# [R] kruskal's MONANOVA algorithm

From: Jaime Brugueras <jbrugueras_at_gmail.com>
Date: Wed, 6 Feb 2008 11:43:52 -0600

I am trying to obtain the Kruskal (1964) secondary least-squares monotonic transformation of a rank variable given 4 categorical variables in order to obtain optimal transformation for regression. The academic problem assigned is to compare R, SPSS (Conjoint Analysis), and SAS' proc transreg in speed and accuracy. Currently, SAS and SPSS are giving similar results, but R's are quite different. There is something I am misunderstanding about acepackage and/or isoMDS.

The data looks like this:

Brand Price Life Hazard Rank
1 Goodstone \$69.99 60,000 Yes 3
2 Goodstone \$69.99 70,000 No 2
...

```7     Pirogi \$69.99 50,000     No    7
8     Pirogi \$69.99 70,000     No    1
9     Pirogi \$74.99 50,000    Yes    8

```

The ace and avas functions transform the y values into very small values of rank, like this:
\$ty
[1] -1.3552125 -1.6732919 0.8859707

and hence the estimates are quite different.

The R-squared is .93 while SAS and SPSS give .99.

The isoMDS from MASS package gives weird results when i choose k=4.

Here is my acepackage code and isoMDS function:

X <- cbind(Brand, Price, Life, Hazard) # independent variables

```Y <-  Rank                                     # response variable
cate <- as.vector(c(1,2,3,4))           # categorical variables(columns) in
```
X

mycon <- avas(x=X, y=Y, cat=cate)

mymatrix <- as.matrix((X)
row.names(mymatrix) <- Rank

Any help is well appreciated.

Thanks.

myc <- isoMDS(dist(mymatrix), k=?)

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