Multivariate regression

[Renee K]

Hello,

I am using SPSS 20.0 and am running a multivariate regression using the GLM
procedure. I would
like to know how to test whether the relationship between one
independent variable (X1) and one dependent variable (Y1) is equivalent
to the relationship between another independent variable (X2) and
another dependent variable (Y2). In other words, if (X1 Y1) = (X2 Y2).
Does anyone know how to write this using syntax? Thank you for any help.

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[Bruce Weaver]

If "relationship" = Pearson correlation, then you can use the modified Pearson-Filon test -- see syntax file number 7 here:

https://sites.google.com/a/lakeheadu.ca/bweaver/Home/statistics/spss/my-spss-page/weaver_wuensch

I don't know off the top of my head how to do it if relationship = regression coefficient (i.e., slope).

HTH.

Renee K wrote

Hello,

I am using SPSS 20.0 and am running a multivariate regression using the GLM
procedure. I would
like to know how to test whether the relationship between one
independent variable (X1) and one dependent variable (Y1) is equivalent
to the relationship between another independent variable (X2) and
another dependent variable (Y2). In other words, if (X1 Y1) = (X2 Y2).
Does anyone know how to write this using syntax? Thank you for any help.

=====================
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[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
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[Maguin, Eugene]

As far as I know, the best method would be to use an SEM program, for example, Amos, which you may have installed with spss, because you can constrain coefficients to be equal and test the change in fit. I don't think that can be done in any GLM structured program. If you use an SEM program, the data should be in wide (multivariate) format rather than long format. Equality requires both slope and intercept equality and, ideally, equal residual variances.

Gene Maguin



-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Renee K
Sent: Wednesday, July 24, 2013 9:46 AM
To: [hidden email]
Subject: Multivariate regression

Hello,

I am using SPSS 20.0 and am running a multivariate regression using the GLM procedure. I would like to know how to test whether the relationship between one independent variable (X1) and one dependent variable (Y1) is equivalent to the relationship between another independent variable (X2) and another dependent variable (Y2). In other words, if (X1 Y1) = (X2 Y2).
Does anyone know how to write this using syntax? Thank you for any help.

=====================
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[Bruce Weaver]

If you don't have Amos, and want to compare the regression slopes (rather than the correlations), here's another approach that might work.  I believe you can get GLM to save the covariance matrix for the coefficients via the /OUTFILE sub-command.  Then a test comparing the two slopes (b1 and b2) would look something like this:

z (or t) = (b1 - b2) / SE_diff

where b1 = slope for (X1 Y1), b2 = slope for (X2 Y2)  
         SE_diff = SQRT( SE1**2 + SE2**2 - 2*COV12 )
         SE1 = SE for b1, SE2 = SE for b2, COV12 = the covariance of b1 and b2
 
No doubt, there's a nice neat matrix algebra method for doing this too, but I can't find it in any of the books I've checked.  

Maguin, Eugene wrote

As far as I know, the best method would be to use an SEM program, for example, Amos, which you may have installed with spss, because you can constrain coefficients to be equal and test the change in fit. I don't think that can be done in any GLM structured program. If you use an SEM program, the data should be in wide (multivariate) format rather than long format. Equality requires both slope and intercept equality and, ideally, equal residual variances.

Gene Maguin



-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Renee K
Sent: Wednesday, July 24, 2013 9:46 AM
To: [hidden email]
Subject: Multivariate regression

Hello,

I am using SPSS 20.0 and am running a multivariate regression using the GLM procedure. I would like to know how to test whether the relationship between one independent variable (X1) and one dependent variable (Y1) is equivalent to the relationship between another independent variable (X2) and another dependent variable (Y2). In other words, if (X1 Y1) = (X2 Y2).
Does anyone know how to write this using syntax? Thank you for any help.

=====================
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=====================
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[Bruce Weaver]

I received this comment from Karl Wuensch, my co-author for the article cited below.

"I think she does want to compare the correlation coefficients.  Comparing slopes would be like comparing apples with bricks.  The regression coefficients (unstandardized slopes) would not be in comparable units.  One would be in units of y1 per unit of X1 and the other in units of y2 per unit of X2."

HTH.

Bruce Weaver wrote

If "relationship" = Pearson correlation, then you can use the modified Pearson-Filon test -- see syntax file number 7 here:

https://sites.google.com/a/lakeheadu.ca/bweaver/Home/statistics/spss/my-spss-page/weaver_wuensch

I don't know off the top of my head how to do it if relationship = regression coefficient (i.e., slope).

HTH.

Renee K wrote

Hello,

I am using SPSS 20.0 and am running a multivariate regression using the GLM
procedure. I would
like to know how to test whether the relationship between one
independent variable (X1) and one dependent variable (Y1) is equivalent
to the relationship between another independent variable (X2) and
another dependent variable (Y2). In other words, if (X1 Y1) = (X2 Y2).
Does anyone know how to write this using syntax? Thank you for any help.

=====================
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command. To leave the list, send the command
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[Andy W]

Here is how I have been told to go about this, assuming the initial equations are;

y1 = a1 + b1(x1)
y2 = a2 + b2(x2)

Stack each sample so you have all the y's and x's in the same column, and you have a dummy variable representing the two samples and estimate the model;

y = a + b3(x) + b4(Dummy) + b5(Dummy*x)

Lets say here the dummy variable represents the 2nd sample. For the first sample, the last two terms drop out, so you are back to the original equation;

y = a + b3(x)

For the second sample, because [Dummy*x] equals [x], you end up with;

y = (a + b4(Dummy)) + (b3+b5)*(x)

Which you can do the math and see how it reduces to the second group equation estimated separately. So in the combined model the interaction term tests the differences between slopes. Note by construction the intercepts are accounted for, so changes in location between samples is "controlled". This extends to multiple variables and different GLMs.

In concordance with Bruce's advice, if stacking and estimating the models doesn't make any sense (e.g. the error variances or distributions are non-sensical to fit using the same model), then you will not want to do this. I have no idea how this compares to Gene's advice about SEM restrictions.