# Chow test

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 | *(Q) Enquiry about the CHOW Test in SPSS <snip> 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!) <snip> *(A) Posted to SPSSX-L on 2001/10/10 by David Matheson (SPSS Technical Support) 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. 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. |

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