``` 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``` ```* This is a macro for testing General Linear Hypotheses * of the type cb = d, where b is a vector of regression * coefficients and c is a matrix of linear constraints * (cf. Searle, 1971, Linear Models (Wiley)). * the code for the example data generation part, comes from David Matheson: * Author: Johannes Naumann (email=johannes.naumann AT uni-koeln.de) * March 22, 2005 . * Build 100 cases in three predictors x1, x2, x3 and one dependent variable y all coming from a standard normal distribution . new file. input program. loop id = 1 to 100. numeric x1 to x3. do repeat z = x1 to x3. compute z = rv.normal(0,1). end repeat. compute y = rv.normal(0,1). end case. end loop. end file. end input program. exe. * make x1 and x2 correlate with y to .70 and each other to .20, while x3 is unrelated to both x1/x2 and y. matrix. get z /variables = x1 x2 x3 y. compute cor = {1.0, 0.2, 0.0, 0.7; 0.2, 1.0, 0.0, 0.7; 0.0, 0.0, 1.0, 0.0; 0.7, 0.7, 0.0, 1.0}. compute cho = chol(cor). compute newz = z*cho. save newz/outfile=* /variables= x1 to x3 y. end matrix. * Test the hypothesis that all Regression coefficients are equal . preserve. save outfile = 'alh__tmp.sav'. set results listing printback on mprint off. define alh_mak (dep = !charend('/') /pred = !charend('/') /cmat = !charend('/') /dmat = !charend('/')). count miss__ = !pred !dep (sysmis missing). select if miss__ = 0. compute eins = 1. matrix. get y /vars = !dep. get x /vars = eins !pred. compute b = (inv(t(x)*x))*t(x)*y. compute c = !cmat. compute d = !dmat. compute q = t(c*b-d)*inv(c*inv(t(x)*x)*t(c))*(c*b-d). compute s = t(y)*y-nrow(y)*((csum(y)/nrow(y))**2). compute z = t(b)*t(x)*y-nrow(y)*((csum(y)/nrow(y))**2). compute e = s-z. compute zdf = nrow(c). compute ndf = nrow(x)-ncol(x). compute f = (q/zdf)/(e/ndf). compute o = {q,e,f,zdf,ndf}. comp xx = inv(t(x)*x). save o /outfile = alh_erg.sav /variables = qs_h qs_e,f_wert,df_h,df_e. compute br = b-xx*t(c)*inv(c*xx*t(c))*(c*b-d). print b /title 'b-unconstrained'. print br /title 'b-constrained'. end matrix. get file = alh_erg.sav. compute p = 1-cdf.f(f_wert,df_h,df_e). execute. formats all (f11.5). formats df_h df_e (f11.0). variable labels qs_h 'SSQ - Hypothesis (Increment in error sum of squares)' /qs_e 'Error SSQ' /f_wert 'F-Value' /df_h 'df - Hypothesis' /df_e 'df - Error' /p 'p-Value'. report /format=list automatic align(left) /variables= qs_h qs_e. report /format=list automatic align(left) /variables= df_h df_e. report /format=list automatic align(left) /variables= f_wert p. get file = alh__tmp.sav. !enddefine. restore. alh_mak pred = x1 x2 x3/ dep = y/ cmat = {0,1,-1,0;0,0,1,-1}/ dmat = {0;0}/. ```
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