Chow Test

[Anthony Santella]

I am trying to write syntax to conduct a Chows test to see if "year
of hospitalization" should be included in my regression model as an
independent variable.

I have 3 models/research questions:
Model 1: dependent variable (Y)= continuous
Model 2: dependent variable (Y)= continuous
Model 3: dependent variable (Y)= categorical

All 3 models have 9 independent variables (X) which are categorical.

In my case, how do I modify the below syntax?  Can you clarify the "Group"
variable?

CHOW TEST IN SPSS
Let's say we have a dependent variable named Y, a continuous predictor
named X, and a categorical variable named Group.  Here are the steps
you'll want to follow to conduct the Chow test.
>
1.  From the menus, go to Analyze->General Linear>Model->Univariate....
2.  In the Univariate dialog box, move Y into the box labeled Dependent
Variable.
3.  Move the grouping variable Group into the box labeled Fixed Factor(s).
4.  Move the continuous predictor X into the box labeled Covariate(s).
5.  Now, instead of clicking OK, click PASTE.  The contents of your syntax
window should appear as follows.
>
>          UNIANOVA
>            y  BY group  WITH x
>            /METHOD = SSTYPE(3)
>            /INTERCEPT = INCLUDE
>            /CRITERIA = ALPHA(.05)
>            /DESIGN = x group .
>
6.  In the SPSS Syntax Editor Window, modify the DESIGN subcommand to read
as shown below.
>
>          UNIANOVA
>            y  BY group  WITH x
>            /METHOD = SSTYPE(3)
>            /INTERCEPT = INCLUDE
>            /CRITERIA = ALPHA(.05)
>            /DESIGN = x group*x.
>
7.  Finally, run the commands by going to the menu in the SPSS

>Syntax Editor Window and selecting Run->All.
>
>Including the Group*X interaction--in the absence of a main effect for
>Group--causes SPSS GLM to pool the Sums of Squares and degrees of freedom
>from the sources Group and Group*X when it reports the F-test for Group*X.
>Given a model that included Group and Group*X, the Group term would test
>differences in intercepts and the Group*X term would test differences in
>slopes.  Pooling these terms into a single Group*X term means that the
>F-test and the associated p-value for the Group*X test is the overall test
>of whether the full set of regression parameters (i.e., the slopes and
>intercepts taken together) differ among groups.  Hence, the Group*X effect
>in this model is the Chow test we are looking for.

[JOHN ANTONAKIS]

Hi Anthony:

A Chow test is used to test whether a SET of regression
coefficients from two populations is equivalent.  What you
are doing is not a Chow test--and in fact, you don't need a
Chow test.

In your case, you have two equations:
y=a + b1x
y=a + b1x + b2z

Where y=DV, x=IV1 and z=IV2, Note: x or z can be dummy
coded (i.e., 0,1) or continuous variables.

If you estimate the first equation, the implicit constrained
you have is that b2 is zero. In the second equation, that
constraint is released. If the nested F-test change is
significant (and b2 is different from zero, which should be
the case if the r-square changes significantly), then you
accept the less constrained model (second equation). This is
the was to proceed if you want to know whether to add a
predictor to an equation. The above equations are easily
estimated in regression module of SPSS.

REGRESSION
  /MISSING LISTWISE
  /STATISTICS COEFF OUTS CI R ANOVA CHANGE
  /CRITERIA=PIN(.05) POUT(.10)
  /NOORIGIN
  /DEPENDENT Y
  /METHOD=ENTER X /METHOD=ENTER Z  .

HTH,
J.

----- Original Message -----
Expéditeur: Anthony Santella <[hidden email]>
à: [hidden email]
Sujet: Chow Test
Date: Thu, 30 Nov 2006 22:54:08 -0500

> I am trying to write syntax to conduct a Chows test to see
> if "year of hospitalization" should be included in my
> regression model as an independent variable.
>
> I have 3 models/research questions:
> Model 1: dependent variable (Y)= continuous
> Model 2: dependent variable (Y)= continuous
> Model 3: dependent variable (Y)= categorical
>
> All 3 models have 9 independent variables (X) which are
> categorical.
>
> In my case, how do I modify the below syntax?  Can you
> clarify the "Group" variable?
>
> CHOW TEST IN SPSS
> Let's say we have a dependent variable named Y, a
> continuous predictor named X, and a categorical variable
> named Group.  Here are the steps you'll want to follow to
> conduct the Chow test. >
> 1.  From the menus, go to Analyze->General
> Linear>Model->Univariate.... 2.  In the Univariate dialog
> box, move Y into the box labeled Dependent Variable.
> 3.  Move the grouping variable Group into the box labeled
> Fixed Factor(s). 4.  Move the continuous predictor X into
> the box labeled Covariate(s). 5.  Now, instead of clicking
> OK, click PASTE.  The contents of your syntax window
> should appear as follows. >
> >          UNIANOVA
> >            y  BY group  WITH x
> >            /METHOD = SSTYPE(3)
> >            /INTERCEPT = INCLUDE
> >            /CRITERIA = ALPHA(.05)
> >            /DESIGN = x group .
> >
> 6.  In the SPSS Syntax Editor Window, modify the DESIGN
> subcommand to read as shown below.
> >
> >          UNIANOVA
> >            y  BY group  WITH x
> >            /METHOD = SSTYPE(3)
> >            /INTERCEPT = INCLUDE
> >            /CRITERIA = ALPHA(.05)
> >            /DESIGN = x group*x.
> >
> 7.  Finally, run the commands by going to the menu in the
> SPSS >Syntax Editor Window and selecting Run->All.
> >
> >Including the Group*X interaction--in the absence of a
> main effect for >Group--causes SPSS GLM to pool the Sums
> of Squares and degrees of freedom >from the sources Group
> and Group*X when it reports the F-test for Group*X. >Given
> a model that included Group and Group*X, the Group term
> would test >differences in intercepts and the Group*X term
> would test differences in >slopes.  Pooling these terms
> into a single Group*X term means that the >F-test and the
> associated p-value for the Group*X test is the overall
> test >of whether the full set of regression parameters
> (i.e., the slopes and >intercepts taken together) differ
> among groups.  Hence, the Group*X effect >in this model is
> the Chow test we are looking for.

___________________________________

Prof. John Antonakis
Faculty of Management and Economics
University of Lausanne
Internef #527
CH-1015 Lausanne-Dorigny
Switzerland

Tel: ++41 (0)21 692-3438
Fax: ++41 (0)21 692-3305

http://www.hec.unil.ch/jantonakis
___________________________________

___________________________________

Prof. John Antonakis
Faculty of Management and Economics
University of Lausanne
Internef #527
CH-1015 Lausanne-Dorigny
Switzerland

Tel: ++41 (0)21 692-3438
Fax: ++41 (0)21 692-3305

http://www.hec.unil.ch/jantonakis
___________________________________