Christopher wrote:
> Hi,
> For 2 continuous variables, we measure the linear relation through
> correlation. For 2 categorical variables, we measure the relation through
> chi-square test.
> But how to measure, non-linear relation for 2 continuous variables.
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I am new to this board and have enjoyed following this thread. I feel sure
this will get me much negative feedback, but cannot resist offering my dos
centavos. Although it was quite some time ago, I thought I recalled that
for X and Y continuous variables, you could use regression analysis where
(1) Y = a0U + a1X
then constuct new variables
X1= X*X , the squared values of X
X2 = X* X1, the cubed values of X
A full model looks like:
(2) Y' = boU + b1X + b2X1 + b3X2
The test of model (2) as the full model with (1) the restricted model tells
if there is significant explanation of variance by squared or cubic
effects. If this model (2) is significant, then one sets out to ascertain
where the differences are, that is, squared or cubic effects. A model is
constucted
(3) Y'' = c0U + c1X + c2X1
Testing model (2) with (3) determines if the cubic effect is significant.
If the comparison of (2) with (3) is non-significant, then the next test is
(4) Y''' = d0U + d1X
Model (3) vs (4) reveals if the squared or quadratic effect is significant.
{the initial test of model (2) vs (1) is done to see if there is any
significance beyond the linear effect, to do otherwise is akin to running
multiple t-tests, especially if one is using 4th or 5th power variables.}
Although one can generate models with powers of X as one sees fit, it seems
to me to defy interpretation much beyond cubic functions. As I recall this
may have been suggested by Bottenberg & Ward or perhaps theirs was the use
of dummy variables for categorical variable model testing? Maybe it was
Kelly, Beggs & McNeil that first suggested this technique.
Be kind, I am a newbie..
