I have columns which sum to one. They are membership dummies, fractions are
allowed - I made an example:

x <- c( 9.899898,6.9555431,-1.251,0.52000000,0.4800000,0.0000000,-2.2384737,
16.791361,6.8924369,-3.286,0.78846154,0.2115385,0.0000000,-0.4720061,
6.115735,-5.8381799,-1.176,1.00000000,0.0000000,0.0000000,-0.6312019,
10.325595,5.4950276,-2.634,1.00000000,0.0000000,0.0000000,1.4729420,
3.800141,4.1287662,-2.243,0.83000000,0.1700000,0.0000000,,0.9314859,
2.159567,-2.3952889,-4.645,0.53000000,0.0000000,0.4700000,0.7252069,
21.536111,3.3844964,-4.352,1.00000000,0.0000000,0.0000000,-0.9931833,
7.526573,-1.1675684,-5.023,1.00000000,0.0000000,0.0000000,0.2397390,
28.684897,-0.4594389,-3.233,0.89000000,0.0700000,0.0400000,0.6017004,
0.894931,-0.9059129,-5.023,0.04347826,0.0000000,0.9565217,0.6081505)
x = matrix(x,ncol=10)
x = t(x)
colnames(x) = c('a','b','c','d','e','f','y')
>  x
              a          b      c          d         e         f          y
 [1,]  9.899898  6.9555431 -1.251 0.52000000 0.4800000 0.0000000 -2.2384737
 [2,] 16.791361  6.8924369 -3.286 0.78846154 0.2115385 0.0000000 -0.4720061
 [3,]  6.115735 -5.8381799 -1.176 1.00000000 0.0000000 0.0000000 -0.6312019
 [4,] 10.325595  5.4950276 -2.634 1.00000000 0.0000000 0.0000000  1.4729420
 [5,]  3.800141  4.1287662 -2.243 0.83000000 0.1700000 0.0000000  0.9314859
 [6,]  2.159567 -2.3952889 -4.645 0.53000000 0.0000000 0.4700000  0.7252069
 [7,] 21.536111  3.3844964 -4.352 1.00000000 0.0000000 0.0000000 -0.9931833
 [8,]  7.526573 -1.1675684 -5.023 1.00000000 0.0000000 0.0000000  0.2397390
 [9,] 28.684897 -0.4594389 -3.233 0.89000000 0.0700000 0.0400000  0.6017004
[10,]  0.894931 -0.9059129 -5.023 0.04347826 0.0000000 0.9565217  0.6081505

> apply(x[,4:6],1,sum)
 [1] 1 1 1 1 1 1 1 1 1 1

I am trying to use lm.ridge and got some problems on how to extract
parameter estimates. E.g., for lambda = 0 case (I cut and pasted at the
bottom), how to backout the coef estimate to match them with lm fit? In
general, for any given lambda, how to back out the original scale coef
estimates?

> lm.fit = lm(y~.-a-1,data=data.frame(x),weights=a)
> ridge.fit = lm.ridge(y~.-a-1,data=data.frame(x),weights=a,lambda=0)
> ridge.fit
         b          c          d          e          f
 0.1125886  0.1748883  0.9122774 -5.9140208  1.8784332
> lm.fit

Call:
lm(formula = y ~ . - a - 1, data = data.frame(x), weights = a)

Coefficients:
       b         c         d         e         f
 0.04232   0.32343   1.36039  -4.67399   3.29727

Thanks so much in advance!

Young

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