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--- multicolinearity [2016/04/27 06:36] – hkimscil
+++ multicolinearity [2018/12/26 02:49] (current) – [regression test with factors] hkimscil
@@ Line 1: / Line 1: @@
-{{keywords>multicollinearity, singularity, statistics}}
+====== Multi-colinearity check in r ======
-====== Multicollinearity and Singularity ======
+required library:
-변인들 간의 상관관계가 극한 정도로 이루어질 때 multicollinearity가 있다고 한다. 예를 들어 IQ score와 수학점수는 상당한 [[Correlation|상관관계]]에 있을 것이다. 이 두 변인은 서로 비숫한 대상(현상)을 측정한 것이기 때문이다. 이 두 변인이 독립변인으로 regression과 같은 test에 사용된다면, 동일한 현상에 대한 설명력을 나눠가지려고 하기때문에 문제를 일으키게 된다.
+  * corrplot
+  * mctest
+    * omcdiag
+    * imcdiag
-만약에 IQ점수와 IQ점수의 세부점수들을 (지각력, 공간력, 수학력, 언어능력이라고 가정하면) 간의 관계는 사실 동일한 것이라고 하겠다. IQ점수는 이 세부점수를 모두 더한 값이기 때문이다. 이와 같은 상황을 Singularity라고 한다.
-[[:Singularity]] \\
+<code>
-[[:Multicolinearity]]
+> cps <- read.csv("http://commres.net/wiki/_media/cps_85_wages.csv", header = T, sep = "\t")
+</code>
-{{tag>multicolinearity singularity regression preassumption statistics }}
+<code>> str(cps)
+'data.frame':	534 obs. of  11 variables:
+ $ education : int  8 9 12 12 12 13 10 12 16 12 ...
+ $ south     : int  0 0 0 0 0 0 1 0 0 0 ...
+ $ sex       : int  1 1 0 0 0 0 0 0 0 0 ...
+ $ experience: int  21 42 1 4 17 9 27 9 11 9 ...
+ $ union     : int  0 0 0 0 0 1 0 0 0 0 ...
+ $ wage      : num  5.1 4.95 6.67 4 7.5 ...
+ $ age       : int  35 57 19 22 35 28 43 27 33 27 ...
+ $ race      : int  2 3 3 3 3 3 3 3 3 3 ...
+ $ occupation: int  6 6 6 6 6 6 6 6 6 6 ...
+ $ sector    : int  1 1 1 0 0 0 0 0 1 0 ...
+ $ marr      : int  1 1 0 0 1 0 0 0 1 0 ...
+> head(cps)
+> head(cps)
+  education south sex experience union  wage age race occupation sector marr
+         8     0   1         21     0  5.10  35    2          6      1    1
+         9     0   1         42     0  4.95  57    3          6      1    1
+        12     0   0          1     0  6.67  19    3          6      1    0
+        12     0   0          4     0  4.00  22    3          6      0    0
+        12     0   0         17     0  7.50  35    3          6      0    1
+        13     0   0          9     1 13.07  28    3          6      0    0
+</code>
+<code>
+> lm1 = lm(log(cps$wage) ~., data = cps)
+> summary(lm1)
+Call:
+lm(formula = log(cps$wage) ~ ., data = cps)
+Residuals:
+     Min       1Q   Median       3Q      Max
+-2.16246 -0.29163 -0.00469  0.29981  1.98248
+Coefficients:
+             Estimate Std. Error t value Pr(>|t|)
+(Intercept)  1.078596   0.687514   1.569 0.117291
+education    0.179366   0.110756   1.619 0.105949
+south       -0.102360   0.042823  -2.390 0.017187 *
+sex         -0.221997   0.039907  -5.563 4.24e-08 ***
+experience   0.095822   0.110799   0.865 0.387531
+union        0.200483   0.052475   3.821 0.000149 ***
+age         -0.085444   0.110730  -0.772 0.440671
+race         0.050406   0.028531   1.767 0.077865 .
+occupation  -0.007417   0.013109  -0.566 0.571761
+sector       0.091458   0.038736   2.361 0.018589 *
+marr         0.076611   0.041931   1.827 0.068259 .
+---
+Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+Residual standard error: 0.4398 on 523 degrees of freedom
+Multiple R-squared:  0.3185,	Adjusted R-squared:  0.3054
+F-statistic: 24.44 on 10 and 523 DF,  p-value: < 2.2e-16
+</code>
+<code>
+plot(lm1)
+</code>
+{{lm1.plot1.png?300}}{{lm1.plot2.png?300}}
+{{lm1.plot3.png?300}}{{lm1.plot4.png?300}}
+<code>
+> library(corrplot)
+> cps.cor = cor(cps)
+> corrplot.mixed(cps.cor, lower.col = "black")
+</code>
+{{cps.corrplot.png?500}}
+<code>
+> install.packages("mctest")
+> library(mctest)
+> omcdiag(cps[,c(-6)], cps$wage) # or "omcdiag(cps[,c(1:5,7:11)], cps$wage)" will work as well.
+Call:
+omcdiag(x = cps[, c(-6)], y = cps$wage)
+Overall Multicollinearity Diagnostics
+                       MC Results detection
+Determinant |X'X|:         0.0001         1
+Farrar Chi-Square:      4833.5751         1
+Red Indicator:             0.1983         0
+Sum of Lambda Inverse: 10068.8439         1
+Theil's Method:            1.2263         1
+Condition Number:        739.7337         1
+--> COLLINEARITY is detected by the test
+--> COLLINEARITY is not detected by the test
+>
+</code>
+<code>
+> imcdiag(cps[,c(-6)],cps$wage)
+Call:
+imcdiag(x = cps[, c(-6)], y = cps$wage)
+All Individual Multicollinearity Diagnostics Result
+                 VIF    TOL          Wi          Fi Leamer      CVIF Klein
+education   231.1956 0.0043  13402.4982  15106.5849 0.0658  236.4725     1
+south         1.0468 0.9553      2.7264      3.0731 0.9774    1.0707     0
+sex           1.0916 0.9161      5.3351      6.0135 0.9571    1.1165     0
+experience 5184.0939 0.0002 301771.2445 340140.5368 0.0139 5302.4188     1
+union         1.1209 0.8922      7.0368      7.9315 0.9445    1.1464     0
+age        4645.6650 0.0002 270422.7164 304806.1391 0.0147 4751.7005     1
+race          1.0371 0.9642      2.1622      2.4372 0.9819    1.0608     0
+occupation    1.2982 0.7703     17.3637     19.5715 0.8777    1.3279     0
+sector        1.1987 0.8343     11.5670     13.0378 0.9134    1.2260     0
+marr          1.0961 0.9123      5.5969      6.3085 0.9551    1.1211     0
+--> COLLINEARITY is detected by the test
+--> COLLINEARITY is not detected by the test
+education , south , experience , age , race , occupation , sector , marr , coefficient(s) are non-significant may be due to multicollinearity
+R-square of y on all x: 0.2805
+* use method argument to check which regressors may be the reason of collinearity
+===================================
+>
+</code>
+<code>
+> round(pcor(cps[,c(-6)], method = "pearson")$estimate,4)
+           education   south     sex experience   union     age    race occupation  sector    marr
+education     1.0000 -0.0318  0.0515    -0.9976 -0.0075  0.9973  0.0172     0.0294 -0.0213 -0.0403
+south        -0.0318  1.0000 -0.0302    -0.0223 -0.0975  0.0215 -0.1112     0.0084 -0.0215  0.0304
+sex           0.0515 -0.0302  1.0000     0.0550 -0.1201 -0.0537  0.0200    -0.1428 -0.1121  0.0042
+experience   -0.9976 -0.0223  0.0550     1.0000 -0.0102  0.9999  0.0109     0.0421 -0.0133 -0.0410
+union        -0.0075 -0.0975 -0.1201    -0.0102  1.0000  0.0122 -0.1077     0.2130 -0.0135  0.0689
+age           0.9973  0.0215 -0.0537     0.9999  0.0122  1.0000 -0.0108    -0.0441  0.0146  0.0451
+race          0.0172 -0.1112  0.0200     0.0109 -0.1077 -0.0108  1.0000     0.0575  0.0064  0.0556
+occupation    0.0294  0.0084 -0.1428     0.0421  0.2130 -0.0441  0.0575     1.0000  0.3147 -0.0186
+sector       -0.0213 -0.0215 -0.1121    -0.0133 -0.0135  0.0146  0.0064     0.3147  1.0000  0.0365
+marr         -0.0403  0.0304  0.0042    -0.0410  0.0689  0.0451  0.0556    -0.0186  0.0365  1.0000
+</code>
+<code>
+> lm2 = lm(log(cps$wage) ~ . -age , data = cps)
+> summary(lm2)
+Call:
+lm(formula = log(cps$wage) ~ . - age, data = cps)
+Residuals:
+     Min       1Q   Median       3Q      Max
+-2.16044 -0.29073 -0.00505  0.29994  1.97997
+Coefficients:
+             Estimate Std. Error t value Pr(>|t|)
+(Intercept)  0.562676   0.160116   3.514 0.000479 ***
+education    0.094135   0.008188  11.497  < 2e-16 ***
+south       -0.103071   0.042796  -2.408 0.016367 *
+sex         -0.220344   0.039834  -5.532 5.02e-08 ***
+experience   0.010335   0.001746   5.919 5.86e-09 ***
+union        0.199987   0.052450   3.813 0.000154 ***
+race         0.050643   0.028519   1.776 0.076345 .
+occupation  -0.006971   0.013091  -0.532 0.594619
+sector       0.091022   0.038717   2.351 0.019094 *
+marr         0.075152   0.041872   1.795 0.073263 .
+---
+Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+Residual standard error: 0.4397 on 524 degrees of freedom
+Multiple R-squared:  0.3177,	Adjusted R-squared:  0.306
+F-statistic: 27.11 on 9 and 524 DF,  p-value: < 2.2e-16
+> summary(lm1)
+Call:
+lm(formula = log(cps$wage) ~ ., data = cps)
+Residuals:
+     Min       1Q   Median       3Q      Max
+-2.16246 -0.29163 -0.00469  0.29981  1.98248
+Coefficients:
+             Estimate Std. Error t value Pr(>|t|)
+(Intercept)  1.078596   0.687514   1.569 0.117291
+education    0.179366   0.110756   1.619 0.105949
+south       -0.102360   0.042823  -2.390 0.017187 *
+sex         -0.221997   0.039907  -5.563 4.24e-08 ***
+experience   0.095822   0.110799   0.865 0.387531
+union        0.200483   0.052475   3.821 0.000149 ***
+age         -0.085444   0.110730  -0.772 0.440671
+race         0.050406   0.028531   1.767 0.077865 .
+occupation  -0.007417   0.013109  -0.566 0.571761
+sector       0.091458   0.038736   2.361 0.018589 *
+marr         0.076611   0.041931   1.827 0.068259 .
+---
+Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+Residual standard error: 0.4398 on 523 degrees of freedom
+Multiple R-squared:  0.3185,	Adjusted R-squared:  0.3054
+F-statistic: 24.44 on 10 and 523 DF,  p-value: < 2.2e-16
+>
+> </code>
+====== regression test with factors ======
+<code>
+> cps$sex <- factor(cps$sex)
+> cps$union <- factor(cps$union)
+> cps$race <- factor(cps$race)
+> cps$sector <- factor(cps$sector)
+> cps$occupation <- factor(cps$occupation)
+> cps$marr <- factor(cps$marr)
+> str(cps)
+'data.frame':	534 obs. of  11 variables:
+ $ education : int  8 9 12 12 12 13 10 12 16 12 ...
+ $ south     : int  0 0 0 0 0 0 1 0 0 0 ...
+ $ sex       : Factor w/ 2 levels "0","1": 2 2 1 1 1 1 1 1 1 1 ...
+ $ experience: int  21 42 1 4 17 9 27 9 11 9 ...
+ $ union     : Factor w/ 2 levels "0","1": 1 1 1 1 1 2 1 1 1 1 ...
+ $ wage      : num  5.1 4.95 6.67 4 7.5 ...
+ $ age       : int  35 57 19 22 35 28 43 27 33 27 ...
+ $ race      : Factor w/ 3 levels "1","2","3": 2 3 3 3 3 3 3 3 3 3 ...
+ $ occupation: Factor w/ 6 levels "1","2","3","4",..: 6 6 6 6 6 6 6 6 6 6 ...
+ $ sector    : Factor w/ 3 levels "0","1","2": 2 2 2 1 1 1 1 1 2 1 ...
+ $ marr      : Factor w/ 2 levels "0","1": 2 2 1 1 2 1 1 1 2 1 ...
+</code>
+<code>
+> lm4 = lm(log(cps$wage) ~ . -age, data = cps)
+> summary(lm4)
+Call:
+lm(formula = log(cps$wage) ~ . - age, data = cps)
+Residuals:
+     Min       1Q   Median       3Q      Max
+-2.36103 -0.28080  0.00362  0.27793  1.79594
+Coefficients:
+             Estimate Std. Error t value Pr(>|t|)
+(Intercept)  1.194821   0.181804   6.572 1.21e-10 ***
+education    0.066603   0.010060   6.621 8.96e-11 ***
+south       -0.093384   0.041931  -2.227  0.02637 *
+sex1        -0.216934   0.041844  -5.184 3.11e-07 ***
+experience   0.009371   0.001725   5.431 8.63e-08 ***
+union1       0.211506   0.051218   4.129 4.24e-05 ***
+race2       -0.033928   0.099051  -0.343  0.73209
+race3        0.079851   0.057392   1.391  0.16472
+occupation2 -0.364444   0.091500  -3.983 7.78e-05 ***
+occupation3 -0.210295   0.076175  -2.761  0.00597 **
+occupation4 -0.383882   0.080990  -4.740 2.77e-06 ***
+occupation5 -0.050664   0.072717  -0.697  0.48628
+occupation6 -0.265348   0.079969  -3.318  0.00097 ***
+sector1      0.114857   0.054862   2.094  0.03678 *
+sector2      0.093138   0.096514   0.965  0.33499
+marr1        0.062211   0.041025   1.516  0.13002
+---
+Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+Residual standard error: 0.4278 on 518 degrees of freedom
+Multiple R-squared:  0.3614,	Adjusted R-squared:  0.3429
+F-statistic: 19.54 on 15 and 518 DF,  p-value: < 2.2e-16
+>
+</code>
+<code>> lm5 = lm(log(cps$wage) ~ . -age -race, data = cps)
+> summary(lm5)
+Call:
+lm(formula = log(cps$wage) ~ . - age - race, data = cps)
+Residuals:
+     Min       1Q   Median       3Q      Max
+-2.34366 -0.28169 -0.00017  0.29179  1.81158
+Coefficients:
+             Estimate Std. Error t value Pr(>|t|)
+(Intercept)  1.224289   0.172070   7.115 3.73e-12 ***
+education    0.068838   0.009912   6.945 1.14e-11 ***
+south       -0.102588   0.041668  -2.462 0.014139 *
+sex1        -0.213602   0.041842  -5.105 4.65e-07 ***
+experience   0.009494   0.001723   5.510 5.65e-08 ***
+union1       0.202720   0.051009   3.974 8.06e-05 ***
+occupation2 -0.355381   0.091448  -3.886 0.000115 ***
+occupation3 -0.209820   0.076149  -2.755 0.006068 **
+occupation4 -0.385680   0.080855  -4.770 2.40e-06 ***
+occupation5 -0.047694   0.072746  -0.656 0.512351
+occupation6 -0.254277   0.079781  -3.187 0.001523 **
+sector1      0.111458   0.054845   2.032 0.042636 *
+sector2      0.099777   0.096481   1.034 0.301541
+marr1        0.065464   0.041036   1.595 0.111257
+---
+Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+Residual standard error: 0.4283 on 520 degrees of freedom
+Multiple R-squared:  0.3573,	Adjusted R-squared:  0.3412
+F-statistic: 22.24 on 13 and 520 DF,  p-value: < 2.2e-16
+>
+</code>
+<code>> lm6 = lm(log(cps$wage) ~ . -age -race -occupation -marr -sector, data = cps)
+> summary(lm6)
+Call:
+lm(formula = log(cps$wage) ~ . - age - race - occupation - marr -
+    sector, data = cps)
+Residuals:
+     Min       1Q   Median       3Q      Max
+-2.13809 -0.28681 -0.00078  0.29376  1.96678
+Coefficients:
+             Estimate Std. Error t value Pr(>|t|)
+(Intercept)  0.731792   0.122217   5.988 3.94e-09 ***
+education    0.094096   0.007942  11.848  < 2e-16 ***
+south       -0.111761   0.042857  -2.608 0.009372 **
+sex1        -0.231978   0.039202  -5.918 5.88e-09 ***
+experience   0.011548   0.001680   6.875 1.75e-11 ***
+union1       0.198360   0.051243   3.871 0.000122 ***
+---
+Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+Residual standard error: 0.4433 on 528 degrees of freedom
+Multiple R-squared:  0.3011,	Adjusted R-squared:  0.2944
+F-statistic: 45.49 on 5 and 528 DF,  p-value: < 2.2e-16
+> </code>