係數表在秩不足時沒有NA行;如何插入它們？

Question

library(lmPerm) 
x <- lmp(formula = a ~ b * c + d + e, data = df, perm = "Prob") 

summary(x) # truncated output, I can see `NA` rows here! 

#Coefficients: (1 not defined because of singularities) 
#     Estimate Iter Pr(Prob) 
#b     5.874 51 1.000 
#c    -30.060 281 0.263 
#b:c     NA NA  NA 
#d1    -31.333 60 0.633 
#d2    33.297 165 0.382 
#d3    -19.096 51 1.000 
#e     1.976 NA  NA 

我想拔出Pr(Prob)結果一切，但

y <- summary(x)$coef[, "Pr(Prob)"] 

#(Intercept)   b   c   d1   d2 
# 0.09459459 1.00000000 0.26334520 0.63333333 0.38181818 
#   d3   e 
# 1.00000000   NA 

這不是我想要的。我也需要b:c排，在正確的位置。

我會從上面的喜歡將是輸出的一個例子：

# (Intercept)   b   c b:c   d1   d2 
# 0.09459459 1.00000000 0.26334520  NA 0.63333333 0.38181818 
#   d3   e 
# 1.00000000   NA 

我也想拉出對應於每個可變的Iter柱。謝謝。

Answer 1

lmp基於lm和summary.lmp也表現得像summary.lm，所以我會先用lm爲了說明，那麼說明我們能爲lmp這樣做。

---

lm和summary.lm

對?summary.lm讀取並注意以下返回值：

coefficients: a p x 4 matrix with columns for the estimated 
       coefficient, its standard error, t-statistic and 
       corresponding (two-sided) p-value. Aliased coefficients are 
       omitted. 

    aliased: named logical vector showing if the original coefficients are 
       aliased. 

當你有秩虧模型，NA係數被省略係數表，它們被稱爲aliased變量。請看下面的小，可重複的例子：

set.seed(0) 
zz <- xx <- rnorm(10) 
yy <- rnorm(10) 
fit <- lm(yy ~ xx + zz) 

coef(fit) ## we can see `NA` here 
#(Intercept)   xx   zz 
# 0.1295147 0.2706560   NA 

a <- summary(fit) ## it is also printed to screen 
#Coefficients: (1 not defined because of singularities) 
#   Estimate Std. Error t value Pr(>|t|) 
#(Intercept) 0.1295  0.3143 0.412 0.691 
#xx   0.2707  0.2669 1.014 0.340 
#zz    NA   NA  NA  NA 

b <- coef(a) ## but no `NA` returned in the matrix/table 
#    Estimate Std. Error t value Pr(>|t|) 
#(Intercept) 0.1295147 0.3142758 0.4121051 0.6910837 
#xx   0.2706560 0.2669118 1.0140279 0.3402525 

d <- a$aliased 
#(Intercept)   xx   zz 
#  FALSE  FALSE  TRUE 

如果你想墊NA行係數表/矩陣，我們可以做

## an augmented matrix of `NA` 
e <- matrix(nrow = length(d), ncol = ncol(b), 
      dimnames = list(names(d), dimnames(b)[[2]])) 
## fill rows for non-aliased variables 
e[!d] <- b 

#    Estimate Std. Error t value Pr(>|t|) 
#(Intercept) 0.1295147 0.3142758 0.4121051 0.6910837 
#xx   0.2706560 0.2669118 1.0140279 0.3402525 
#zz     NA   NA  NA  NA 

---

lmp和summary.lmp

什麼都不需要改變。

library(lmPerm) 
fit <- lmp(yy ~ xx + zz, perm = "Prob") 
a <- summary(fit) ## `summary.lmp` 
b <- coef(a) 

#    Estimate Iter Pr(Prob) 
#(Intercept) -0.0264354 241 0.2946058 
#xx   0.2706560 241 0.2946058 

d <- a$aliased 
#(Intercept)   xx   zz 
#  FALSE  FALSE  TRUE 

e <- matrix(nrow = length(d), ncol = ncol(b), 
      dimnames = list(names(d), dimnames(b)[[2]])) 
e[!d] <- b 

#    Estimate Iter Pr(Prob) 
#(Intercept) -0.0264354 241 0.2946058 
#xx   0.2706560 241 0.2946058 
#zz     NA NA  NA 

如果，要提取Iter和Pr(Prob)，只是做

e[, 2] ## e[, "Iter"] 
#(Intercept)   xx   zz 
#  241   241   NA 

e[, 3] ## e[, "Pr(Prob)"] 
#(Intercept)   xx   zz 
# 0.2946058 0.2946058   NA