Re: A Challenge : Enquiry about the CHOW Test in SPSS

[Anthony Santella]

David and Listservers,

I am also trying to write syntax to conduct a Chows test to see if "year
of hospitalization" (1998, 1999, 2000, 2001, 2002, 2003) 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?

Thank you in advance.

Anthony



On Wed, 10 Oct 2001 11:18:01 -0500, Matheson, David <[hidden email]>
wrote:

>Jean,
>  There are a pair of solutions on our AnswerNet for performing the Chow
>test - no pen & paper work required. I've pasted them below. The first
>solution was written more recently and uses the UNIANOVA procedure
>(Analyze->General Linear Model->Univariate in the menus). The second
>solution is older, uses the Regression procedure and is slighltly more
>labor-intensive in that it requires you to compute some interaction
>variables before running the Regression.
>
>David Matheson
>SPSS Technical Support
>[hidden email]
>[phone]
>Try the SPSS AnswerNet at http://www.spss.com/tech/answer .
>
>Solution 100009917: An easy way to perform a Chow test
>
>Q.
>Can you show me how to perform a Chow test in SPSS?
>
>
>A.
>The Chow test provides a test of whether the set of linear regression
>parameters (i.e., the intercepts and slopes) is equal across groups.  SPSS
>AnswerNet Solution ID 100000298 presents a thorough description of what

the
>Chow test is, how it may be calculated, and how to use COMPUTE statements
>and the SPSS REGRESSION procedure to obtain a Chow test.  The present
>solution shows a more convenient way to conduct this test using SPSS's
>General Linear Model (GLM) procedure.
>
>The easiest way to do this is to build a simple model from the dialog
boxes,
>paste the syntax into an SPSS Syntax Editor window, make a slight
>modification to the DESIGN subcommand, and then run the commands from the
>editor window.  We'll show you how to do this using a hypothetical
example.
>
>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.
>
>*****************************
>
>Solution 100000298 : Chow test for equal sets of regression coefficients
>across groups
>
>Q.
>What is the formula for the Chow test for equal regression
>parameters across groups?  Will SPSS perform this test?
>
>
>A.
>There is no SPSS procedure or keyword which requests the Chow test
>by name, but the test is easy to obtain from the REGRESSION procedure.
>The Chow test provides a test of whether the set of linear regression
>parameters, i.e. the intercepts and slopes, is equal across groups.
>For example, suppose we use the variable SALNOW from SPSS for
>Windows' bank.sav sample data set as our dependent variable and
>EDLEVEL as our predictor. Also suppose that we want to know whether
>the intercept and slope for this regression are equal for men and women.
>The algorithm for the Chow test is as follows:
>
>1. Run the regression on men and women together and note the
>   residual sum of squares and degrees of freedom. Call this
>   RSS1 and DF1.
>2. Run the regression separately for men and women and total
>   the residual sums of squares and degrees of freedom from the
>   two regressions. Call these RSS2 and DF2.
>3. Find (RSS1 - RSS2)/(DF1 - DF2) .
>4. Divide the result of step3 by RSS2/DF2 and compare this result to
>   the F distribution with (DF1-DF2) and DF2 degrees of freedom.
>   The null hypothesis for this test is that the regression intercept
>   and slope are both independent of gender.
>
>You can perform this test in SPSS REGRESSION and also obtain separate
>tests for the equality of intercept and slope across genders. The group
>variable should be a dummy variable which equals 0 for 1 group; 1 for
>the other. The bank.sav variable SEX is already in this form, with a
>value of 1 representing female. An interaction term is computed as the
>product of the predictor of interest (EDLEVEL) and SEX. REGRESSION is
>run first with only EDLEVEL as a predictor. SEX and the interaction
>term, called EDSEX in this example, are then entered in a second step
>with a second /METHOD = ENTER subcommand. The change in R square is
>requested with the keyword CHA in the /STATISTICS subcommand. This
>keyword also requests a test of whether the change in R square is
>greater than 0. This test is equivalent to the CHOW test as calculated
>from steps 1 to 4 above. The standard statistical output from
>REGRESSION also provides tests and confidence intervals for the SEX
>and EDSEX coefficients, which are effectively adjustments to the
>intercept and slope parameters, respectively, for female respondents.
>The REGRESSION command to perform this analysis is presented below.
>
>COMPUTE edsex = edlevel * sex .
>REGRESSION
>  /DESCRIPTIVES MEAN STDDEV CORR SIG N
>  /MISSING LISTWISE
>  /STATISTICS COEFF OUTS CI R ANOVA END CHA
>  /CRITERIA=PIN(.05) POUT(.10)
>  /NOORIGIN
>  /DEPENDENT salnow
>  /METHOD=ENTER edlevel
>  /METHOD=ENTER sex edsex  .
>
>The above command can be run from the graphic user interface (GUI) in

SPSS.
>The interaction terms can be computed from the Transform->Compute menu.
>Blocks of variables can be entered by clicking the Next button (above the
>Independent(s) box in the main Regression dialog) after entering the
>predictors for each block except the last. The 'Change in R squared' (CHA)
>test is available from
>the Statistics dialog of the Regression procedure. Users of SPSS versions
>prior to SPSS 7.5 should note that the test of change in R squared can not
>be requested from the dialog boxes. The simplest workaround for this
absence

>is
>to build most of the command in the dialogs, paste the command to a syntax
>window,
>and add the CHA keyword to the /Statistics subcommand.
>
>If there were K groups whose regression coefficients were to be
>compared, you would compute K-1 dummy variables and multiply each of
>these by the independent variable(s) to produce K-1 (sets of)
>interaction variables.
>
>The Chow Test is introduced in Gregory Chow's paper, 'Tests of Equality
>Between Sets of Coefficients in Two Linear Regressions', Econometrica,

1960,

>28(3), 591-605.
>
>For discussions of the dummy variable approach to the Chow test, see a
>pair of papers by Damodar Gujarati in The American Statistician,
>1970, 24(1), 50-52; and 1970, 24(5), 18-22.
>
>
>-----Original Message-----
>From: J.Russell [mailto:[hidden email]]
>Sent: Wednesday, October 10, 2001 5:47 AM
>To: [hidden email]
>Subject: A Challenge : Enquiry about the CHOW Test in SPSS
>
>
>Dear All
>
>This is one of those frustrating times when someone has asked me
>something. I know that give a week or so I probably could do the
>programming required but I simply do not have the time.
>
>The user is looking for the CHOW test in SPSS.
>
>If you want to know what that is there is a clear description at:
>
>http://www.stata.com/support/faqs/stat/chow.html
>
>(No I am not advertising a competitor as it is not in stata apparently
>either!)
>
>No I can see how to get the figures require out of  three
>regressions, one regression or a single ANOVA in SPSS.
>
>The thing is the last bit of the job seems to be a calculator, book of
>tables, pen and paper job.
>
>Now I can get UNIANOVA to put the relevant table into a data file
>but then comes the hard part of calculating the actual statistic.
>
>Please has anyone done it other than by pen or paper? If so would
>they mind letting me have the code so I can pass it on?
>
>Thanks a lot.
>
>Jean M. Russell
>
>
>------------------------------------------------------
>Jean M. Russell M.A. M.Sc.   [hidden email]
>Corporate Information & Computing Services,
>University of Sheffield
>285 Glossop Road
>Sheffield
>S10 2HB
>United Kingdom
>Phone:  [phone]
>Fax  :  [phone]