them into an object called 'corrs'
+corrs                 # print corrs
+pairs(scholar)        # pairwise scatterplots
+attach(scholar)
+# install.packages("corrplot")
+library(corrplot)
+corrplot(cor(scholar), method = "number")
+</code>
+{{:pasted:20230517-114950.png}}
+독립변인인 SATV와 HSGPA 간의 상관관계가 상당히 높다는 것을 알 수 있다 (r = 0.87).
+====== using Tolerance ======
+<code>
+m.tolerance <- lm(SATV~HSGPA, data=scholar)
+summary(m.tolerance)
+- summary(m.tolerance)$r.squared
+# 0.1보다 작으면 가능성이 아주 많음
+# 위의 이야기는 자신을 제외한 다른 독립변인들과의 상관관계가 0.9 이상이면 문제라는 이야기
+</code>
+<code>
+> m.tolerance <- lm(SATV~HSGPA, data=scholar)
+> summary(m.tolerance)
+Call:
+lm(formula = SATV ~ HSGPA, data = scholar)
+Residuals:
+    Min      1Q  Median      3Q     Max
+-101.86  -19.29    1.14   28.31   54.13
+Coefficients:
+            Estimate Std. Error t value Pr(>|t|)
+(Intercept)    -19.4      114.6   -0.17  0.86967
+HSGPA          176.7       34.6    5.10  0.00093 ***
+---
+Signif. codes:
+‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+Residual standard error: 48.2 on 8 degrees of freedom
+Multiple R-squared:  0.765,	Adjusted R-squared:  0.735
+F-statistic:   26 on 1 and 8 DF,  p-value: 0.00093
+> tol <- 1 - summary(m.tolerance)$r.squared
+> tol
+[1] 0.2352
+</code>
+====== using VIF (Variance Inflation Factors) ======
+Variance Inflation Factor 는 독립변인의 계수값에 인플레이션이 있는지 확인해 보는 방법으로 VIF = 1 인 경우, 해당 독립변인이 다른 변인들에 의해 영향을 받지 않았다는 것을 의미한다. 아래처럼 구한다. 일반적으로 VIF 값이 5 이상이면 주목하여 살펴본다. 10 이상이면 multicollinearity를 의미한다고 한다.
+<code>
+tol <- 1- summary(m.tolerance)$r.squared
+tol
+m.vif <- 1/tol
+m.vif
+</code>
+<code>
+> tol <- 1- summary(m.tolerance)$r.squared
+> tol
+[1] 0.2352
+> m.vif <- 1/tol
+> m.vif
+[1] 4.251
+>
+</code>
+R 에서는
+<code>
+m.a <- lm(FGPA ~ SATV+HSGPA, data = scholar)
+summary(m.a)
+# install.packages("olsrr")
+# library(olsrr)
+ols_vif_tol(m.a)
+</code>
+<code>
+> m.a <- lm(FGPA ~ SATV+HSGPA, data = scholar)
+> summary(m.a)
+Call:
+lm(formula = FGPA ~ SATV + HSGPA, data = scholar)
+Residuals:
+    Min      1Q  Median      3Q     Max
+-0.2431 -0.1125 -0.0286  0.1269  0.2716
+Coefficients:
+            Estimate Std. Error t value Pr(>|t|)
+(Intercept) 0.233102   0.456379    0.51    0.625
+SATV        0.000151   0.001405    0.11    0.917
+HSGPA       0.845192   0.283816    2.98    0.021 *
+---
+Signif. codes:
+‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+Residual standard error: 0.192 on 7 degrees of freedom
+Multiple R-squared:  0.851,	Adjusted R-squared:  0.809
+F-statistic: 20.1 on 2 and 7 DF,  p-value: 0.00126
+> # install.packages("olsrr")
+> # library(olsrr)
+> ols_vif_tol(m.a)
+  Variables Tolerance   VIF
+      SATV    0.2352 4.251
+     HSGPA    0.2352 4.251
+>
+</code>
+====== using condition index ======
+<code>
+ols_eigen_cindex(m.a)
+</code>
+<code>
+> ols_eigen_cindex(m.a)
+  Eigenvalue Condition Index intercept      SATV     HSGPA
+   2.983908            1.00  0.001961 0.0006461 0.0004659
+   0.013568           14.83  0.837019 0.1204555 0.0222304
+   0.002524           34.38  0.161020 0.8788984 0.9773037
+>
+</code>
 {{tag>multicollinearity singularity regression preassumption statistics }}