15장: 공분산분석(Analysis of Covariance)

[안재형]

# "Cont"를 reference로 지정

> anorexia = read.csv("anorexia.csv")
> levels(anorexia$Treat)
[1] "CBT"  "Cont" "FT" 
> anorexia$Treat = relevel(anorexia$Treat, ref="Cont")
> levels(anorexia$Treat)
[1] "Cont" "CBT"  "FT" 

# Fit ANCOVA & ANOVA table

> out = lm(Postwt ~ Prewt + Treat, data=anorexia)
> anova(out)
Analysis of Variance Table

Response: Postwt
          Df Sum Sq Mean Sq F value    Pr(>F)   
Prewt      1  506.5  506.51 10.4017 0.0019364 **
Treat      2  766.3  383.14  7.8681 0.0008438 ***
Residuals 68 3311.3   48.70                     
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

> summary(out)

Call:
lm(formula = Postwt ~ Prewt + Treat, data = anorexia)

Residuals:
     Min       1Q   Median       3Q      Max
-14.1083  -4.2773  -0.5484   5.4838  15.2922

Coefficients:
            Estimate Std. Error t value Pr(>|t|)   
(Intercept)  45.6740    13.2167   3.456 0.000950 ***
Prewt         0.4345     0.1612    2.695 0.008850 **
TreatCBT      4.0971   1.8935   2.164 0.033999 * 
TreatFT       8.6601     2.1931   3.949 0.000189 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 6.978 on 68 degrees of freedom
Multiple R-squared: 0.2777,     Adjusted R-squared: 0.2458
F-statistic: 8.713 on 3 and 68 DF,  p-value: 5.719e-05

## Multiple Comparisons

> library(multcomp)
> dunnett = glht(out, linfct=mcp(Treat="Dunnett"))
> summary(dunnett)

         Simultaneous Tests for General Linear Hypotheses

Multiple Comparisons of Means: Dunnett Contrasts

Fit: lm(formula = Postwt ~ Prewt + Treat, data = anorexia)

Linear Hypotheses:
                Estimate Std. Error t value Pr(>|t|)   
CBT - Cont == 0  4.097      1.893   2.164 0.062939 . 
FT - Cont == 0     8.660      2.193   3.949 0.000373 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Adjusted p values reported -- single-step method)

> plot(dunnett)

### tri.csv

> tri = read.csv("tri.csv")
> out = lm(trichg ~ hgba1c + trt, data=tri)
> anova(out)
Analysis of Variance Table

Response: trichg
          Df Sum Sq Mean Sq F value    Pr(>F)   
hgba1c     1 5442.7  5442.7 58.1068 1.353e-08 ***
trt             1  865.4   865.4  9.2387  0.004783 **
Residuals 31 2903.7    93.7                     
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1