AVAS Transformation Interpretation of Multiple Factor Regression Equation

Question

I implemented AVAS on my data in R.

$y = \text{weight}$, $x =$ matrix with several predictors, e.g. age, height, gender.

From what I understand, AVAS estimates transformations of $x$ and $y$ such that the regression of $y$ on $x$ is approximately linear with constant variance.

I followed the help file and did a plot for the following:

plot(a$y,a$ty) – this looks like a cubic curve which is not on any of the graphs on the help file. plot(a$x,a$tx) – this looks like a big blob of black.

My question is – how do I interpret the results, and how do I know what transformation was used to transform the data? E.g if I have a linear model: $\text{weight = age + height + gender}$ then how do I transform this using AVAS in R?

Also – if AVAS transforms the data – can I then perform variable selection on this data to 'eliminate' variables? Or does it also eliminate variables in the process?

Answer 1

There's no reason the y-transformation for your data would look like any of the graphs in the help file.

Can you show the plot for the $x$? Something sounds odd there.

You can only "know" what the transformation is from the plot; it's empirical -- it doesn't have a specific functional form. That is, the plots you mentioned show the transformations.

If you need a specific functional form for the transformations, the empirical transformations will help you identify good choices.

E.g if I have a linear model: weight = age + height + gender then how do I transform this using AVAS in R?

You don't transform a linear model using AVAS. AVAS fits additive, variance-stabilized models to transformed Y. You supply weight as y, and age, height, & gender as x's, and AVAS will try to find optimal transforms of the y and the x's so that an additive model $h(y) = \sum_j g_j(x_j) + e$ fits well and has approximately constant variance.

Also – if AVAS transforms the data – can I then perform variable selection on this data to 'eliminate' variables? Or does it also eliminate variables in the process?

AVAS doesn't eliminate variables. You can choose what variables you fit, but I am unsure how well the properties of AVAS carry through variable selection procedures.