讨论:怎样做lack-of-fit test

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proc glm data=msexam.fall08reg outstat=backwardr;
model P= G_G GA_G FA_5_5 SA_G PP;
run;
proc glm data=msexam.fall08reg outstat=backward;
model P= G_G GA_G;
run;

%macro ftest (dataset1, dataset2);
/* this macro is counting on the data sets being created by proc glm's outdata*/
data ftest;
set &dataset1 &dataset2;
if _source_= "ERROR";
sse0=lag(ss);
dfe0=lag(df);
drop _name_ _type_;
f= ((sse0-ss)/(dfe0-df))/(min(of ss, sse0)/min(of df,dfe0));
prob =1 - cdf('F',f,abs(dfe0-df),min(of df,dfe0));
if f='.' then delete;
run;
proc print data=ftest;
var f prob;
run;
%mend;
%ftest(backward, backwardr);

以上是俺写过的一个macro。是检验linear regression下full model和nested model的F-test（model selection）。
听讲9.2的proc reg可以检验lack-of-fit，毕竟能用得上9.2的只是少数人。所以今天抛砖引玉，放出这一F-test的code，来换取高手做lack-of-fit的code。

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关键词：lack-of-fit test lack Est fit 讨论 test

1# Isscaliu

1. 
   
2. data have;
   
3. missing A;
   
4. input x y@@;
   
5. c =(ranuni(11) >0.65);
   
6. x2 =x*x; xc =x*c;
   
7. datalines;
   
8. 8.3 227 8.3 312
   
9. 12.1 362 12.1 521
   
10. 17.0 640 17.0 539 17.0 728
    
11. 24.3 945 24.3 738 24.3 759
    
12. 33.6 1263 33.6 A
    
13. ;
    
14. 
    
15. **lack of fit in rsreg directly-SAS9.2;
    
16. proc rsreg data =have;
    
17. model y =x c x2 xc/lackfit covar =4;
    
18. run;
    
19. ***compute our own lack of fit;
    
20. ods listing close;
    
21. proc means data =have nway vardef =df;
    
22.   class x c;
    
23.   var y;  
    
24.   output out =_means_ css =_css N =_N;
    
25. run;
    
26. proc reg data =have;
    
27. model y =x c x2 xc; ods output anova =_aa_;
    
28. run;
    
29. data _null_;
    
30. if _n_ =1 then do i = 1 to nobs;
    
31.   set _means_ nobs =nobs;
    
32.   sum_css ++_css; m ++(_N >0); N ++_N;
    
33. end;
    
34. set _aa_ end =Eof;
    
35.   array _dfss{3, 2} _temporary_;
    
36.   _dfss[_n_, 1] =df; _dfss[_n_, 2] =ss;
    
37.   if Eof then do;                        
    
38.    p = _dfss[1, 1];  q =N;
    
39.    sse =_dfss[2, 2]; ss_pe =sum_css; ss_lf =sse -ss_pe;
    
40.    df_err =_dfss[2, 1]; df_pe =q -m; df_lf =df_err -df_pe;   
    
41.    mse_err =sse/df_err; mse_pe =ss_pe/df_pe; mse_lf =ss_lf/df_lf;   
    
42.    F =mse_lf/mse_pe;
    
43.    p =sdf('F', F, df_lf, df_pe);
    
44.    put @1 'Lack of Fit';
    
45.    put @1 '------------------------------------------------------------------';
    
46.    put @1 'Residual'    @15 'DF'    @20 'Sum of Squares' @35 'Mean Square' @50 'F Value' @60 'Pr > F';
    
47.    put;
    
48.    put @1 'Lack of Fit' @15 df_lf    @20 ss_lf   F10.2          @35 mse_lf    F10.2 @50 F F6.2 @60 p pvalue7.4;
    
49.    put @1 'Pure Error'  @15 df_pe  @20 ss_pe F10.2          @35 mse_pe  F10.2;
    
50.    put @1 'Total Error' @15 df_err @20 sse    F10.2           @35 mse_err F10.2;
    
51.    put @1 '------------------------------------------------------------------';
    
52.   end;  
    
53. run;
    
54. ods listing;

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Hi,
I am not worrying too much about lack of fit for my newest SAS version. That is just for my interest. It yields the matched results as from proc rsreg. On the other hand, I do believe you can compute it in a more direct way.
My question is, when no replicates in the data, there is obviously no pure error. How to deal with this for lack of fit test?
JingJu

厉害，受教了。对于你的问题，很乐意讨论。
Obviously, there is no pure error when there is no replicate observations available. The text book says we can conduct a approximate lack of fit by grouping similar vectors if there are the cases. However, in my point of view, this will be resulting loss of information in dealing with continuous data.  Another thing is, putting similar observations into pseudo-replicates are very subjective.