Date: Thu, 1 Jun 2006 13:27:53 -0400 Richard Ristow "SPSSX(r) Discussion" Richard Ristow Re: Comparing regression coefficients To: "Baglioni, Tony" <8AE883D86DBAAF4E9924E984A06927F20286F1E6@mcintire6.comm.vi rginia.edu> text/plain; charset=us-ascii; format=flowed; x-avg-checked=avg-ok-4FA329B5

At 09:32 AM 6/1/2006, Baglioni, Tony wrote:

>I have comparable data for two years. I have obtained the regression >equations for each year and now I want to compare the obtained >coefficients. I had a text that showed a simple t or z test for doing >this it's been lost through the ages. Does anyone know a simple test >for this comparison?

It's reasonably simple, but it takes a little calculation in the transformation language. And you have to re-run the regression, so you need to have the data available.

Y = C + SUM(i=1,k:c(i)X(i)).

Here, Y is the independent; C is the constant; and there are k independents, X(1) to X(k), with coefficients c(1) to c(k).

You solve the problem by re-casting it as a test that certain coefficients are zero. Here's where you need the data:

A. Combine the data for the two years. Let there be a variable YEAR2 which is an indicator variable for the second year: it is 0 for year 1, 1 for year 2. (You can do this with IN= clauses on ADD FILES, plus some computation.)

B. Calculate, for i = 1 to k, X2(I) = 0 if YEAR2 = 0 X2(I) = X(I) if YEAR2 = 1. (This is a fairly simple exercise in DO REPEAT).

C. Estimate the model

Y = C + YEAR2 + SUM(i=1,k:c(i)X(i))+ SUM(i=1,k:c2(i)X2(i)).

(WARNING: variable YEAR2 *must* be in the model.)

D. Test for equality of coefficients is then the test that all the c2(i) are zero. In SPSS regression, this would be (code not tested)

REGRESSION DEPENDENT=y /METHOD = ENTER(YEAR2,X_1 TO X_k) /METHOD = TEST (X2_1 TO X2_k).

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