``` 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179``` ```********************************************************************** White's test with SPSS: ====================== * First of all, read "Heterocedasticity: testing and correcting in SPSS", by Gwilym Pryce http://pages.infinit.net/rlevesqu/spss.htm#Heteroscedasticity This macro is based on his paper. * SPSS Code by Marta Garcia-Granero 2002/04/04. * Steps: * Create several new variables: * The square of the unstandardized residuals. * The square of every predictor variable in the model you want to test. * The cross-product of all the predictors. * Run a regression model to predict the squared residuals with the predictors, their squares and cross-products. * Multiply the model R-square (unadjusted) by the sample size (n*R-square). * This is the White's statistic. Its significance is tested by comparing it with the critical value of the Chi-square distribution with "p" degrees of freedom, where "p" is the total number of regressors in the last regression model (original+squares+cross-products). * IMPORTANT: * If any of the original predictors is binary (dummy variable), then its square will be identical to the original, and they will correlate perfectly. * In this case, the regression model will drop one of them (the original or its square), and "p" has to be decreased in 1 unit for each binary predictor in the model. * WHITE'S TEST MACRO * * The MACRO needs 5 arguments: * a) the number of predictors, * b) the number of cross-products that will be created: " predictors*(predictors-1)/2" * [I could not find other way of making VECTOR to accept the number], * c) "P" (predictors+squares+cross-products), corrected for binary predictors, * d) the name of the dependent variable and * e) the list of predictors in the form 'first predictor TO last predictor' * (ordered and consecutive in the database). * MACRO definition. DEFINE whitest(!POSITIONAL !TOKENS(1) /!POSITIONAL !TOKENS(1) /!POSITIONAL !TOKENS(1) /!POSITIONAL !TOKENS(1) /!POSITIONAL !CMDEND). * >>>> 1st regression model to get the residuals <<<< *. REGRESSION /STATISTICS R ANOVA /DEPENDENT !4 /METHOD=ENTER !5 /SCATTERPLOT=(*ZRESID,*ZPRED) /SAVE RESID(residual) . * >>>> New variables <<<< *. * New dependent variable. COMPUTE sq_res=residual**2. * Getting rid of superfluous variables (dependent and residuals). SAVE OUTFILE='c:\\windows\\temp\\tempdat_.sav' /keep=sq_res !5. GET FILE='c:\\windows\\temp\\tempdat_.sav'. EXECUTE. * Vectors for all new predictor variables. VECTOR v=!5 /sq(!1) /cp(!2). * Squares of all predictors. LOOP #i=1 to !1. COMPUTE sq(#i)=v(#i)**2. END LOOP. * Cross-products of all predictors. * Modification of a routine by Ray Levesque. COMPUTE #idx=1. LOOP #cnt1=1 TO !1-1. LOOP #cnt2=#cnt1+1 TO !1. COMPUTE cp(#idx)=v(#cnt1)*v(#cnt2). COMPUTE #idx=#idx+1. END LOOP. END LOOP. EXECUTE. * >>>> White's test <<<< *. * Regression of sq_res on all predictors. REGRESSION /VARIABLES=ALL /STATISTICS R /DEPENDENT sq_res /METHOD= ENTER /SAVE RESID(residual) . * Final report. * Routine by Gwilym Pryce (slightly modified). matrix. compute p=!3. get sq_res /variables=sq_res. get residual /variables=residual. compute sq_res2=residual&**2. compute n=nrow(sq_res). compute rss=msum(sq_res2). compute ii_1=make(n,n,1). compute i=ident(n). compute m0=i-((1/n)*ii_1). compute tss=transpos(sq_res)*m0*sq_res. compute regss=tss-rss. print regss /format="f8.4" /title="Regression SS". print rss /format="f8.4" /title="Residual SS". print tss /format="f8.4" /title="Total SS". compute r_sq=1-(rss/tss). print r_sq /format="f8.4" /title="R-squared". print n /format="f4.0" /title="Sample size (N)". print p /format="f4.0" /title="Number of predictors (P)". compute wh_test=n*r_sq. print wh_test /format="f8.3" /title="White's General Test for Heteroscedasticity" + " (CHI-SQUARE df=P)". compute sig=1-chicdf(wh_test,p). print sig /format="f8.4" /title="Significance level of Chi-square df=P (H0:" + "homoscedasticity)". end matrix. !ENDDEFINE. * Sample data Nr. 1: continuous predictors *. INPUT PROGRAM. - VECTOR x(5). - LOOP #I = 1 TO 100. - LOOP #J = 1 TO 5. - COMPUTE x(#J) = NORMAL(1). - END LOOP. - END CASE. - END LOOP. - END FILE. END INPUT PROGRAM. execute. * x1 is the dependent and x2 TO x5 the predictors. rename variables x1=y. execute. * MACRO call: there are 4 predictors, therefore, 6 cross-products and 14 regressors. whitest 4 6 14 y x2 TO x5. * Sample data Nr. 2: one binary predictor *. INPUT PROGRAM. - VECTOR x(5). - LOOP #I = 1 TO 100. - LOOP #J = 1 TO 5. - COMPUTE x(#J) = NORMAL(1). - END LOOP. - END CASE. - END LOOP. - END FILE. END INPUT PROGRAM. execute. RECODE x2 (Lowest thru 0=0) (0 thru Highest=1) . EXECUTE . * x1 is the dependent and x2 TO x5 the predictors. rename variables x1=y. execute. * MACRO call: as before, 4 predictors, 6 cross-products but ONLY 13 regressors. whitest 4 6 13 y x2 TO x5. * As you can see from the output, X2 is not included in the model. ```
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