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sequential_regression [2019/10/18 07:18] – [r] hkimscilsequential_regression [2022/05/22 21:50] (current) – hkimscil
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 +====== Sequential or Hierarchical regression ======
 +연구자가 판단하여 독립변인들 중 필요한 것들을 묶어서 스테이지 별로 (단계 별) 넣고 분석하는 것을 말한다. Stepwise regression은 이를 컴퓨터나 계산방법을 통하여 수행하게 된다.  
 ====== 데이터 ====== ====== 데이터 ======
 ^  DATA for regression analysis   ^^^ ^  DATA for regression analysis   ^^^
Line 55: Line 57:
 x1sq - x1psq  ~= x2sq - x2psq x1sq - x1psq  ~= x2sq - x2psq
 0.311211 ~= 0.311583 0.311211 ~= 0.311583
 +
 +R에서 보는 예는 아래를 참조
 +
 </WRAP> </WRAP>
 ====== Seq. ====== ====== Seq. ======
Line 105: Line 110:
  
 </code> </code>
 +<code>
 +> datavar <- read.csv("http://commres.net/wiki/_media/regression01-bankaccount.csv")
 +> datavar 
 +   bankaccount income famnum
 +1            6    220      5
 +2            5    190      6
 +3            7    260      3
 +4            7    200      4
 +5            8    330      2
 +6           10    490      4
 +7            8    210      3
 +8           11    380      2
 +9            9    320      1
 +10           9    270      3
 +> m1 <- lm(bankaccount~income+famnum, data=datavar)
 +> summary(m1)
 +
 +Call:
 +lm(formula = bankaccount ~ income + famnum, data = datavar)
 +
 +Residuals:
 +    Min      1Q  Median      3Q     Max 
 +-1.2173 -0.5779 -0.1515  0.6642  1.1906 
 +
 +Coefficients:
 +             Estimate Std. Error t value Pr(>|t|)   
 +(Intercept)  6.399103   1.516539   4.220  0.00394 **
 +income       0.011841   0.003561   3.325  0.01268 * 
 +famnum      -0.544727   0.226364  -2.406  0.04702 * 
 +---
 +Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
 +
 +Residual standard error: 0.9301 on 7 degrees of freedom
 +Multiple R-squared:  0.7981, Adjusted R-squared:  0.7404 
 +F-statistic: 13.84 on 2 and 7 DF,  p-value: 0.003696
 +
 +> library(ppcor)
 +> spcor(datavar)
 +$estimate
 +            bankaccount    income     famnum
 +bankaccount   1.0000000 0.5646726 -0.4086619
 +income        0.7171965 1.0000000  0.2078919
 +famnum       -0.6166940 0.2470028  1.0000000
 +
 +$p.value
 +            bankaccount   income    famnum
 +bankaccount  0.00000000 0.113182 0.2748117
 +income       0.02964029 0.000000 0.5914441
 +famnum       0.07691195 0.521696 0.0000000
 +
 +$statistic
 +            bankaccount    income     famnum
 +bankaccount    0.000000 1.8101977 -1.1846548
 +income         2.722920 0.0000000  0.5623159
 +famnum        -2.072679 0.6744045  0.0000000
 +
 +$n
 +[1] 10
 +
 +$gp
 +[1] 1
 +
 +$method
 +[1] "pearson"
 +
 +> pcor(datavar)
 +$estimate
 +            bankaccount    income     famnum
 +bankaccount   1.0000000 0.7825112 -0.6728560
 +income        0.7825112 1.0000000  0.3422911
 +famnum       -0.6728560 0.3422911  1.0000000
 +
 +$p.value
 +            bankaccount     income     famnum
 +bankaccount  0.00000000 0.01267595 0.04702022
 +income       0.01267595 0.00000000 0.36723388
 +famnum       0.04702022 0.36723388 0.00000000
 +
 +$statistic
 +            bankaccount    income     famnum
 +bankaccount    0.000000 3.3251023 -2.4064253
 +income         3.325102 0.0000000  0.9638389
 +famnum        -2.406425 0.9638389  0.0000000
 +
 +$n
 +[1] 10
 +
 +$gp
 +[1] 1
 +
 +$method
 +[1] "pearson"
 +
 +## zero-order correlation
 +> cor(datavar)
 +            bankaccount     income     famnum
 +bankaccount   1.0000000  0.7944312 -0.6922935
 +income        0.7944312  1.0000000 -0.3999614
 +famnum       -0.6922935 -0.3999614  1.0000000
 +> 
 +
 +</code>
 +semipartial (part): spcor()
 +
 +|           | bankaccount  | income    | famnum  |
 +| bankaccount  | 1.0000000  | <fc #ff0000>0.5646726</fc>$(1)$  | <fc #ff0000>-0.4086619</fc>$(2)$  |
 +| income   | 0.7171965  | 1.0000000  | 0.2078919  |
 +| famnum      | -0.6166940  | 0.2470028  | 1.0000000  |
 +
 +
 +
 +|            | bankaccount  | income  | famnum    | 
 +| bankaccount  | 1.0000000  | <fc #ff0000>0.7825112</fc>  | <fc #ff0000>-0.6728560</fc>    | 
 +| income  | 0.7825112  | 1.0000000  | 0.3422911    | 
 +| famnum  | -0.6728560  | 0.3422911  | 1.0000000    | 
 +
 +
 +|  | bankaccount  | income  | famnum   | 
 +| bankaccount  | 1.0000000  | 0.7944312$(3)$  | -0.6922935$(4)$  | 
 +| income  | 0.7944312  | 1.0000000  | -0.3999614   | 
 +| famnum  | -0.6922935  | -0.3999614   | 1.0000000    | 
 +
 +<code>
 +sp.b.i <- 0.5646726 ## (1)
 +c.b.i <- 0.7944312 ## (3)
 +
 +sp.b.f <- -0.4086619 ## (2)
 +c.b.f <- -0.6922935 ## (4)
 +
 +c.b.i.sq <- c.b.i^2 ## (3)^2
 +sp.b.i.sq <- sp.b.i^2 ## (1)^2
 +c.b.i.sq - sp.b.i.sq 
 +
 +c.b.f.sq <- c.b.f^2 ## (4)^2
 +sp.b.f.sq <- sp.b.f^2 ## (1)^2
 +c.b.f.sq - sp.b.f.sq
 +</code>
 +
 +<code>
 +> sp.b.i <- 0.5646726
 +> c.b.i <- 0.7944312
 +> 
 +> sp.b.f <- -0.4086619
 +> c.b.f <- -0.6922935
 +> 
 +> c.b.i.sq <- c.b.i^2 ## (3)^2
 +> sp.b.i.sq <- sp.b.i^2
 +> 
 +> c.b.i.sq - sp.b.i.sq 
 +[1] 0.3123
 +> 
 +> c.b.f.sq <- c.b.f^2 ## (4)^2
 +> sp.b.f.sq <- sp.b.f^2
 +> 
 +> c.b.f.sq - sp.b.f.sq
 +[1] 0.3123
 +</code>
 +
 +0.3123 가 두 독립변인이 DV에 같이 (공히) 미치는 영향력 분량이다.  
 +
 +<code>
 +pcor.test(datavar$bankaccount, datavar$income, datavar$famnum)
 +pcor.test(datavar$bankaccount, datavar$famnum, datavar$income)
 +
 +spcor.test(datavar$bankaccount, datavar$income, datavar$famnum)
 +spcor.test(datavar$bankaccount, datavar$famnum, datavar$income)
 +</code>
 +. . . 
 +<code>
 +> pcor.test(datavar$bankaccount, datavar$income, datavar$famnum)
 +   estimate    p.value statistic  n gp  Method
 +1 0.7825112 0.01267595  3.325102 10  1 pearson
 +> pcor.test(datavar$bankaccount, datavar$famnum, datavar$income)
 +   estimate    p.value statistic  n gp  Method
 +1 -0.672856 0.04702022 -2.406425 10  1 pearson
 +>
 +> spcor.test(datavar$bankaccount, datavar$income, datavar$famnum)
 +   estimate  p.value statistic  n gp  Method
 +1 0.5646726 0.113182  1.810198 10  1 pearson
 +> spcor.test(datavar$bankaccount, datavar$famnum, datavar$income)
 +    estimate   p.value statistic  n gp  Method
 +1 -0.4086619 0.2748117 -1.184655 10  1 pearson
 +> 
 +> 
 + 
 +</code>
 +
 +====== e.g. 3. College enrollment in New Mexico University ======
 +<code>
 +> datavar <- read.csv("http://commres.net/wiki/_media/r/dataset_hlr.csv")
 +> str(datavar)
 +'data.frame': 29 obs. of  5 variables:
 + $ YEAR : int  1 2 3 4 5 6 7 8 9 10 ...
 + $ ROLL : int  5501 5945 6629 7556 8716 9369 9920 10167 11084 12504 ...
 + $ UNEM : num  8.1 7 7.3 7.5 7 6.4 6.5 6.4 6.3 7.7 ...
 + $ HGRAD: int  9552 9680 9731 11666 14675 15265 15484 15723 16501 16890 ...
 + $ INC  : int  1923 1961 1979 2030 2112 2192 2235 2351 2411 2475 ...
 +> 
 +</code>
 +
 +<code>
 +onePredictorModel <- lm(ROLL ~ UNEM, data = datavar)
 +twoPredictorModel <- lm(ROLL ~ UNEM + HGRAD, data = datavar)
 +threePredictorModel <- lm(ROLL ~ UNEM + HGRAD + INC, data = datavar)
 +</code>
 +
 +<code>summary(onePredictorModel)
 +summary(twoPredictorModel)
 +summary(threePredictorModel)
 +</code>
 +
 +<code>> summary(onePredictorModel)
 +
 +Call:
 +lm(formula = ROLL ~ UNEM, data = datavar)
 +
 +Residuals:
 +    Min      1Q  Median      3Q     Max 
 +-7640.0 -1046.5   602.8  1934.3  4187.2 
 +
 +Coefficients:
 +            Estimate Std. Error t value Pr(>|t|)  
 +(Intercept)   3957.0     4000.1   0.989   0.3313  
 +UNEM          1133.8      513.1   2.210   0.0358 *
 +---
 +Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
 +
 +Residual standard error: 3049 on 27 degrees of freedom
 +Multiple R-squared:  0.1531, Adjusted R-squared:  0.1218 
 +F-statistic: 4.883 on 1 and 27 DF,  p-value: 0.03579
 +</code>
 +
 +<code>> summary(twoPredictorModel)
 +
 +Call:
 +lm(formula = ROLL ~ UNEM + HGRAD, data = datavar)
 +
 +Residuals:
 +    Min      1Q  Median      3Q     Max 
 +-2102.2  -861.6  -349.4   374.5  3603.5 
 +
 +Coefficients:
 +              Estimate Std. Error t value Pr(>|t|)    
 +(Intercept) -8.256e+03  2.052e+03  -4.023  0.00044 ***
 +UNEM         6.983e+02  2.244e+02   3.111  0.00449 ** 
 +HGRAD        9.423e-01  8.613e-02  10.941 3.16e-11 ***
 +---
 +Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
 +
 +Residual standard error: 1313 on 26 degrees of freedom
 +Multiple R-squared:  0.8489, Adjusted R-squared:  0.8373 
 +F-statistic: 73.03 on 2 and 26 DF,  p-value: 2.144e-11
 +
 +> </code>
 +<code>
 +> summary(threePredictorModel)
 +
 +Call:
 +lm(formula = ROLL ~ UNEM + HGRAD + INC, data = datavar)
 +
 +Residuals:
 +     Min       1Q   Median       3Q      Max 
 +-1148.84  -489.71    -1.88   387.40  1425.75 
 +
 +Coefficients:
 +              Estimate Std. Error t value Pr(>|t|)    
 +(Intercept) -9.153e+03  1.053e+03  -8.691 5.02e-09 ***
 +UNEM         4.501e+02  1.182e+02   3.809 0.000807 ***
 +HGRAD        4.065e-01  7.602e-02   5.347 1.52e-05 ***
 +INC          4.275e+00  4.947e-01   8.642 5.59e-09 ***
 +---
 +Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
 +
 +Residual standard error: 670.4 on 25 degrees of freedom
 +Multiple R-squared:  0.9621, Adjusted R-squared:  0.9576 
 +F-statistic: 211.5 on 3 and 25 DF,  p-value: < 2.2e-16
 +
 +</code>
 +
 +<code>anova(onePredictorModel, twoPredictorModel, threePredictorModel)
 +Analysis of Variance Table
 +
 +Model 1: ROLL ~ UNEM
 +Model 2: ROLL ~ UNEM + HGRAD
 +Model 3: ROLL ~ UNEM + HGRAD + INC
 +  Res.Df       RSS Df Sum of Sq      F    Pr(>F)    
 +1     27 251084710                                  
 +2     26  44805568  1 206279143 458.92 < 2.2e-16 ***
 +3     25  11237313  1  33568255  74.68 5.594e-09 ***
 +---
 +Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
 +> 
 +</code>
 +
 +====== e.g. 4. Happiness  ======
 +{{:hierarchical.regression.data.csv}}
 +
 +<code>
 +# Import data (simulated data for this example)
 +# myData <- read.csv('http://static.lib.virginia.edu/statlab/materials/data/hierarchicalRegressionData.csv')  
 +myData <- read.csv("http://commres.net/wiki/_media/hierarchical.regression.data.csv")
 +</code>
 +
 +<code>
 +> str(myData)
 +'data.frame': 100 obs. of  5 variables:
 + $ happiness: int  5 5 6 4 3 5 5 5 4 4 ...
 + $ age      : int  24 28 25 26 20 25 24 24 26 26 ...
 + $ gender   : chr  "Male" "Male" "Female" "Male" ...
 + $ friends  : int  12 8 6 4 8 9 5 6 8 6 ...
 + $ pets     : int  3 1 0 2 0 0 5 2 1 4 ...
 +> myData$gender <- factor(myData$gender)
 +> str(myData)
 +'data.frame': 100 obs. of  5 variables:
 + $ happiness: int  5 5 6 4 3 5 5 5 4 4 ...
 + $ age      : int  24 28 25 26 20 25 24 24 26 26 ...
 + $ gender   : Factor w/ 2 levels "Female","Male": 2 2 1 2 1 2 2 2 2 2 ...
 + $ friends  : int  12 8 6 4 8 9 5 6 8 6 ...
 + $ pets     : int  3 1 0 2 0 0 5 2 1 4 ...
 +> 
 +</code>
 +
 +<code>
 +> m0 <- lm(happiness ~ 1, data = myData)
 +> anova(m0)
 +Analysis of Variance Table
 +
 +Response: happiness
 +          Df Sum Sq Mean Sq F value Pr(>F)
 +Residuals 99 240.84  2.4327               
 +> 
 +</code>
 +
 +<code>
 +# 불필요하지만 위의 분석이 variance와 
 +# 같은 것이라는 것을 아래처럼 확인한다.
 +> attach(myData)
 +The following objects are masked from myData (pos = 3):
 +
 +    age, friends, gender, happiness, pets
 +
 +> var(happiness)
 +[1] 2.432727
 +> length(happiness)
 +[1] 100
 +> df.happiness <- length(happiness) - 1
 +> df.happiness # degrees of freedom 
 +[1] 99
 +> ss.happiness <- var(happiness)* df.happiness # sum of square (ss) value for happiness variable
 +> ss.happiness 
 +[1] 240.84
 +> 
 +</code>
 +
 +<code>
 +> m1 <- lm(happiness ~ age + gender, data=myData)  # Model 1
 +> summary(m1)
 +
 +Call:
 +lm(formula = happiness ~ age + gender, data = myData)
 +
 +Residuals:
 +    Min      1Q  Median      3Q     Max 
 +-3.6688 -1.0094 -0.1472  0.8273  4.2973 
 +
 +Coefficients:
 +            Estimate Std. Error t value Pr(>|t|)    
 +(Intercept)  7.66778    2.01364   3.808 0.000246 ***
 +age         -0.13039    0.07936  -1.643 0.103611    
 +genderMale   0.16430    0.31938   0.514 0.608106    
 +---
 +Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
 +
 +Residual standard error: 1.553 on 97 degrees of freedom
 +Multiple R-squared:  0.02855, Adjusted R-squared:  0.008515 
 +F-statistic: 1.425 on 2 and 97 DF,  p-value: 0.2455
 +
 +> 
 +</code>
 +
 +<code>
 +# m1은 이미 위에서 실행
 +> m2 <- lm(happiness ~ age + gender + friends, data=myData)  # Model 2: Adding friends variable 
 +> m3 <- lm(happiness ~ age + gender + friends + pets, data = myData) # Model 3: Adding pets variable
 +</code>
 +
 +<code>
 +> anova(m1, m2, m3)
 +Analysis of Variance Table
 +
 +Model 1: happiness ~ age + gender
 +Model 2: happiness ~ age + gender + friends
 +Model 3: happiness ~ age + gender + friends + pets
 +  Res.Df    RSS Df Sum of Sq       F    Pr(>F)    
 +1     97 233.97                                   
 +2     96 209.27  1    24.696 12.1293 0.0007521 ***
 +3     95 193.42  1    15.846  7.7828 0.0063739 ** 
 +---
 +Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
 +> 
 +</code>
 +
 +<code>
 +> summary(m1)
 +
 +Call:
 +lm(formula = happiness ~ age + gender, data = myData)
 +
 +Residuals:
 +    Min      1Q  Median      3Q     Max 
 +-3.6688 -1.0094 -0.1472  0.8273  4.2973 
 +
 +Coefficients:
 +            Estimate Std. Error t value Pr(>|t|)    
 +(Intercept)  7.66778    2.01364   3.808 0.000246 ***
 +age         -0.13039    0.07936  -1.643 0.103611    
 +genderMale   0.16430    0.31938   0.514 0.608106    
 +---
 +Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
 +
 +Residual standard error: 1.553 on 97 degrees of freedom
 +Multiple R-squared:  0.02855, Adjusted R-squared:  0.008515 
 +F-statistic: 1.425 on 2 and 97 DF,  p-value: 0.2455
 +
 +> summary(m2)
 +
 +Call:
 +lm(formula = happiness ~ age + gender + friends, data = myData)
 +
 +Residuals:
 +    Min      1Q  Median      3Q     Max 
 +-3.5758 -1.0204  0.0156  0.8087  3.7299 
 +
 +Coefficients:
 +            Estimate Std. Error t value Pr(>|t|)   
 +(Intercept)  6.21730    1.96220   3.169  0.00206 **
 +age         -0.12479    0.07546  -1.654  0.10146   
 +genderMale   0.14931    0.30365   0.492  0.62405   
 +friends      0.18985    0.05640   3.366  0.00110 **
 +---
 +Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
 +
 +Residual standard error: 1.476 on 96 degrees of freedom
 +Multiple R-squared:  0.1311, Adjusted R-squared:  0.1039 
 +F-statistic: 4.828 on 3 and 96 DF,  p-value: 0.003573
 +
 +> summary(m3)
 +
 +Call:
 +lm(formula = happiness ~ age + gender + friends + pets, data = myData)
 +
 +Residuals:
 +    Min      1Q  Median      3Q     Max 
 +-3.0556 -1.0183 -0.1109  0.8832  3.5911 
 +
 +Coefficients:
 +            Estimate Std. Error t value Pr(>|t|)   
 +(Intercept)  5.78540    1.90266   3.041  0.00305 **
 +age         -0.11146    0.07309  -1.525  0.13057   
 +genderMale  -0.14267    0.31157  -0.458  0.64806   
 +friends      0.17134    0.05491   3.120  0.00239 **
 +pets         0.36391    0.13044   2.790  0.00637 **
 +---
 +Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
 +
 +Residual standard error: 1.427 on 95 degrees of freedom
 +Multiple R-squared:  0.1969, Adjusted R-squared:  0.1631 
 +F-statistic: 5.822 on 4 and 95 DF,  p-value: 0.0003105
 +
 +> 
 +</code>
 +
 +Report in research paper
 +{{:pasted:20201201-140842.png}}
 +{{:pasted:20201201-141106.png}}
 +
 +====== e.g. 5: Stock Market ======
 +see [[:r:multiple_regression#partial_semi-partial_correlation_and_r_squared_value|Partial and semipartial example in r]]
 +
 +====== e.g. 6: SWISS ======
 +
  
sequential_regression.1571350683.txt.gz · Last modified: 2019/10/18 07:18 by hkimscil
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